tag:blogger.com,1999:blog-143290132017-02-27T23:52:52.668+09:00Travel Diary of Makoto Sakuraimakoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.comBlogger115125tag:blogger.com,1999:blog-14329013.post-7054579600135994562017-02-16T02:06:00.000+09:002017-02-27T23:52:52.691+09:00Shortening the Theoretical Minimum: We can learn. We can choose.Since my Russian is terrible, I can only understand some translations of the Russian literature in math and physics. I recaptured the "theoretical minimum" of the good old Landau school. These textbooks were translated to many languages including English and Japanese.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-kAszadCoB7w/WKR-WsApQpI/AAAAAAAAAR8/8OQxZFSp6Pk4uPm_57_emITZlgeiejI0ACLcB/s1600/IMG_3170.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://4.bp.blogspot.com/-kAszadCoB7w/WKR-WsApQpI/AAAAAAAAAR8/8OQxZFSp6Pk4uPm_57_emITZlgeiejI0ACLcB/s400/IMG_3170.JPG" width="400" /></a></div><br />I zoomed the first easier chapters of the classical mechanics, the classical field theory, and the non-relativistic quantum mechanics. These materials are everywhere including the scattering theory (the so-called S-matrix theory and the related algebraic analysis [D-modules] of the RIMS, Kyoto).<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-yECU1BYETVM/WKR-WnomkcI/AAAAAAAAAR0/enPeB03yXXMi8rfELorJnoJUf_LAxGEygCLcB/s1600/IMG_3173.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://1.bp.blogspot.com/-yECU1BYETVM/WKR-WnomkcI/AAAAAAAAAR0/enPeB03yXXMi8rfELorJnoJUf_LAxGEygCLcB/s400/IMG_3173.JPG" width="400" /></a></div><br />However, the materials treated in the Landau textbooks are obsolete in a sense. I mean, the quantum electro-dynamics (QED) is not well-described in the Landau course -- the Feynman diagram does not have a standard space-time axis and the [single / double] arrows of the modern theoretical physics after 't Hooft. Landau abandoned the quantum field theory at his later years.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-ELkwpHeocyg/WKR-WroTYqI/AAAAAAAAAR4/Mg1nasXaGswTnm_kZBS33875WmDGehOBQCLcB/s1600/IMG_3176.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://2.bp.blogspot.com/-ELkwpHeocyg/WKR-WroTYqI/AAAAAAAAAR4/Mg1nasXaGswTnm_kZBS33875WmDGehOBQCLcB/s400/IMG_3176.JPG" width="400" /></a></div><br />Apart from the advanced materials of (quantum) statistical physics / stochastic calculus [not always the condensed matter physics for the applied engineering and high-temperature superconductivity], we can see some of better modern textbooks. It is like Bourbaki. Bourbaki was a classic and it was written at the highest level at those ages, but now we have better textbooks and we can understand the curriculum more easily.<br /><br />Although the fluid mechanics of the 19th century (well, I don't want to talk much about the plasma physics) and the elastic theory are not well inherited, we have the books of "<a href="https://www.amazon.com/Ginzburg-stability-analysis-mathematics-4000075616/dp/4000075616/ref=sr_1_1?ie=UTF8&qid=1487208936&sr=8-1&keywords=9784000075619" target="_blank">[the] Ginzburg-Landau Equations and Stability Analysis</a>" [Iwanami Press, still no English translation available] by Shuichi Jimbo and Yoshihisa Morita [ISBN=978-4000075619] and "<a href="https://www.amazon.com/Introduction-Quantum-Theory-Frontiers-Physics-ebook/dp/B0052TUEM8/ref=sr_1_1?s=books&ie=UTF8&qid=1487173629&sr=1-1&keywords=Introduction+to+Quantum+Field+Theory+Kindle" target="_blank">An Introduction to Quantum Field Theory</a>" by Michael E. Peskin and Daniel V. Schroeder. [ISBN=978-0201503975]<br /><br />I read the Peskin-Schroeder at the junior and senior [the 3rd and 4th year of the UTokyo, the academic year 2000-2001]. I performed the <a href="https://en.wikipedia.org/wiki/Peskin%E2%80%93Takeuchi_parameter" target="_blank">Peskin-Takeuchi</a>'s "Physics beyond the standard model" [phenomenology of elementary particle theory including muons [leptons: the anomalous magnetic moment g-2] & (Yukawa's) pions [pi mesons of quarks decayed to multiple photons: chiral abelian anomaly and the Riemann-Roch-like theorem of Fujikawa's method by chiral fermions] but without any sound mathematical foundation] at the 1st year summer seminar of my master's period.<br /><br />Peskin seminar was after the seminar of "<a href="https://www.amazon.com/Renormalization-Introduction-Theoretical-Mathematical-Physics/dp/3642084303/ref=sr_1_1?ie=UTF8&qid=1487176828&sr=8-1&keywords=Renormalization%3A+An+Introduction+Salmhofer" target="_blank">Renormalization: An Introduction</a>" by Manfred Salmhofer [Springer, ISBN=978-3642084300] during the winter holidays [a little before 2002-March] with the theoretical physics students working on the condensed matter physics. I didn't sufficiently understand the Fermi surface problem [still a mystery in the AdS/CFT correspondence conjecture] at those days, which is not treated in the renormalization group theory in the quantum field theory of the elementary particle theory.<br /><br />To sum up, the Feynman rules [including the statistical factors of second quantization of Bose-Einstein / Fermi-Dirac statistics of identical particles] for the perturbative [asymptotic series of] Feynman integrals [as well as symmetry breakings after the late Yoichiro Nambu, the phase transition theory, and some of the so-called standard model] are treated more shortly in the textbook of Peskin-Schroeder. Non-perturbative effects of solitons, supersymmeties, and D-branes / M-branes [of the so-called superstring theory, which I still doubt in the effectiveness to the real-world problems] are not treated in this pedagogical textbook.<br /><br />I still think Peskin is worthy of attention for undergraduate physics students and determined mathematical physicists [including mirror symmetrists and twistor theorists among other geometric representation theorists at the math department]. Of course, I mentioned no classic literature of quantum field theories including <a href="https://en.wikipedia.org/wiki/Jean_Zinn-Justin" target="_blank">Zinn-Justin</a> and <a href="https://en.wikipedia.org/wiki/James_Bjorken" target="_blank">Bjorken</a>-Drell. <a href="https://www.amazon.com/Quantum-Field-Theory-Lewis-Ryder/dp/0521478146/ref=pd_cp_14_1?_encoding=UTF8&psc=1&refRID=3N81QSK2KWSA2HF5APDX" target="_blank">Ryder</a> [ISBN=978-0521478144] might be a second choise and <a href="https://books.google.com/books/about/Quantum_Field_Theory.html?id=nnuW_kVJ500C&redir_esc=y" target="_blank">available on the web</a>.makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.comtag:blogger.com,1999:blog-14329013.post-16912704851145826382016-04-30T02:29:00.000+09:002016-05-16T06:44:29.349+09:00The signature problem in the obsolete supergravity<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML" type="text/javascript"></script> I looked up the old textbook of ``Supersymmetry and Supergravity" (Princeton, 2nd edition, 1992 - Japanese translation and footnotes from Maruzen press, 2011) of Julius Wess (1934-2007) and Jonathan Bagger at my nearby library for some reasons. The English edition in my bookshelf says the old super-gravity theory (believed to be renormalizable at the old days of 1980s?) of Physics Letters B (1978) and Nuclear Physics B (1976) was (at page 145, Chapter XVIII The Supergravity Multiplet) \begin{align*} \delta \bar{\psi}_{m \dot{\alpha}} = -2 \mathcal{D}_m \bar{\zeta}_{\dot{\alpha}} - ie_m^{\quad c}\\ \times \left\{ \frac13 M^{\ast} (\zeta \sigma_c)_{\dot{\alpha}} + b_c \bar{\zeta}_{\dot{\alpha}} - \frac13 b^d (\bar{\sigma}_c \sigma_d \bar{\zeta})_{\dot{\alpha}} \right\}. \end{align*} In the Japanese edition, some corrections were done under the guideline of the posthumous writings of Prof. Wess (according to the translater Kazunari Shima). [page 141, Chapter 18] \begin{align*} \delta \bar{\psi}_{m \dot{\alpha}} = -2 \mathcal{D}_m \bar{\zeta}_{\dot{\alpha}} - ie_m^{\quad c}\\ \times \left\{ \frac13 M^{\ast} (\zeta \sigma_c)_{\dot{\alpha}} + b_c \bar{\zeta}_{\dot{\alpha}} + \frac13 b^d (\bar{\sigma}_c \sigma_d \bar{\zeta})_{\dot{\alpha}} \right\}. \end{align*} The theoretical physics and mathematical physics students (graduate students) had to handwrite a tremendous amount of dirty typesetting and calculation at the old days before the superstring theory and M / F theory. [Maybe this is an official press release of the Princeton Press (at least the Maruzen Press). So, this is not my original contribution to the theoretical physics of this historic literature.]makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.comtag:blogger.com,1999:blog-14329013.post-16775586705132578392016-03-22T16:58:00.000+09:002016-03-22T16:58:06.199+09:00Spring = Revival.I was thinking about the future of mathematics. Why was it divorced from the mainstream physics? Where did the `natural' definition of mathematics come from? Has it passed away? Still in development?