Sunday, July 31, 2005

Baseball game to the Safeco Field


I went with 4 people to the Sefeco Field at the right edge of downtown. To be more precise, we meet together at 12:30 in front of the left gate. Only I have reserved the seat so that, when they bought the ticket, it was already 13:05, that is, the time the game starts.

The game itself was interesting because we could see many hits and scores with a fine play by Ichiro. However, he had no hits today although he did 2 homeruns yesterday. The last batting of Ichiro at the bottom of 9th was especially exciting. The audience stands and shouted "Ichiro-Ichiro". If he had a timely hit, it was "Sayonara" (come-from-behind), but he couldn't.

We went to the international areas to take the dinner of soup and they let us come back to the doom by their car.

Saturday, July 30, 2005

Weekend trip to the downtown, Temporary update



Albert Biestadt (American 1830-1902), Puget Sound on the Pacific Coast, 1870.

Friday, July 29, 2005

5th day of Seattle'05 week 1

Pandharipande was on the old topic of GW/DT correspondence including relative GW / DT. Hori was extensive including topological open string theory (with short comment on the hetetoric string), homological mirror symmetry with dg category language / Fukaya cateory (FOOO), RR charge, Uhlenbeck compactification of bubbles, and Elementary T-duality / SYZ.

Afternoon sessions, I took Arcara, Y.Ruan, and Jun Li. Arcara was on the moduli space in the derived category of a K3 surface including a review of (semi-)stable bundles, Harder-Narasimhan filtration, Bridgeland's sense of alpha-stability and central charges, tilting, and Mukai flops (Bertram). Y.Ruan changed his title from "Landau-Ginzburg Gromov-Witten theory" to "Twisted K-theory and its product". It is the so-called Chen-Ruan orbifold cohomology or twisted K-theory of Freed-Hopkins-Teleman. The 1st main focus was how we can modify the native definition of exteritor product in order that they have the associativity incorpolaring the obstruction class. The 2nd was on the transgression map, multiplicative property, and Pontrajgin product. Jun Li was on "Dimension zero Donaldson-Thomas invariants"; a trial on defining Gromov-Witten invariants in terms of stable sheaves on X = 3-fold target spaces. However, his talk included the case of X=C smooth curve, X=smooth alg. surface (with some speculation). When it came to the story on the 3-fold case, he talked about the Gopakumar-Vafa and Donaldson-Thomas invariants with proof of MNOP [Maulik-Nekrasov-Okounkov-Pandharipande] conjecture utilizing some standard facts of Hilbert scheme of points. How do you derive the Hilbert scheme of points from the Ziv Ran space of Beilinson-Drinfeld chiral algebras? After his talk, I asked him several questions personally.

After the lecture, we took lunch at the terrace of MacMahon with some friends. I caught a cold and so that I could not go, but some people left the Hall at the evening or at the next morning to the Olympic National Park.

Thursday, July 28, 2005

4th day of Seattle'05 week 1

Okounkov was on the equivariant localization in Donaldson-Thomas theory. It was something like melting crystals. The closing was something like this: What about non-toric case? Not a rhetorical question.

Huybrechts wes on "twisted"/ polarized K3 surfaces, in the same sense of Yoshioka. It is a generalization of the global Torelli theorem of Mukai and Orlov. Katzarkov was on generalized Hodge structures (GHS) & homological mirror symmetry, using the white board. The question was "Are there examples of 4 dimensional simply connected homeomorphic symplectic manifolds X1, X2 such that GW(X1) = GW (X2) but not X1 \cong X2". He talked some definitions and exmaples of genux two curves and del Pezzo surfaces. The final theorem was "GHS forms a Tannakian category". Teleman was on the quantum Hitchin systems (and some topological field theories). I was first surprised that the number of audience was 18 before the lecture starts, although it became about 35. The talk started from some history like Atiyah-Bott, but reached Beilinson-Drinfeld chiral algebras (D-modules), chiral de Rham complex, Verlinde formula for WZW model (flag variety or affine D-module), the equivariant GW theory. "Moral of understanding so far" was "K-theory better than cohomology", "non-abelian localization", Teleman-Woodward theorem, and Newstead conjecture. I asked whether he knew about the recent work of Drinfeld (2003) personally.