<br /><br />No answer. But we want to know.makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.comtag:blogger.com,1999:blog-14329013.post-19716616808428091012015-08-26T00:02:00.005+09:002016-08-13T18:16:59.384+09:00The Theoretical Minimum (not Susskind but Lev Davidovich Landau): at least (orbital / spin) angular momentum <script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML" type="text/javascript"></script> <br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img border="0" height="265" src="http://1.bp.blogspot.com/-Wh3JwujuoQY/VdxWnJD84_I/AAAAAAAAAQw/Dfc6ARBt2a0/s400/LandauLifshitzAllClip.jpg" style="margin-left: auto; margin-right: auto;" width="400" /></td></tr><tr><td class="tr-caption" style="text-align: center;">From right to left: "<i>A Shorter Course of Theoretical Physics</i> (Japanese) [=<span class="citation"><span style="font-family: "times" , "times new roman" , serif;">Краткий курс теоретической физики. В двух томах</span> (Russian)</span>]" Volume 1 and 2 (Mechanics and Electrodynamics / Quantum Mechanics respectively), <i>Mechanics</i> (Volume 1, Japanese), <span class="citation book"><i>The Classical Theory of Fields</i> (Volume 2, Japanese), </span><span class="citation book"><span class="citation book"><i>Quantum Mechanics: Non-Relativistic Theory</i></span> (Volume 3, English), </span><span class="citation book"><span class="citation book"><i>Quantum Mechanics: Non-Relativistic Theory</i></span> 1/2 & 2/2 (Volume 3, Japanese)</span><span class="citation book">, </span><span class="citation book"><span class="citation book"><i>Quantum Electrodynamics </i></span></span><span class="citation book"><span class="citation book">1/2 & 2/2 </span>(Volume 4, Japanese)</span><span class="citation book">, </span><span class="citation book"><span class="citation book"><i>Quantum Electrodynamics</i></span></span><span class="citation book"><span class="citation book"> </span>(Volume 4, Russian)</span><span class="citation book">, </span><br /><span class="citation book"><i>Statistical Physics, Part1</i>, 1/2 & 2/2 (Volume 5, Japanese), </span><br /><span class="citation book"><i>Fluid Mechanics 1/2 & 2/2</i> (Volume 6, Japanese), </span><br /><span class="citation book"><i>Theory of Elasticity</i> (Volume 7, Japanese), </span><br /><span class="citation book"><i>Electrodynamics of Continuous Media 1/2 & 2/2</i> (Volume 8, Japanese), </span><br /><span class="citation book"><i>Statistical Physics, Part 2: Theory of the Condensed State</i> (Volume 9, Russian), </span><br /><span class="citation book"><i>Physical Kinetics</i> (Volume 10, Russian).<i><br /></i></span></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Although there is no "<i><b>volume 9, Statistical Physics Part 2</b></i>" (and no "<i><b><span class="citation book">volume 4, Quantum Electrodynamics, Part 2</span></b></i>" & no "<span class="citation book"><i><b>volume 10, Physical Kinetics</b>"</i></span>) on the web, the well-known <a href="https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics" target="_blank">Course of Theoretical Physics</a> was a mandatory<i> (before the entrance exam of graduate schools of those days) series of textbooks <u>written by students of L.D.Landau (Nobel Laureate in Physics [the prize for the theory of liquid helium's superfluidity], <a href="http://www.nobelprize.org/nobel_prizes/physics/laureates/1962/" target="_blank">1962</a> and <a href="http://www.nobelprize.org/nobel_prizes/physics/laureates/1962/press.html" target="_blank">his Nobel speech</a>)</u>,</i> which is now available for free <a href="https://archive.org/search.php?query=creator%3A%22E.M.%20Lifshitz%22" target="_blank">here</a> (U.S. archives) and <a href="http://alexandr4784.narod.ru/lktf.html" target="_blank">here</a> (an old version of the Russian original). However, editions of English translation are not up-to-date and such editions do not have a good TeX typesetting; there are some things like the followings: \begin{align*} <M \mid L_{+} \mid M-1 >=<M-1\mid L_{-}\mid M>\\ =\sqrt{ }[(L+M)(L-M+1)]. (27.12) \end{align*} [from the Quantum Mechanics [Volume 3, English ed.]] The Japanese edition is TeXnically correct.</div><div class="separator" style="clear: both; text-align: center;">\begin{align*} <M \mid L_{+} \mid M-1 >=<M-1\mid L_{-}\mid M>\\ =\sqrt{(L+M)(L-M+1)} (27.12) \end{align*}(a period or a comma should be inserted.) Likewise, the semi-classical approximation is</div><div class="separator" style="clear: both; text-align: center;">\begin{align*} f_{12} \sim \exp \left\{ -\frac{1}{\hbar} \text{im} \Big[ \int^{x_0} \sqrt{ } [2m (E_2-U)] dx\\ - \int^{x_0} \sqrt{ } [2m (E_1 - U)] dx \Big] \right\} (51.6) \end{align*} in the English edition. It should be \begin{align*} f_{12} \sim \exp \Bigl( -\frac{1}{\hbar} \text{Im} \Big[ \int^{x_0} \sqrt{2m (E_2-U)} dx\\ - \int^{x_0} \sqrt{2m (E_1 - U)} dx \Big] \Bigl) (51.6) \end{align*} as is written in the Japanese edition. (Russian originals of volumes 4, 9, 10 seem OK for the square roots including fractions.)</div><div class="separator" style="clear: both; text-align: center;"><br /></div>Today, I added three up-to-date editions (<i><b>volume 4 [year 2006, 4th ed.] "<span style="font-family: "times" , "times new roman" , serif;">Квантовая электродинамика</span>"=Q</b></i><i><b><span class="citation book"><i>uantum Electrodynamics [2nd ed.] (</i></span></b></i><i><b><span class="citation book"><i><i><b>or </b></i><i><b><span class="citation book"><i>Relativistic Quantum Theory [1st ed.]</i></span>)</b></i></i></span>, 9 [year 2004, 4th ed.] "<span style="font-family: "times" , "times new roman" , serif;">Статистическая физика. Часть 2. Теория конденсированного состояния</span>"=Statistical Physics Part 2: Condensed Matter Theory (or Statistical Physics, Part 2: Theory of the Condensed State), 10 [year 2007, 2nd ed.] "</b></i><i><b><span style="font-family: "times" , "times new roman" , serif;"><span class="citation">Физическая кинетика</span></span>"=Physical Kinetics</b></i>) of the original Russian to my bookshelf -- since the new / re-print editions of Japanese translation are no longer available for a long time. This situation is the same for the undergraduate students at the University of Tokyo of 17 years ago, and we had to share the old sombre fragile archives of the [physics / liberal arts / city] library (a stack room for books including Russian), or physics-oriented students can purchase some of the easier-to-obtain editions from secondhand booksellers at <a href="http://bit.ly/1NGz3ej" target="_blank">the Kanda (Jimbo-cho -- where I went and buy the three books above) city</a> in Tokyo. [The exceptionally well-sold editions of volume 1, 2, 3 1/2 from the Tokyo-Tosho press and the volume 5 1/2, 5 2/2 of <i><b>Statistical Physics, Part 1</b></i> from the Iwanami press are not out-of-print].<br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">I was lucky in my undergraduate days that I could obtain (by a reasonable price) the volume 6 1/2 & 2/2 (=3rd ed. of <a href="https://ru.wikipedia.org/wiki/%D0%9A%D1%83%D1%80%D1%81_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B8_%D0%9B%D0%B0%D0%BD%D0%B4%D0%B0%D1%83_%D0%B8_%D0%9B%D0%B8%D1%84%D1%88%D0%B8%D1%86%D0%B0" target="_blank">original Russian</a>) of <i><b>Fluid Mechanics</b></i> and the volume 7 (=4th ed. of <a href="https://ru.wikipedia.org/wiki/%D0%9A%D1%83%D1%80%D1%81_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B8_%D0%9B%D0%B0%D0%BD%D0%B4%D0%B0%D1%83_%D0%B8_%D0%9B%D0%B8%D1%84%D1%88%D0%B8%D1%86%D0%B0" target="_blank">original Russian</a>) of <span class="citation book"><i><b>Theory of Elasticity</b> </i></span>in the Japanese translation from the CO-OP (student union) of the University of Tokyo in my undergraduate days (1998 April-2002 March). I did not buy the volume 9 of <i><b>Statistical Physics, Part 2</b></i> from the Iwanami press in my undergraduate days.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">More nostalgically speaking, I was reading the volume 1 of Mechanics and the volume 5 of Statistical Physics when I was a freshman of the University of Tokyo of the year 1998-1999. This was only the prologue of my professional work of theoretical & mathematical physics in addition to pure algebraic (& arithmetic) geometry and algebraic analysis. While I was thinking about becoming a professional mathematician, it turned out my pursuit of learning both modern math [including number theory and arithmetic geometry] and theoretical physics [including elementary particle theory] was impossible at the governance system of the University of Tokyo at those days -- there was no Kavli-IPMU institute, there was no double major Ph.D., and there was a strong bashing / adversity against pure science and pure math. There was no communication between the physics department of UT's Hongo campus and the math department of UT's Komaba campus.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">In my undergraduate days, some of the applied physicists and literature / social science students accused my particular interest was "inside the philosophy" or "religion-like" -- which was (as if) the same words <a href="https://en.wikipedia.org/wiki/Paul_Gordan" target="_blank"><span class="st">"This is <i>not mathematics</i>; this is <i>theology</i>.</span>"</a> [1890s] as the critics (of Paul Gordon) to Hilbert when Hilbert tried to defend the set theory <b><i>[its ultimate initial plan of so-called Hilbert's program was not achieved -- but I don't write about this misleading popular science in this post. I just draw your attention to the fact that the Hilbert program was something that the earlier-20th-century mathematical physicists (including von Neumann) were sharing but its historical meaning has no consensus between arithmetic geometers and mathematical physicists.]</i> </b>of Cantor at the beginning of the 20th century (from Kronecker -- whose argument with Cantor was reconciled at the very end of Kronecker's life [but it is not confirmed in the literature]). The initial goal to establish the set theory was not the topology or the real / complex number, but the uniqueness of the Fourier transform / inverse transform as the trigonometric series. This concrete goal was not achieved as the unification of number theory and physical mathematics, but its idea (or, Cantor's dream) is still alive in another form of the category theory of homotopy algebras in arithmetic geometry and higher topos theory (and the elementary topos theory [not always Grothendieck topos] of sheaves in logic and the type theory).</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">At the days of Cantor, there was no delta function, no Bourbaki, no Grothendieck, no Landau-Lifshitz, no CERN LHC for Higgs bosons, and no superstring theory / M-theory. However, the pure mind of Cantor is still alive everywhere in the garden of modern mathematics.</div>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.comtag:blogger.com,1999:blog-14329013.post-6387052937273813312015-01-20T04:40:00.000+09:002016-05-15T22:19:46.568+09:00André Weil on GaussI'm not trying to recall the history of the 20th century by Bourbaki before the late Grothendieck. I'm not a historian and not a nostalgic mathematician. Rather, I would like to reminisce the phrase by one of the greatest mathematicians of the 20th century, André Weil, who was admired by Japanese mathematicians including Prof. Kunihiko Kodaira of complex algebraic geometry.<br /><br />Other words by A. Weil (not his sister Simone Weil) were usually cited in French or in English translations like Wikiquote, but I found out that the very famous phrase is not well-known to non-Japanese mathematicians when I googled on the web. The followings are my quotation of his words from Japanese reference.<br /><br />(night of 10-Oct-1955, when Weil came to Japan, Fuji hotel.)<br />"Well, start with your own idea.<br />Gauss did like that.<br />You start like Gauss as well.<br />Then, soon you will realize you are not Gauss.<br />It is OK.<br />Anyhow, start like Gauss."<br />(by Weil, a feeble translation by Makoto Sakurai)<br /><br />Some mathematical physicists misunderstood these words were by Atiyah or Serre, but it is not true. In the original bibliography of the complete posthumous works of Yutaka Taniyama (1927-1958), it is written at the first page of the article "In touch with A. Weil" (page 199-208 of the second edition, 1994).<br /><br />The words were so famous that they were cited elsewhere in different Japanese expressions, but the original precise Japanese did not appear at the Sugaku seminar or Japanese popular literature.<br /><br />In the above, I did not mean to reflect the past mathematics, but I meant young mathematicians and mathematical physicists were extremely inclined to copy-and-paste the works of (Fields / Nobel or any other kinds) medalists. The grant agency is very crucial in the career of young scientists, so that the competition is harsh.<br /><br />However, it is a sad situation that some wrong translations of physics works by "pure" mathematicians are prevalently overwhelming the original works by either pure mathematicians or (let me say) native physicists. I do not accuse any individual case that I regret in this post, but let me recall this episode of Weil as a warning against such prize-winners.<br /><br />As I wrote above, I do not like to cite eminent people's articles (including Weil). Nevertheless, the copy-and-paste machines on the web are so harmful that their plagiarism will eradicate the sincere efforts of young talented mathematicians and physicists.<br /><br />It is like Japanese classic musicians; the music students are said to learn the music score very well, but there is no joy of discovery. As I'm not a musician, let me say about mathematics that the abroad conferences or symposiums are in any case very rejoicing.<br /><br />On the other hand, the Japanese people are not so involved with the speakers when it comes to the cases of Japanese symposiums or international conferences in English. The organizers are trying to ask questions, but the communications among participants and speakers are not so active. Well, there are language problems as well, but I said to the Chicago people, "my English is not so good, but it is better than ordinary Japanese English." (The Chicago person said that my English was very good.) A French mathematician said language was not the problem, the problem was always mathematics.makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.comtag:blogger.com,1999:blog-14329013.post-2914753988101227522014-09-27T05:03:00.000+09:002015-04-23T11:29:34.496+09:00Weighted Arithmetic-Geometric means and logarithm<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML" type="text/javascript"></script>This was what I wrote yesterday after the April visit for the University of Chicago. This short article is written as a test of MathJax and the complement of the freshman math lecture at the year 2011. There is an extraction of my 9 page PDF file. \begin{eqnarray} \sum_{k=1}^N w_k a_k & = & w_1 a_1 + w_2 a_2 + \cdots + w_N a_N \nonumber\\ & \ge & a_1^{w_1} a_2^{w_2} \cdots a_N^{w_N} \\ & = & \prod_{k=1}^N a_k^{w_k} \nonumber\\ & := & \prod_{k=1}^N \exp \left[ w_k \ln a_k \right]. \end{eqnarray} The auxiliary conditions of antilogarithm and weight are as follows. \begin{eqnarray} 0 < a_1, a_2, \cdots, a_N \\ \Longleftrightarrow & a_k \in \mathbb{R}_{>0}, \\ 0 < w_1, w_1, \cdots, w_N (< 1)\ s.t.\\ w_1 + w_2 + \cdots + w_N = & \sum_{k=1}^N w_k = 1,\end{eqnarray}, where the equality holds if and only if a<sub>1</sub> = a<sub>2</sub> = ... = a<sub>N</sub>.<br /><br />For the plan to avoid the misuse of ill-definition of general logarithmic function (of complex variables or matrix elements, or even some other completion of non-Archimedean / quantum dilogarithm), I showed the inequality without using Jensen's inequality (convex inequality). [I used the elementary calculus of polynomials in one variable for N->N+1. Or, I simplified the forward-backward induction by a one-step backward induction.]<br /><br />See the PDF resume of mine, later.</sub1>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.comtag:blogger.com,1999:blog-14329013.post-86837793413896760522013-01-01T04:28:00.000+09:002017-02-23T05:49:31.220+09:00Gauss WayJapan has already leaped the end of year 2012, but California is still before the beginning of year 2013.<br /><br />The MSRI (Mathematical Sciences Research Institute) at <a href="https://maps.google.co.jp/maps?f=q&source=s_q&hl=en&geocode=&q=Gauss+Way+and+MSRI+California&aq=&sll=28.921631,129.550781&sspn=28.862071,36.826172&vpsrc=0&brcurrent=3,0x0:0x0,0&ie=UTF8&hq=Gauss+Way+and+MSRI+California&hnear=&radius=15000&ll=37.950154,-122.189941&spn=0.102334,0.143852&t=m&z=12&iwloc=A&cid=17059224402918504293" target="_blank">the Gauss Way, California</a>, is planning a series of workshops: <a href="http://www.msri.org/web/msri/scientific/programs/show/-/event/Pm145" target="_blank">Noncommutative Algebraic Geometry and Representation Theory</a> including<br /><ul><li>Jan 24, 2013 to Jan 25, 2013 : <a href="http://www.msri.org/web/msri/scientific/workshops/show/-/event/Wm9061" target="_blank">Connections for Women: Noncommutative Algebraic Geometry and Representation Theory</a></li><li>Jan 28, 2013 to Feb 1, 2013 : <a href="http://www.msri.org/web/msri/scientific/workshops/show/-/event/Wm9062" target="_blank">Introductory Workshop: Noncommutative Algebraic Geometry and Representation Theory</a></li></ul>, but I cannot visit California in January 2013 for the following reasons. <br /><br />1. I have to teach my students as the academic calendar of Japan is written.<br />2. I cannot afford to visit California without the financial support of Japan and/or the USA, which is on the verge of serious budget cut (fiscal cliff (財政の崖) or fiscal wall (財政の壁)).<br /><br />About the no.2, I have more things to append. Although European people are still thinking Japanese people are "economic animals," it is not the case. Since the so-called financial bubbles, IT-bubbles, and biotechnology bubbles are gone within this/these 2 decades, Japanese people have been struggling to overcome simultaneous crises in the tax rate, the employment rate, the welfare, and some civilian control of nuclear plants after the aftershocks of Tohoku earthquakes and Tsunami at 14:46, 11-March-2011 (JST).