After the BBQ (6-8pm), I talked to Okada and Iritani for about 1 hour and went to a Chinese restaurant.

3rd day of Seattle'05 week 1

Today we had only the moning session. Pandharipande talked the obstruction theory, the Hodge bundle, symplectic approaches / creation-annihilation operator representation (Frobenius manifolds), GW-SW for surfaces (Taubes: minimal surfaces), and some conjectures. Seidel was on Karoubi completion, Picard-Lefschetz and the fact that the fuctor between both derived categories induces a subcategory. He also mentioned some reviews like dg-category as A_{\infty} category or new claims including the isotopy invariance of Floer cohomology. Hori illustrated the Landau-Ginzburg (linear sigma model) phase, some N=2 supersymmetry algebras, and mirror symmetry for Fano manifolds (Hori-Vafa) from vortex configuration.

Wednesday, July 27, 2005

2nd day of Seattle'05 week 1

I skipped the morning talk because I was a little tired. Seidel's talk should be the definition of Fukaya A^{\infty} category, but I am not sure whether he talked about the Hamiltonian deformation and the completion of Fukaya category by coisotropic manifolds. During the lunch time, I received the parcel from Amazon.com.

Afternoon session was busy; Auroux (Sieg Hall) - Hausel (Elec. Eng.) - Wei-Dong Ruan (Mech. Eng.). Auroux was on the recent work with Katzrkov-Orlov on the homological mirror symmetry for dP_n (n=0,1,\cdtos,9) as a generalization of Seidel's work on CP^2. He first review the HMS (Homological Mirror Symmetry) conjecture and the definition of Fukaya category for Calabi-Yaus. Then the story came to the Fano / Landau-Ginzburg mirror symmetry ulitizing the Lefschetz fibration of disk Lagrangian cycles, which vanished at the critical points with some deformation by B-fields and checks on the areas of vanishing cycles. Hausel was on explicit calculations on the H polynonial for mixed Hodge structures utilizing some non-Abelian Hodge theory (Riemann-Hilbert map) for GL(N) and some finite field harmonic analysis. Wei-Dong Ruan was again on the Homological Mirror, but a little more review-oriented talk. He derived the HMS from SYZ from local picture (cpx=log structure) and global structure(Fourier-Mukai). The new work is on the construction of sheaves as an extended work of Seidel.

At 8 pm, about 12 graduate students came to the lecture room and one of them talked about his recent interest on the "deformation of singularities and variations of GIT quotients". It started from the history of 70s-80s on the low modality (parameters for defining equation): simple singularity of ADE from the viewpoints of Dynkin diagrams including the theorem of Looijenga as well as unimodal singularity. Then he tried to tie to the Hodge theory and more complicated singularities for the GIT construction of parameter space. The conclusion was the dependance of GIT on the line bundle and Thaddeux-Dulgachev-Hu works on the case Picard = Z^2 and the slope of lattice denotes how complicated the singularity is.

Tuesday, July 26, 2005

1st day of Seattle'05 week 1

The institute (conference?) started from Pandharipande on GW in low dimensions (0,1,2,3). His talk was on Kontsevich's combinatorial model, the Comb model, the cohomology structure of low genera, and the topological ring. Next was Hori on "Mirror symmetry" starting with an applaud. He reviewed some basic history of Mirror symmetry from the viewpoint of physical strings (non-topological twisted superstrings), but including the Mirror symmetry for Landua-Ginzburg model. His resume on the formal website is not complete, but will include the homological mirror symmetry. The audience's question was whether there is a physical interpretation of Deligne-Mumford compactification and he answered that "To be honest, I do not know it but it works. And other physicists may say another thing." Maybe T.Eguchi once said in the lunch seminar that it was related to the worldsheet instantons, but I am not confident.

For the afternoon session, I heard the talked by Nakajima, Markman, and Donagi. Nakajima was on the works with Yoshioka in K-theoretical interpretation of Donaldson theory (rather than homological theoretic) and rigorous treatment of the work of Nekasov. Markman started from the Mukai paring and Mukai vectors on K3 surfaces, and the work of Yoshioka. We can attach to each orthogonal complementary space of Mukai vector (with some conditions), a monodromy invariant related to a (weighted) Hodge structure / Hodge isometry. The theorem states on the functor Mon: \cal{G}(groupoind) \to Algebras, which consists of two groupoinds of deformation of surface and equivalence of derived categories. Donagi was on the recent work with Dijkgraaf et.al. on the "geometric transition and integrable systems". I was not sure whether he showed the large N duality as a categorical equivalence. Also I was inspired by the statement that the Mukai integrable system degenerates to the Hitchin system.