<br /><br />On the contrary, before the Diet (Japanese Parliament or the Lower House) campaign at the December of 2012, I have done some electric annual ballot for the AMS (American Mathematical Society) vice-president, Boards, and Councils. The financial circumstance of AMS is not optimistic; as an AMS member of 8 years, I was asked for signature against the budget cut:<br /><h1><a href="http://www.ams.org/policy/government/advocacy/January2013Sequestration" target="_blank">Tell Congress to Avoid January 2013 Sequestration</a></h1>Although I am not a resident of the U.S.A., I am affiliated with the American Mathematical Society for a long term, including some eminent immigrant mathematicians from the overseas to American universities, but I do not cite individual researchers' names in this post.<br /><br />OK. Let me go back to my personal financial problem. Even though I registered in the <a href="http://www.msri.org/web/msri/scientific/workshops/show/-/event/Wp9062" target="_blank">participants' list</a> of the MSRI, they say they cannot afford to financially support my visit for the travel and living expenses while the vice deputy sent me an encouragement message about attending one or more workshops of the MSRI at the last year. I really interpreted this letter in the literal sense, but the U.S. mathematicians are now planning <a href="http://jointmathematicsmeetings.org/jmm" target="_blank">the January (9-12) 2013's San Diego, CA, Joint Meetings</a> with the SIAM, the MAA(Mathematical Association of America) and so on, which encourage graduate students' NSF grant proposals with a little chance of travel expenses.<br /><br />Needless to say, I am not a graduate student any more, but Japanese policy on the science development is not promising for post-doctoral members or part-time lecturers. Thus I was much interested in the events of January-2013, but neither Japanese researchers nor American institutes let me join in such important meetings since I have not obtained the (three or more) strong recommendation letters from eminent mathematicians in the world-wide. All I can do is write my original preprint from my original motivation, but the number of papers is not large.<br /><br />As Carl Friedrich Gauss -- the prince of mathematics in the 19th century -- said, a genuine mathematician does not always have plenty numbers of recommendation letters; whereas he said "Few, but ripe" for his remarkable achievements in pure mathematics and mathematical physics by himself while writing his diaries.makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.comtag:blogger.com,1999:blog-14329013.post-51446441267720448802012-10-09T10:04:00.001+09:002013-09-13T15:07:46.687+09:00Higgs HunterLast month, I visited Kyushu University, which lies in one of the southern islands of Japan, for the oral presentation at the Mathematical Society of Japan. Before the presentation at the morning session (at 21-Sep-2012) of algebraic geometry, I submitted my update of Ph.D. thesis with the elimination of some of my typos and obsolete references. I also noticed my change of permanent receivable e-mail address of the University of Tokyo. See <a href="http://arxiv.org/abs/0712.2318">Mixed anomalies of chiral algebras compactified to smooth quasi-projective surfaces</a> and the <a href="http://researchmap.jp/?action=cv_download_main&upload_id=35164">slides</a> uploaded at the <a href="http://researchmap.jp/read0152878/?lang=english">researchmap database</a>. The conference hall was at the "2nd Centre Zone" of the university, which was a little far from the Fukuoka (福岡) airport; we need to connect two railways of subway and local trains, and the transportation of school (semi-shuttle) bus was necessary from the nearby train station to the "Big Orange Station" at the entrance of Ito Campus.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-6f5iWsCgGzA/UHNhNrWPBTI/AAAAAAAAAMM/imCIxC3K54c/s1600/IMG_1747.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="300" src="http://3.bp.blogspot.com/-6f5iWsCgGzA/UHNhNrWPBTI/AAAAAAAAAMM/imCIxC3K54c/s400/IMG_1747.JPG" width="400" /></a></div>My presentation was about the "Geometric Quantization of Wess-Zumino-Witten model" and not "Geometric Quantization of Chern-Simons theory". In addition, my presentation was a revisit of Spontaneous Symmetry Breaking by Nambu-Goldstone bosons and soliton's micro-local calculus (Dynamical Symmetry Breaking) of co-tangent bundle of beta-gamma conformal field theory without explicitly assuming the motivic integration of Kontsevich-Soibelman or Feynman's oscillator integrals. See the English abstract for the conference at <a href="http://mathsoc.jp/en/meeting/kyushu12sept/summary.html">the MSJ official website</a>. The latter half of my presentation title was on the "virtual localization formula", but it is not the WKB (semi-classical) approximation of pre-quantization and polarization after the Oxford's school of differential geometers. My trial was to formulate the (topologically half-twisted) Super-Conformal Field Theories as an extension of Wess-Zumino-Witten term of level 1, which was claimed by N.Nerasov[2005] but not uploaded to the arXiv unlike proposed.<br /><br />Last but not least, let me mention my travel airline briefly. The Skymark airline, which is a recently hot topic of an LCC (Low-Cost-Carrier) airline agency, was used from 06:20am to 08:15am (Japan's Standard Time) at 20-Sep-2012, from Haneda (羽田) airport in Tokyo to Fukuoka in order to attend the domestic meeting of the Algebra Session.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-aVXs9H6EyQ0/UHNmypRhtyI/AAAAAAAAAMg/G1U45LAk9ZQ/s1600/IMG_1745.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="300" src="http://1.bp.blogspot.com/-aVXs9H6EyQ0/UHNmypRhtyI/AAAAAAAAAMg/G1U45LAk9ZQ/s400/IMG_1745.JPG" width="400" /></a></div>However, the returning way back from Fukuoka to Haneda was terribly delayed. I first waited more than half an hour at the Big Orange Station, which made me thirsty and sunburnt. I arrived at the Fukuoka airport one hour before the schedule while I left the conference hall at 14:00. I had to wait for the boarding at the gate 2 since the aircraft of LCC was delayed to arrive for the schedule of departure time 17:55, which was postponed to be after 18:15 and I had patiently awaited since otherwise I would have to wait for the next LCC flight of more than 2 hours later at night.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-Qry4HI3W6Ys/UHNpBkbSz8I/AAAAAAAAAMs/LbAfg1p2y60/s1600/IMG_1749.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="300" src="http://2.bp.blogspot.com/-Qry4HI3W6Ys/UHNpBkbSz8I/AAAAAAAAAMs/LbAfg1p2y60/s400/IMG_1749.JPG" width="400" /></a></div>Unlike supposed, my oral presentation was not performed regularly because of the irregularly worked projector from my EEEPC901 net-book with Fedora 17, which I used for several times and demonstrated twice within the conference dates. The Algebra Session was tight in schedule, so that I used my OHP backup for the optical camera with the use of my green laser pointer. I hope my above-mentioned slide file will be useful for someone who is interested in the relation between the Higgs mechanism (of physicist's sense) and the chiral algebra (Hamiltonian method on the worldsheet Riemann surface) theory with the base change of target space Kaehler manifolds (Lagrangian method of factorization algebra).<br /><br />The chairperson's question was about my next research plan and I said "I have worked more than 5 years on this topic. From the beginning around the AMS talk of Okounkov, an extension to non-toric cases is a long-standing problem. I also would like to apply the DGA method to quantum invariants." It was because Japanese mathematics is under a serious view from the outside society and Japanese mathematicians have to explain the value to the general public; since Japanese economy faces 20 years of serious decline and the universities are under severe budget cuts.<br /><br />In the good-old-days of Greek geometry, mathematicians can naively and Platonically quote <span class="reference-text"><span class="citation book">"Evidently Euclid did not stress the practical aspects of his subject, for there is a tale told of him that when one of his students asked of what use was the study of geometry, Euclid asked his slave to give the student threepence, "since he must make gain of what he learns.""</span></span><br /><br /><span class="reference-text"><span class="citation book">Nevertheless, nowadays world economics suggests a serious reconsideration of our position of academics in the real-world of general public. So I just started my oral explanation of presentation by saying "If you have to talk to a person in an area other than mathematics, you can appeal algebraic geometry has useful applications (such as blow-ups) to natural science, and not just calculus alone".</span></span><br /><span class="reference-text"><span class="citation book"><br /></span></span><span class="reference-text"><span class="citation book">I hope I can keep my trial on the recovery of academic value in the calculation-based financial society.</span></span>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-37189013689572811982012-01-01T23:59:00.002+09:002012-01-02T10:05:30.995+09:00Earth Top and Spin RotationGreetings.<br /><br />Today I prepared some academic documents to submit, so that I did not have time to take a sufficient rest.