After a short supper with Okada, Iritani, and Shimizu, we had the reception at the veranda of Hagget Hall at 7-9 pm, where I talked to Iritani, Okada, Lotte, Ben-Zvi, and Donagi. Afterwards I went to the same Indian restaurant as I ate with Bryan et.al last week. It was 11 pm when I came back to the doom and I wrote some abstract mail to the "informal semiar" in some of GSWW members.

Monday, July 25, 2005

Encounter with Japanese participants -- registration of Seattle'05

After the breakfast and before 9 am, I had to check-in and check-out to another room because the GSWW and the Seattle'05 are organized by different people.

My current room is in the same block as other two Japanese people including Yuji Shimizu. I first talked to him in English but he found out that we both are Japanese. We three left the McMahon during the bed making time, and with another graduate student Okada went to the Student Union, the Mechanical Engineering Buindling (where the registartion will take place in 5-9pm), and the Univeristy Way. In addition to the lunch at the same Thai restrant as Okada and I ate last week, we went to the University Bookstore, the drug store, and the convinient store.
We have a nice scenary of Elliot Bay from the veranda and the "famous" bridge is especially beautiful.

After the registration, where I revised "Makota Sakurai" to "Makoto Sakurai", we met many Japanese teachers including Kawamata and Nakajima. We (9 people) took dinner at the downstairs of McMahon and I saw Iritani there.

Sunday, July 24, 2005

Weekend trip to downtown (temporary update)

Today we (Peter, Okada and I) went to the down-town by bus (line 71-73) because the Seattle Mariners does not have home games until next Monday. The first visit was the book-store where I bought a map and "Guns, germs, and steel". Then we went to the farmers' market. I again bought a mug-cup. There was the Elliot Bay (with many seagulls) close to the market place and so that we went there and take some pictures.














It was about 3.40 and we decided to go back to the University because we got tired. Here is the picture of Seattle City although we didn't go to the Space Needle nor saw the famous beautiful night spot.
















We went strait to the Spike Street through a garden and there was the moving object in front of the Seattle Museum (linked in the below photo).

Saturday, July 23, 2005

5th day of GSWW

Morning lectures were Geometric Langlands (Ben-Zvi): "Algebraic geometer's harmonic analysis" or "Fourier transformation between Schwartz distributions", Rational points (Hassett), and combinational positivity (Miller).

Afternoon session was a review work on the pseudo-modular form of Bryan-Leung on the blow-ups of CP^2. This is the continuation of the group work of yesterday; division into the each nodal fibration, multiplication counting, and the Cremona relation, and the Russian notation of Young tableau. It was similar to the Hilbert scheme for K3 surface and instanton calculus, but I was not sure about the direct relation between them.

After the reception, we went to a Indian restaurant with Bryan and Miller et.al. I said to Bryan that Ooguri cited Bryan-Pandharipande at the Strings 2005.

Friday, July 22, 2005

4th day of GSWW


We started from the homework on the large quantum cohomlogy for CP^2, Goettsche-Pandharipande, and the Kontsevich formula. Then we studied 2 intersection generic cubics F_0 and F_1 which define a linear combinationF=s F_0 + t F_1 and this pencil therefore introduce an elliptic fibration. The canonical class for "del Pezzo 9" is -K_X = 3H-E_1-...-E_9 which has 12 nodal curve fibration over the exceptional divisor E_9.


Then we moved on to the classification of the components consisting of \beta = S + bF. This is essentially a study on the universal covering space (or multiplication and orientation) or a nodal curve fibration.

Thursday, July 21, 2005

3rd day of GSWW



Morning lessons were interesting, which consists of Roth (Hilbert schemes: decomposition of Hilbert polynomials), Mantovan (Langlands' and Shimura's abelian varieties) , and Mckernan (Birational classification of surfaces: Mori cone and minimal model programme). The last one was done by Red Hat slides so that I could not take notes sufficiently. At the coffee break in the morning session, we took a photo.