<br /><br />Indeed, we had another earthquake (fortunately far southern to Japanese islands and Tokyo) with Magnitude M=7.0. As the Energy Magnitude is (in a conventional definition) defined as a logarithmic scale of effective Joule energy, we had 1/1000 times Energy if compared to that of the Tohoku earthquake (M=9.0).<br /><br /><object width="320" height="266" class="BLOG_video_class" id="BLOG_video-75eab9cd573950d0" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"><param name="movie" value="https://www.youtube.com/get_player"><param name="bgcolor" value="#FFFFFF"><param name="allowfullscreen" value="true"><param name="flashvars" value="flvurl=https://redirector.googlevideo.com/videoplayback?id%3D75eab9cd573950d0%26itag%3D5%26source%3Dblogger%26requiressl%3Dyes%26app%3Dblogger%26cmo%3Dsecure_transport%3Dyes%26cmo%3Dsensitive_content%3Dyes%26ip%3D0.0.0.0%26ipbits%3D0%26expire%3D1490391990%26sparams%3Dip,ipbits,expire,id,itag,source,requiressl%26signature%3D8A1F526CD1825DA1348869540F2D5A59E7C9B482.303B4AAE85FDB5C8683ED2B8AB94D473B78E0F33%26key%3Dck2&iurl=http://video.google.com/ThumbnailServer2?app%3Dblogger%26contentid%3D75eab9cd573950d0%26offsetms%3D5000%26itag%3Dw160%26sigh%3DSSPFHlu3jFR26mJCQy1BIJR-MJ0&autoplay=0&ps=blogger"><embed src="https://www.youtube.com/get_player" type="application/x-shockwave-flash" width="320" height="266" bgcolor="#FFFFFF" flashvars="flvurl=https://redirector.googlevideo.com/videoplayback?id%3D75eab9cd573950d0%26itag%3D5%26source%3Dblogger%26requiressl%3Dyes%26app%3Dblogger%26cmo%3Dsecure_transport%3Dyes%26cmo%3Dsensitive_content%3Dyes%26ip%3D0.0.0.0%26ipbits%3D0%26expire%3D1490391990%26sparams%3Dip,ipbits,expire,id,itag,source,requiressl%26signature%3D8A1F526CD1825DA1348869540F2D5A59E7C9B482.303B4AAE85FDB5C8683ED2B8AB94D473B78E0F33%26key%3Dck2&iurl=http://video.google.com/ThumbnailServer2?app%3Dblogger%26contentid%3D75eab9cd573950d0%26offsetms%3D5000%26itag%3Dw160%26sigh%3DSSPFHlu3jFR26mJCQy1BIJR-MJ0&autoplay=0&ps=blogger" allowFullScreen="true" /></object><br /><br />The image above "The Earth Top" (taken by me) is what I am preparing for the last two lectures of dynamics and electro-magnetics at the year 2012 (Winter semester of 2011) at Tokyo. We will compute the inertia momentum "I", diagonalization by diag(I1, I2, I3) for non-symmetric gyro top, and the introduction of the coordinate transformation.<br /><br />Galileo's episode (made up by historians?) is quoted as "Yes, that's right" (Answer to "Isn't the earth moving?") This saying has several variations, such as "Yet the earth does move." However, at the era of Galileo Galilei, it was still possible to study mechanics as a mathematical hypothesis like the heliocentric model by Nicolaus Copernicus in the 15C's and 16C's. Galileo's accused point [1564-1642] was to study his relativity principle (coordinate changes between two inertia frames) as a guiding principle of real-world problem.<br /><br />I wish a happy new year and good documents for (special) relativity.makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-82618213795450078692011-12-21T22:38:00.009+09:002013-09-13T15:17:00.987+09:00Newton's Festival at the University of Tokyo<div class="post-header-line-1"><br />Dear friends;<br /><br />My homepage is temporarily closed for some reasons (, but I preserve its files and information). For almost one year, I worked for my mathematics lecture [brush-up and undergraduate mathematics at the summer semester] as well as my physics lecture [brush-up and introduction to dynamics / analytical mechanics (including some classical integrable systems of tops with inertia momentum tensor), and electro-magnetic special relativity at the winter semester].<br /><br />Here is some mini-blogs (I'm sorry it is written in Japanese) for this year; I have a Facebook account for more English posts (or sometimes in French, German, or Japanese [from Twitter or Android cell phone]).<br /><br />http://twilog.org/makotosakuraijp/<br /><br /><a href="http://makotosakurai.blogspot.com/2006/03/1st-day-of-jps-march-2006.html">My old diary</a> described my trip to a university of Japan, which had an "apple tree of Newton". Today was the "Newton Festival 2011" of Department of Physics, the University of Tokyo. However, as I explained above, I could not leave the lecture until 18:15, so that I could not attend the party at the Sanjo-Kaikan (山上会館) inside the Hongo Campus of the University of Tokyo.<br /><br />As all of you must know, Japan is under the revival from the Tohoku earthquake at 11-March-2011, 14:46, and the nuclear crisis afterwards. (I explained some of the radioactivity information and radioactivity protection to my colleagues and students.) Therefore, I could not travel much for conferences or workshops far from Tokyo, so that it was very difficult to keep my research activity.<br /><br />I wish you would have happy holidays and a "better" new year!<br /><br />Best wishes,<br /><br />Makoto Sakurai</div><br /><iframe allowtransparency="true" frameborder="0" scrolling="no" src="//www.facebook.com/plugins/like.php?href=http%3A%2F%2Fmakotosakurai.blogspot.com%2F2011%2F12%2Fnewtons-festival-at-university-of-tokyo.html&send=false&layout=button_count&width=450&show_faces=true&action=like&colorscheme=light&font&height=21" style="border: none; height: 21px; overflow: hidden; width: 450px;"></iframe>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-6491009832423550982011-01-01T07:53:00.003+09:002011-01-01T08:15:54.601+09:00Japanese Rising Sun 2011<object width="320" height="266" class="BLOG_video_class" id="BLOG_video-1cf2673f9c08659" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"><param name="movie" value="https://www.youtube.com/get_player"><param name="bgcolor" value="#FFFFFF"><param name="allowfullscreen" value="true"><param name="flashvars" value="flvurl=https://redirector.googlevideo.com/videoplayback?id%3D01cf2673f9c08659%26itag%3D5%26source%3Dblogger%26requiressl%3Dyes%26app%3Dblogger%26cmo%3Dsecure_transport%3Dyes%26cmo%3Dsensitive_content%3Dyes%26ip%3D0.0.0.0%26ipbits%3D0%26expire%3D1490391990%26sparams%3Dip,ipbits,expire,id,itag,source,requiressl%26signature%3DB574574C7BFFFD098026E45572BECF22DFA4ACB4.11114101FADC6DCD41D827B8A5B18F0CFC983C0E%26key%3Dck2&iurl=http://video.google.com/ThumbnailServer2?app%3Dblogger%26contentid%3D01cf2673f9c08659%26offsetms%3D5000%26itag%3Dw160%26sigh%3DuhO2gXz1q7piuV1KOrZyh3E-Jcw&autoplay=0&ps=blogger"><embed src="https://www.youtube.com/get_player" type="application/x-shockwave-flash" width="320" height="266" bgcolor="#FFFFFF" flashvars="flvurl=https://redirector.googlevideo.com/videoplayback?id%3D01cf2673f9c08659%26itag%3D5%26source%3Dblogger%26requiressl%3Dyes%26app%3Dblogger%26cmo%3Dsecure_transport%3Dyes%26cmo%3Dsensitive_content%3Dyes%26ip%3D0.0.0.0%26ipbits%3D0%26expire%3D1490391990%26sparams%3Dip,ipbits,expire,id,itag,source,requiressl%26signature%3DB574574C7BFFFD098026E45572BECF22DFA4ACB4.11114101FADC6DCD41D827B8A5B18F0CFC983C0E%26key%3Dck2&iurl=http://video.google.com/ThumbnailServer2?app%3Dblogger%26contentid%3D01cf2673f9c08659%26offsetms%3D5000%26itag%3Dw160%26sigh%3DuhO2gXz1q7piuV1KOrZyh3E-Jcw&autoplay=0&ps=blogger" allowFullScreen="true" /></object><br /><br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_FGOg_XWX-R4/TR5hlbtSTlI/AAAAAAAAALc/R3kBziyVsQI/s1600/RisingSun2011-4.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 400px; height: 300px;" src="http://4.bp.blogspot.com/_FGOg_XWX-R4/TR5hlbtSTlI/AAAAAAAAALc/R3kBziyVsQI/s400/RisingSun2011-4.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5556986285942525522" /></a><br /><br />The sun is rising. I had observed before the dawn to the sunrise of New Year's Day 2011. The photos are listed anti-chronologically.<br /><br />Have happy holidays and a good new year.<br /><br />Makoto Sakurai<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_FGOg_XWX-R4/TR5hfb5PuiI/AAAAAAAAALU/2SrsUol4_DY/s1600/RisingSun2011-3.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 400px; height: 300px;" src="http://1.bp.blogspot.com/_FGOg_XWX-R4/TR5hfb5PuiI/AAAAAAAAALU/2SrsUol4_DY/s400/RisingSun2011-3.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5556986182913473058" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_FGOg_XWX-R4/TR5hNa3ltBI/AAAAAAAAALE/5x1pJ-tD2pg/s1600/RisingSun2011-2.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 400px; height: 300px;" src="http://3.bp.blogspot.com/_FGOg_XWX-R4/TR5hNa3ltBI/AAAAAAAAALE/5x1pJ-tD2pg/s400/RisingSun2011-2.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5556985873400443922" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_FGOg_XWX-R4/TR5hIIQqlMI/AAAAAAAAAK8/q22fc2YqXXg/s1600/RisingSun2011.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 400px; height: 300px;" src="http://3.bp.blogspot.com/_FGOg_XWX-R4/TR5hIIQqlMI/AAAAAAAAAK8/q22fc2YqXXg/s400/RisingSun2011.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5556985782506001602" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_FGOg_XWX-R4/TR5hAs_vYbI/AAAAAAAAAK0/3xKh5KIv8zI/s1600/RedDawning2011.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 400px; height: 300px;" src="http://2.bp.blogspot.com/_FGOg_XWX-R4/TR5hAs_vYbI/AAAAAAAAAK0/3xKh5KIv8zI/s400/RedDawning2011.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5556985654928171442" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_FGOg_XWX-R4/TR5g5P_9yAI/AAAAAAAAAKs/cJfHrRV6pH4/s1600/Moon2011.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 400px; height: 300px;" src="http://2.bp.blogspot.com/_FGOg_XWX-R4/TR5g5P_9yAI/AAAAAAAAAKs/cJfHrRV6pH4/s400/Moon2011.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5556985526885402626" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_FGOg_XWX-R4/TR5gzE7TifI/AAAAAAAAAKk/Oz-vAtH-AA0/s1600/MoonStar2011.JPG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 400px; height: 300px;" src="http://4.bp.blogspot.com/_FGOg_XWX-R4/TR5gzE7TifI/AAAAAAAAAKk/Oz-vAtH-AA0/s400/MoonStar2011.JPG" border="0" alt="" id="BLOGGER_PHOTO_ID_5556985420833851890" /></a>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-3847780618554097272010-09-15T19:01:00.000+09:002015-01-17T04:17:23.369+09:00Japan Physical Society 2010 Fall in Kyushu<img alt="" border="0" src="http://3.bp.blogspot.com/_FGOg_XWX-R4/TJCh0zZVq1I/AAAAAAAAAJA/ihOfTQQxHyo/s400/IMG_0627.JPG" id="BLOGGER_PHOTO_ID_5517087472050613074" style="cursor: hand; display: block; height: 300px; margin: 0px auto 10px; text-align: center; width: 400px;" /> <br /><div><a href="http://1.bp.blogspot.com/_FGOg_XWX-R4/TJCfUgMwe7I/AAAAAAAAAIw/gaOzjTTChXw/s1600/IMG_0612.JPG"><img alt="" border="0" src="http://1.bp.blogspot.com/_FGOg_XWX-R4/TJCfUgMwe7I/AAAAAAAAAIw/gaOzjTTChXw/s400/IMG_0612.JPG" id="BLOGGER_PHOTO_ID_5517084718118501298" style="cursor: hand; float: right; height: 260px; margin: 0px 0px 10px 10px; width: 292px;" /></a><br /><br /></div><div><div>The Japan Math-Phys Society became separated after the Nobel winning paper by Yukawa at about 64 years ago. So my presentation to the JPS (Japan Physical Society) is the first time since I did at the year 2006; which was a joint meeting with the USA at Hawaii. (See the past blog.)<br /><br />In this week, I visited the Kyushu-Kogyo University by staying for only 2(+1) days at a hotel near Kokura (小倉:a bullet train station). The travel was nice, because I took a very-early-morning flight from Haneda to Kita-Kyushu; my flight was the retirement of the aircraft (type MD87) for 25 years, whose schedule for departure was 5-minute-delayed, but the arrival was just on time. (The speed of flight was 820 km/hour: the second figure is the Kofu-basin 甲府盆地) Then the third figure is the mono-rail and bullet-train station Kokura seen from the station square. </div><div></div><br /><a href="http://2.bp.blogspot.com/_FGOg_XWX-R4/TJChc6EEREI/AAAAAAAAAI4/mISNp5FrVlc/s1600/IMG_0625.JPG"><img alt="" border="0" src="http://2.bp.blogspot.com/_FGOg_XWX-R4/TJChc6EEREI/AAAAAAAAAI4/mISNp5FrVlc/s400/IMG_0625.JPG" id="BLOGGER_PHOTO_ID_5517087061523579970" style="cursor: hand; float: right; height: 256px; margin: 0px 0px 10px 10px; width: 293px;" /></a>Then I took a shuttle bus before an early-checked-in at the hotel for my suit case, and checked the way to the university presentation room. It (Sep-12) was Sunday and there were just accelerator experimentalists and I heard a public lecture at the auditorium.<br /><br />The second day was by the lattice gauge theory, quantum integrable systems, AdS/CFT, and quantum mechanics. I heard some physics discussions by senior staffs, and I had become very exhausted.<br /><br />The final day was my presentation day at the string theory session, for the illumination of my past 2-3 years of development of "pure math" to see how the S-duality conjecture is seen from an algebraic-geometer with some physics background. The slide is available at:<br /><a href="http://www.ms.u-tokyo.ac.jp/~makoto/JPS2010Fall.pdf">Moduli space of chiral conformal field theories and compactification to Kahler manifolds</a></div><br /><br />The final figure is the panel guiding the participants to the presentation halls.<br /><img alt="" border="0" src="http://2.bp.blogspot.com/_FGOg_XWX-R4/TJCjk3xY0VI/AAAAAAAAAJQ/2LOllM9QbqQ/s400/IMG_0626.JPG" id="BLOGGER_PHOTO_ID_5517089397370573138" style="cursor: hand; display: block; height: 300px; margin: 0px auto 10px; text-align: center; width: 400px;" />makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-4283514559245354582010-08-11T07:49:00.000+09:002010-08-11T08:02:01.295+09:00Virtual visit at KITP California, QFT and Langlands<a href="http://www.itp.ucsb.edu/activities/dbdetails?acro=duallang_m10">Langlands-Type Dualities in Quantum Field Theory</a>, KITP, California, USA, Aug 9, 2010 - Aug 27, 2010 is delivering the videos (and lecture notes) in several formats at <a href="http://online.kitp.ucsb.edu/online/duallang_m10/">the wikispace</a>. This conference is more on physi-cians' mathematics on low dimensional topology (or sometimes with extra dimensions or relative dimension of embeddings).<br /><br />Unfortunately, I do not have time nor budgets to travel this month, but I hope to learn (and contribute to in some sense) something fruitful in this occasion. My old colleagues and friends attend the meetings, so I will do what I can do by myself.makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-34766188055417052992010-08-05T13:25:00.000+09:002013-10-02T17:03:12.059+09:00Jet sky and Differential Graded Lie Algebras<div align="right">Today I have a fine sky at Komaba, Tokyo and I am going to visit the string topology by Voronov at Kashiwa campus of the University of Tokyo. The video is the jet sky over the ground of Komaba campus, where we have an "open campus".</div><div align="right"></div><div align="center"></div><object width="320" height="266" class="BLOG_video_class" id="BLOG_video-a5ea93015adf5159" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"><param name="movie" value="https://www.youtube.com/get_player"><param name="bgcolor" value="#FFFFFF"><param name="allowfullscreen" value="true"><param name="flashvars" value="flvurl=https://redirector.googlevideo.com/videoplayback?id%3Da5ea93015adf5159%26itag%3D5%26source%3Dblogger%26requiressl%3Dyes%26app%3Dblogger%26cmo%3Dsecure_transport%3Dyes%26cmo%3Dsensitive_content%3Dyes%26ip%3D0.0.0.0%26ipbits%3D0%26expire%3D1490391990%26sparams%3Dip,ipbits,expire,id,itag,source,requiressl%26signature%3D7F89D95959C6145C0085B7B503A44CC0E58B8BAA.288E9706435CC0953AAC060CEB522A4758A48337%26key%3Dck2&iurl=http://video.google.com/ThumbnailServer2?app%3Dblogger%26contentid%3Da5ea93015adf5159%26offsetms%3D5000%26itag%3Dw160%26sigh%3DkGcGx8rsQAUyLzWKmjfKrK1dvZI&autoplay=0&ps=blogger"><embed src="https://www.youtube.com/get_player" type="application/x-shockwave-flash" width="320" height="266" bgcolor="#FFFFFF" flashvars="flvurl=https://redirector.googlevideo.com/videoplayback?id%3Da5ea93015adf5159%26itag%3D5%26source%3Dblogger%26requiressl%3Dyes%26app%3Dblogger%26cmo%3Dsecure_transport%3Dyes%26cmo%3Dsensitive_content%3Dyes%26ip%3D0.0.0.0%26ipbits%3D0%26expire%3D1490391990%26sparams%3Dip,ipbits,expire,id,itag,source,requiressl%26signature%3D7F89D95959C6145C0085B7B503A44CC0E58B8BAA.288E9706435CC0953AAC060CEB522A4758A48337%26key%3Dck2&iurl=http://video.google.com/ThumbnailServer2?app%3Dblogger%26contentid%3Da5ea93015adf5159%26offsetms%3D5000%26itag%3Dw160%26sigh%3DkGcGx8rsQAUyLzWKmjfKrK1dvZI&autoplay=0&ps=blogger" allowFullScreen="true" /></object>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-72577662715601178882010-06-30T22:24:00.000+09:002010-06-30T22:39:20.412+09:00Rainbow Connection<a href="http://photos1.blogger.com/blogger/4668/1293/1600/NiagaraRainbow4.jpg"><img style="MARGIN: 0px 0px 10px 10px; WIDTH: 614px; FLOAT: right; HEIGHT: 461px; CURSOR: hand" border="0" alt="" src="http://photos1.blogger.com/blogger/4668/1293/1600/NiagaraRainbow4.jpg" /></a><br /><div><br />Today's post is a déjà-vu of Strings 2005 conference in Toronto.<br /><br />See the original: <a href="http://makotosakurai.blogspot.com/2005/07/3rd-day-of-strings-2005.html">3rd day of Strings 2005</a></div>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-85699304027153598922010-06-03T11:05:00.000+09:002010-06-18T06:10:35.510+09:00Firework in Tokyo<p><object width="320" height="266" class="BLOG_video_class" id="BLOG_video-77062446e645256c" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"><param name="movie" value="https://www.youtube.com/get_player"><param name="bgcolor" value="#FFFFFF"><param name="allowfullscreen" value="true"><param name="flashvars" value="flvurl=https://redirector.googlevideo.com/videoplayback?id%3D77062446e645256c%26itag%3D5%26source%3Dblogger%26requiressl%3Dyes%26app%3Dblogger%26cmo%3Dsecure_transport%3Dyes%26cmo%3Dsensitive_content%3Dyes%26ip%3D0.0.0.0%26ipbits%3D0%26expire%3D1490391990%26sparams%3Dip,ipbits,expire,id,itag,source,requiressl%26signature%3D41150097689B4C4DCEBD43E49E0FF82A467F7F4B.45431C376AC4F66B0EF9B104D46BDC5A16579827%26key%3Dck2&iurl=http://video.google.com/ThumbnailServer2?app%3Dblogger%26contentid%3D77062446e645256c%26offsetms%3D5000%26itag%3Dw160%26sigh%3DixxNhTU4xxhjIGgfK3gbCHmTEOw&autoplay=0&ps=blogger"><embed