At the workgroup time, we difined small / large quantum cohomolgy as well as Gromov-Witten invariants (virtual fundamental class) although we did not do the virtual localization yet. Actually we did the divisor equation, the point axiom, the splitting axiom, and the associativity (Witten-Dijkgraaf-Verlinde-Verlinde eq.), but we have not yet done the proof of the associativity by potential (partition function), which is a homework in the case X=CP^2.

Those who once did the closed GW for CP^n worked on the small quantum cohomology ring for del Pezzo surfaces, which I suggested to do because it is related to the work of Orlov el.al. / Ueda on the mirror symmety for del Pezzo surfaces. I printed the classic works of Goettsche-Pandharipande and Eguchi-Hori-Xiong during the coffee break. I have to check up some definitions like flatness bacause I learned them long time ago and do not remember well.

Wednesday, July 20, 2005

2nd day of GSWW











I had the morning lectures of Garber(stacks), Donagi(hetetoric standard model), and Gibuey(moduli space). I went to the math library to confirm something about champs algebraique (Laumon) and Langlands program(Asterisque).

At the workgroup, we had some explicit homological calculations with moduli space of stable curves. I went to a Japanese-Korean restrant for dinner, but it was not so delicious. There was a music concert outside another hall when I return back to the McMahon.

Tuesday, July 19, 2005

1st day of GSWW

I waked up at 6 am and took the breakfast using my pre-paid card. My work group will be group C (Bryan) for one week, which will talk about closed / open Gromov-Witten invariants in the A-model side in the Savery Hall.

However, before that, we had three elementary lectures by Allocok (Chevalley groups), Jim Bryan (algebro-geometry and physics), and Mustata (motivic integration of Kontsevich, Denef-Loeser) in the same building. I could not use my wireless LAN card at the lecture room because it demands the student ID. The lecture of Bryan was almost what I studied until last summer. And there were some handouts.


I went the general library and the communication center for photo copy cards and printing papers. I also went to the math library, but it was closed (opens during 9 - 17 pm).

Afterwards, I went to the University Way (the Ave) again for supper and I spent about 2 hours for reviewing today's lectures. I look forward to seeing the library for some literature.

Monday, July 18, 2005

Reception of GSWW at McMahon Hall


I left Toronto early around 5 pm -- the weather was terrible and I was saturate with the rain. I took the shuttle bus in stead of TTC because one of my friends recommended me to do so.

After two short flights, I arrived at Seattle. The security was not tight. In deed, there was no checks at the buggage claim. Rather, there was a internal train from the flight gate to the outside.

We have a short (30-40 minutes) drive from Seattle to the University of Washington. I will visit in the McMahon Hall for the next one month. The scenary is beautiful and the air is clean -- more "transparent" than Toronto.

Then we had a reception from 6 to 8 pm. We have non-alcoholic drinks with some cheese. I talked to Bryan and Lotte and went with a Japanese participant to a Thai restaurant. I didn't know it but my room mate came late at night.

Saturday, July 16, 2005

6th day of Strings 2005



Shoke Sen: "Entropy is the legendgre transform of Lagrangian density". Yau wrote on the transparency during the presentation.

After the presentation, we went to the CN (Canadian National) tower: 553 m tall, until 4 pm and then to the Starbucks for tea. It was with other three students in the U.S. Click the photo above for the movie of elevator.

5th day of Strings 2005


Today was on matrix models, which included the talk of Takayanagi. The formal website of Strings 2005 is preparing to upload the audio and slide files.

At noon, there was an entertainment by several participants of strings 2005. It was like street music -- singing "Strings 2005", and somebody started to throw coins to the guitar case. It was amusing. Then we went with A.Sen et.al. to a Chinese restraurant for lunch, but it was 1 pm when we started to eat, so that we had to hurry to come back to the auditorium.

After 4 pm, I had to clean up my poster at the hall. I sent my poster to Japan at the postoffice in the student office. After that , I went to the mathematics library to confirm something about the central extension of loop groups in the Hitchin systems. However, it was already closed. After that, I went with my laboratory members to "little Italy" for dinner, whose name was Amsterdam (why?).