src="https://www.youtube.com/get_player" type="application/x-shockwave-flash" width="320" height="266" bgcolor="#FFFFFF" flashvars="flvurl=https://redirector.googlevideo.com/videoplayback?id%3D77062446e645256c%26itag%3D5%26source%3Dblogger%26requiressl%3Dyes%26app%3Dblogger%26cmo%3Dsecure_transport%3Dyes%26cmo%3Dsensitive_content%3Dyes%26ip%3D0.0.0.0%26ipbits%3D0%26expire%3D1490391990%26sparams%3Dip,ipbits,expire,id,itag,source,requiressl%26signature%3D41150097689B4C4DCEBD43E49E0FF82A467F7F4B.45431C376AC4F66B0EF9B104D46BDC5A16579827%26key%3Dck2&iurl=http://video.google.com/ThumbnailServer2?app%3Dblogger%26contentid%3D77062446e645256c%26offsetms%3D5000%26itag%3Dw160%26sigh%3DixxNhTU4xxhjIGgfK3gbCHmTEOw&autoplay=0&ps=blogger" allowFullScreen="true" /></object></p><p>Today I observed a firework in this season. Tokyo is about to welcome the summer season. </p>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-57193331980881652272010-03-27T18:20:00.001+09:002010-03-28T12:20:25.908+09:00Level structures and moduli space of chiral conformal field theories<a href="http://1.bp.blogspot.com/_FGOg_XWX-R4/S63N9FE5zsI/AAAAAAAAAH4/_GUJCBIJm3c/s1600/IMG_0390.JPG"><img style="margin: 0px 0px 10px 10px; width: 400px; float: right; height: 300px;" id="BLOGGER_PHOTO_ID_5453241173033995970" alt="" src="http://1.bp.blogspot.com/_FGOg_XWX-R4/S63N9FE5zsI/AAAAAAAAAH4/_GUJCBIJm3c/s400/IMG_0390.JPG" border="0" /></a> This week, I delivered a talk on holonomic $\mathcal{D}$-modules and their level structure. In order to explain the moduli space of chiral (holomorphic) conformal field theory, I explained some categorical aspects of topological string theory as well as the DG-scheme of Fontaine-Kapranov theory of integration over formal loop space on (hyper-)kahler manifolds with mild singularity.<br /><br />As is always, the slides are avaible on the official website:<br /><br /><a href="http://www.ms.u-tokyo.ac.jp/%7Emakoto/JMS2010March.pdf">Level structures and moduli space of chiral conformal field theories.</a><br /><br /><a href="http://4.bp.blogspot.com/_FGOg_XWX-R4/S63OC4UtfFI/AAAAAAAAAIA/9s2uw4LGW8U/s1600/IMG_0391.JPG"><img style="margin: 0px 10px 10px 0px; width: 400px; float: left; height: 300px;" id="BLOGGER_PHOTO_ID_5453241272689851474" alt="" src="http://4.bp.blogspot.com/_FGOg_XWX-R4/S63OC4UtfFI/AAAAAAAAAIA/9s2uw4LGW8U/s400/IMG_0391.JPG" border="0" /></a> In summary, I explained the "super-"conformal field theories as well as the "supersymmetric" gauge theory, in the language of Differential Graded Category as well as the stack singularity for the Chan-Paton factor, as a generalization of quiver gauge theory.makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-71025871209991999992010-02-24T16:35:00.001+09:002010-08-01T01:42:24.836+09:00Eseen 2010 5th day, Algebraic Geometry and Arithmetic2010-Feb-20th was the final day of the official day of Essen 2010, whose schedule was adapted to the carnival that I mentioned previously. <div><br /></div><div>Thelene (CNRS & Paris) and Lazarsfield were the speakers of this day. Thelene talked about the universal invariant and algebraic cycles of higher codimension. The main result was</div><div><br /></div><div>Z^{2i} (X) = H^{2i}_{Hodge} (X, ¥mathbb{Z}) / H^{2i}_{alg} (X, ¥mathbb{Z})</div><div><br /></div><div>(where i = 1: Lefshectz, d-1, or 2). He considered Bloch-Ogus theorem and Betti cohomology.</div><div><br /></div><div>Lazarsfield talked about the positivity (Eckart Viehweg and Esnault) of cycles on abelian varieties. I. Review of positivity for divisors of X = smooth projective variety / ¥mathbb{C}. </div><div><br /></div><div>-- 1960's (Kodaira and Kleiman) for numerical theory of positivity.</div><div><br /></div><div>II. Higher codimension:</div><div><br /></div><div>-- product structure on the nef class (after the letter of Grothendieck to Mumford in the collection Vol. II.), especially on whether nef class is in the pseudo-effective divisors.</div><div><br /></div><div>III. Positivity of Abelian varieties of real (k,k)-forms on V, where we set B = V / ¥Lambda for abelian variety. He stated the notion of strong / weak positivity of (k,k)- differential form.</div><div><br /></div><div>After the conference, some of the participants are guided to the coal mine called Zeche Zollverein, which was about 20 minutes far from the Berliner Platz station by "tram".</div><div><br /></div><div>I could have talked to famous professors as well as young fellows in this week. Therefore I appreciated this occasion of conference on the memory of Prof. Eckard Viehweg.</div>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-32494514796224567212010-02-24T16:35:00.000+09:002010-06-18T06:10:21.653+09:00Eseen 2010 4th day, Algebraic Geometry and ArithmeticThe 4th day (February 19) morning was by Takuro Mochizuki, Venjakob, Fantechi. Mochizuki was on the recent development on the irregular singularity after Sabbah. The motivation came from \mathbb{Q}-holonomic D-module \mathcal{M} / X. Regular singularity case has Riemann-Hilbert correspondence for f_{\ast}, f_!, f^{\ast}, f^!, \otimes, RHom, \psi_g (nearby cycle), \phi_g (vanishing cycle). [Saito-Terasoma: \mathcal{M} regular singular meromorphic bundle, Beilinson-Bloch-Deligne-Esnault: regular, dim X = 1]. Then, rather than naive hope for "pre-Betti structure", he worked on an extra condition of "canonical Betti strucutre" for functoriality of "Stokes structure" (Stokes filration rather than Deligne filtration) after gluing of \mathbb{C}-perverse sheaves.<br /><br />Venjakov was on the non-commutative Iwasawa main conjecture for elliptic curves with complex multiplication (CM). The definition of Iwasawa was on p-adic zeta function \zeta_p up to unit, and L_p for elliptic curve. The CM case was E \ \mathbb{Q} with \mathcal{O}_K = End (E).<br /><br />Fantechi (SISSA) talked about "Twists or logs as you please", Degeneration form for Gromov-Witten invariants. She defined the Gromov-Witten invariants, which were numerical invariants of smooth projective variety over \mathbb{C}. Rather than computing symplectic invariants of Li-Ruan (and relative version by Ionel-Parker), here came the algebraic geometry of Jun Li (2001). After the talks, I went to the student restaurant and a cafe, and explained to participants about the recent understanding of mirror symmetry conjecture on Gromov-Witten potential and generating function of correlation function of cohomological field theory (and Frobenius structure on the Gauss-Manin integrable connection).<br /><br />Afternoon talk was only by Prof. Hida on analytic number theory of 'big' Hecke algebra. As is often the case with automorphic forms, he introduced the space of cusp forms S_{k+1} with weight k+1. He explained something important for definition of analytic L-function by Greenberg's definition written in his books.makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-25675274381555714862010-02-20T16:27:00.001+09:002010-02-22T17:54:22.679+09:00Eseen 2010 3rd day, Algebraic Geometry and Arithmetic3rd day morning (Feb.18) was by Kramer, Geisser, and Kim. Kramer's talk was on the Arakelov geometry (a la Gillet et Soule', Faltings, Bismut) by Quillen metric and arithmetic Riemann-Roch theorem by Burger, Kuehn, utilizing heat kernel regulator. The main goal was on the log singular-metric \mu on modular curves and he assumed the Peterson metric induced by \mu on the relative dualizing sheaf. The spectral zeta function worked for the regularization, which seems to be the anomaly formula of string theory. However, I do not know about how supersymmetry can work to regularize the trace and the determinant bundle.<br /><br />Geisser was on Suslin homology (which is a Torsion of simplicial complexes with coefficient A: abelian group, assuming the resolution of singularity) and his recent preprint on Parshin's conjecture. Let k be a perfect field, and X / k separated of finite type. We divided the cohomology paring into torsion-free part and torsion part. Then the Suslin-Voevodsky theorem asserts the equivalence of Suslin and etale cohomology with coefficient \mathbb{Z}/m, where k is algebraically closed, char k doesn't divide m. Then he worked on base finite fields. Under the use of Weil group generated by Frobenius, the Conjecture P_0 (by Parshin's conjecture) is the vanishing of non-zero Suslin homology of rational coefficient for smooth proper scheme. Tate conjecture and Beilinson conjecture deduce Parshin's conjecture, and if further assume Kimura-O'Sullivan finite dimensnionality, conjecture P_0 holds. Then he finally asserted the equivalence of Conj. P_0 and generalized Kato conjecutre, in which for smooth X, we have the abelianization of the fundamental group.<br /><br />Minhhyang Kim was on the Diophantine geometry and Galois theory. 1. Abelian case (elliptic curves, Abelian motives: Fontaine-Mazure & Beilinson & Bloch-Kato), 2. Non-abelian Albanase map (Pro-finite version, the section conjecture of Grothendieck, motivic version).<br /><br />After the morning talk, we took a group photo which is available on the web. We went to the Mensa restaurant and ate a frankfur sausage with vegetable.<br /><br /><a href="http://m2.geometry.de/conference-foto.jpg"><img style="WIDTH: 621px; HEIGHT: 200px" src="http://m2.geometry.de/conference-foto-small.jpg" /></a><br /><br />Afternoon was by Beilinson and Huybrechts. Beilinson was on the Ziv Ran space's contractiblity, which is used in the arc space (formal loop space) formalism of factorization algebra. For X: topological space, R(X) := the set of finite irreducible subsets of X. The proposition was that if X is any connected cell complex (CW complex), then R(X) is contractible. Then the story was on the category $\mathcal{S}$ of finite non-empty sets and surjectivity for the index set I and Ran space R(X). The claim was that homotopy colimit of M_{X^I} in \mathcal{S} is homotopic to Rat(X,Y) (presheaf of rational map from X to Y). Then, for X a curve, Maps (X \ {x_i}, Y) is an ind-affine ind-scheme, and conctractible if Y = Z \subset \neq \mathbb{A}^d.<br /><br />Huybrechts was on the stability conditions on derived categoies of (polarized) K3 surfaces, after Douglas and Bridgeland's pi-stability condition, which is a modern reformulation of Harder-Narasimhan property and t-structure on derived category of coherent sheaves with heart. I asked him about the quintic 3-fold, but we do not know about the compact Calabi-Yau 3-folds, except for the local Calabi-Yau 3-fold by Nekrasov-Okounkov, algorithms of Landau-Ginzburg model for quiver variety with path algebra, (and recent work of Walcher for quintic 3-fold and its real Langrangian submanifold).makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-61442440084200138232010-02-18T23:23:00.000+09:002012-11-11T13:43:16.083+09:00Eseen 2010 2nd day, Algebraic Geometry and ArithmeticYesterday was the banquet day. But, before reporting the party, I will make an academic stuff.<br /><br />Edinxhoven was on the polynomial time algorithm to compute 2-dimensional Galois representations. To be more precise, if we fix the weight k, we obtain a (deterministic) computation of the Hecke operator T_p within a polynomial time in log p. If we further assume the generalized Riemann hypothesis, it is also in poly. time in the weight k. Jannsen was on excellent schemes of dimension 2 and their strong resolution. This was after the recent progress of posotive characteristic case by Prof. Hironaka et.al. Jannsen mentioned the history of canonical, non-embedding, and functorial resolutions of sigularities. Laza was on the minimal model program (Hatching, de Jong-Oort), ADE hypersurface singularity, and GIT quotient.<br /><br />Afternoon was by Nicaise and Abramovich. Nicaise talked about Neron model's existence, Grothendieck ring, motivic integration for monodromy of tame ramifications utilizing Chai's base change conductor. Abramovich talked about "Varieties with a twist" rather than "Geometry & moduli of stacks". He mentioned one of the books of Viehweg (Q.P. model of var. of general type) and a new ongoing book by Kollar. He talked about some family (moduli) of stable varieties. He finally mentioned the recent paper by Hacon-Mckernan on the log minimal model program.makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-29234311265241728432010-02-17T16:02:00.000+09:002013-10-17T06:06:05.340+09:00Eseen 2010 1st day, Algebraic Geometry and Arithmetic<a href="http://3.bp.blogspot.com/_FGOg_XWX-R4/S3uWMzIaTFI/AAAAAAAAAHI/7ycHdSVRcJY/s1600-h/IMG_0174.JPG"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5439106121608088658" src="http://3.bp.blogspot.com/_FGOg_XWX-R4/S3uWMzIaTFI/AAAAAAAAAHI/7ycHdSVRcJY/s400/IMG_0174.JPG" style="float: right; height: 300px; margin: 0px 0px 10px 10px; width: 400px;" /></a><br /><div>Yesterday was the 1st day of the conference on algebraic geometry and arithmetic in Essen, Germany. The internet connection (WiFi) was not established until now, so that I read the e-mail for the first time in Germany at the conference room.</div><br /><a href="http://3.bp.blogspot.com/_FGOg_XWX-R4/S3uXXN7FCiI/AAAAAAAAAHY/YK0rIjRUxrk/s1600-h/IMG_0193.JPG"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5439107400110246434" src="http://3.bp.blogspot.com/_FGOg_XWX-R4/S3uXXN7FCiI/AAAAAAAAAHY/YK0rIjRUxrk/s400/IMG_0193.JPG" style="float: left; height: 400px; margin: 0px 10px 10px 0px; width: 300px;" /></a> <br /><div></div><br /><div>Before the lecture, I had to look for how to reach the yellow building. While I was thinking about a public street (and the tram station) around the campus, it was found out that the lecture room is not at the math department, bur rather at the center of Duisburg-Essen University. </div><br /><div>The morning talks were delivered by Vistoli and Chenever. Before that the organizer delivered a speech on the passing away of Prof. Viehweg. Vistoli was on the "essential dimension" of a curve and the genericity theorem. After the definition of Merkuriev, the theorem of Brousnan-Retchtustein-Vistov holds for any ground filed with characteristic 0 (genus 0: 2, genus 1: +infty, genus 2: 5, genus >= 3, 3g - 3). After the theorem on smooth connected Deligne-Mumford stack of finite type over a field, the genericity theorem (Beosnan-Reichstein-Vistoli) holds. After thinking about the Artin stack and stable curves with n points, one conjectured that the automorphism group G should be "extremely reductive". Then we switched the case for d & n (especially for whether 3 divides d). </div><br /><a href="http://2.bp.blogspot.com/_FGOg_XWX-R4/S3uYulFKc1I/AAAAAAAAAHw/Q3Q4Zv1NNcQ/s1600-h/IMG_0195.JPG"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5439108900975178578" src="http://2.bp.blogspot.com/_FGOg_XWX-R4/S3uYulFKc1I/AAAAAAAAAHw/Q3Q4Zv1NNcQ/s400/IMG_0195.JPG" style="float: right; height: 300px; margin: 0px 0px 10px 10px; width: 400px;" /></a><br /><div>After the first talk, I could see Prof. Beilinson and talked about my research projects and his recent works with Gaitsogry. I reported my current updates at the topological methods (Jacob Lurie et al.) in mathematical physics at the Komaba compus and the Kavli IPMU of the University of Tokyo. </div><div><br />Chenever was on the analytic number theoretical methods to the modularity problem of complex multiplication. Mazur's results for p > 13 (p not 631) for Ramanujan delta function were stated, and the theorem of Graber-Mazur was that the quasi-modular points are Zariski dense. After the theorem on the first cohomology on generic situation, its kernel is isomorphic to 2nd cohomology. </div><br /><div>The lunch was at the shopping mall, and I took a Thai-Reise Spaghetti, which was very hot and I feel refreshed. After the lunch, we went to a cafe and we saw a carnival with bright costume.</div><br /><div>The afternoon session was by Ngo and Brosnan. Ngo talked about the Langlands program. It started from some classical results about Godement, Jacquet, Authur on the L-funciton. The endoscopy and analytic continuation were analyzed on the pole. After the Beilinson-Drinfeld Grassmanian (n=1 case and geometric Langlands), he showed the intersection cohomology of perverse sheaf (Hecke) on the Grassmanian. For the adelization of the trace formula, he utilized the Lie group and its Haar measure, Tamagawa measure on the coset. Then the Poisson resummation formula enables us to make the summation absolutely convergent.</div>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-13814719070664123192010-01-01T13:02:00.000+09:002010-01-01T14:14:37.594+09:00New Year 2010 in Tokyo<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_FGOg_XWX-R4/Sz10GlpO3lI/AAAAAAAAAHA/Kq-h32GxRAs/s1600-h/NewYear2010.jpg"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 400px; height: 225px;" src="http://4.bp.blogspot.com/_FGOg_XWX-R4/Sz10GlpO3lI/AAAAAAAAAHA/Kq-h32GxRAs/s400/NewYear2010.jpg" alt="" id="BLOGGER_PHOTO_ID_5421617182957035090" border="0" /></a>Greetings.<br /><br />There are several environmental changes in Komaba campus, the University of Tokyo. For example, the entrance of mathematical science building now has a flower garden as is seen in the picture.<br /><br />Although no colleague I have seen for the first time today, I feel like a freshman of this research institute.<br /><br />Now that I am writing a long paper, I think I cannot attend a lot of conferences for this month. I also have to prepare for a travel to Europe of next month.<br /><br />All the best,<br /><br />Makoto Sakuraimakoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.comtag:blogger.com,1999:blog-14329013.post-85447335073458309912009-11-27T19:03:00.001+09:002009-11-28T23:50:28.751+09:00Desplasability and Lagrangean submanifolds<span style="font-size:130%;"><a href="http://2.bp.blogspot.com/_FGOg_XWX-R4/Sw-j-BSk9EI/AAAAAAAAAG4/U7vyMUHkgWU/s1600/SN3E1345-716182.JPG"><img style="width: 412px; height: 231px;" src="http://2.bp.blogspot.com/_FGOg_XWX-R4/Sw-j-BSk9EI/AAAAAAAAAG4/U7vyMUHkgWU/s320/SN3E1345-716182.JPG" alt="" id="BLOGGER_PHOTO_ID_5408721963388826690" border="0" /></a></span><br />IPMU is on the verge of winter. Today's seminar by Tamarkin was on Fukaya category and Hamiltonian symplectomorphisms.<p>Kashiwa has the atmosphere of Christmas.</p>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0tag:blogger.com,1999:blog-14329013.post-63124514818900278052009-10-22T03:24:00.001+09:002009-11-28T23:49:50.042+09:00Visual F# 1.9.7 availableDon Syme annouced the new version of F# compiler. MSDN subscription enables us to use Visual Studio 2010 Beta 2, but Visual Studio Shell 2008 is ready for today's new F#.<p>enjoy.</p>makoto (真)http://www.blogger.com/profile/00791929720800973411noreply@blogger.com0