Thursday, July 14, 2005

4th day of Strings 2005


Beisert talked about spin chains (integrable systems) viewpoints on gauge theory. Their story of spin chains are not directly related to Hitchin's 2D integrable systems -- Riemann-Hilbert problem on monodromy algebra and Serre relations for perturbative bi-local generators (pure spinors). Why not Beilinson-Drinfeld and Hitchin systems? Is there any relation among them?

Maldacena was on free fermions, but it was again not the chiral algebra. Sugimoto was on the QCD string / SUGRA analysis (AdS/CFT) on the prediction of particle masses.

Anyway, we had the reception and banquet at the Chestnut. There were many famous people and I could not recognize all of them. I must have been rude to them. Dijkgraaf and Mukhi et.al. delivered nice speeches at the end of party.

3rd day of Strings 2005


Douglas talked about something like landscape with flux background from phenomenological and algebro-geometrical viewpoints, but his font was too small. How do you count moduli? Are there something like Weil-Peterson metrics?

Bena was on geometric transitions etc starting from Mathur's principle. Three charges Black ring was discussed from the M2/M5 viewpoint and resolved singularities. Dual cycles are essential for geometric transitions (flux instead of branes).

Kapustin was not on chiral de Rham complex or even strings. It was gauge theories starting from 2d Ising models, topological disorder parameters, then loop groups and Langlands dual groups in connection with magnetic fields ("magnetic dual" of Wilson loops), S-duality, and well-defined subgroup of elliptic full modular groups. His talk was interesting, but there were no questions from audience.

Hanany had a good slide with big fonts although several ones were illegible because of encoding. He was on D3 probe on singular Calabi-Yau target space, del Pezzo 3, conifolds and so on.

Then we went to the recursion of Niagara Falls. It took us 2 hours each to go from Toronto (North of Ontario lake) to the Niagara fall (South of Ontario). We were at the same bus and ship as Witten.

Link
On the left, there is a link to a short movie of Niagara fall.

















There is also another exiting movie linkLink corresponding to the left photo.







There was an accident when we went to dinner at Niagara. Suddenly strong wind blew and some glass cups were blew and flew close to one of my colleagues.

2nd day of Strings 2005

I am not sure why Vafa cancelled this conference yesterday.

Today's talks started from Denef on the Landscape and the cosmological constant problem. String phenomenology is popular this year, which was one of the main topics at the panel discussion.

Anyway, the laptop of Witten worked very badly, and we were interrupted by some computer errors. His talk was on the m_u = 0 / Axion (symmetry preserving / breaking phase) scenario starting from the strong CP problem. After his talk, there was an applaud.

Arkani-Hamed was eloquent on our current status of LHC physics. He said the worst scenario is "nothing but Higgs bosons at LHC".

OK. Again from the panel discussion. "Why is string theory worth trying even today?" (It was phrased in a different way.) Some said "it is mathematically beautiful but phenomenologically poor" and some said "it is the only known consistent theory of gravity" (how do you prove its consistency?). My viewpoint is not equal to them. What do you think?

Tuesday, July 12, 2005

1st day of Strings 2005



I waked up at 5 am and walked along to the seeshore and found out the College street -- there was another Seven-Eleven. The New College Inn does not have many facilities but we have many colleagues and good natural environments here.



After the breakfast, I brought my baggages with the poster to the Medical Science Building. Again, a lady talked to me on the street and I showed her my map; she said she has been to this building long time ago.

OK, the right picture is the main buildings for the poster presentation with another auditorium building next to it. The left one is the monument there. There was also a beautiful old residence on the circle.












The talks begin from the Dean of the school, then Ooguri about topological strings from the past, the present, to the future on the "definition of topological string theory". Today's talks were mainly on 2d YM and stringy cosmology.

There were not so many people in the poster session booth -- about 50 posters there and audience seems to pay little attention to individual presentation. There was little time for me to take care of my poster at noon because I went to two computer shops for a French-Canadian keyboard and the Cirrus ATM on the Bloor Street; it was after the lunch with 8 Japanese acquaintances at a Chinese restaurant. I also have to configure my wireless LAN (WG111 of NETGEAR), but this may be another story.

Arrived at the Fields Institute -- Wilson Hall




I arrived at the New College Inn at about 8 pm -- a residence in the University of Toronto.

A kind old lady, who said that she worked in the university hospital, helped me to transfer from the subway to the street bus. I should have read my guide book carefully.

There are many Asian people. For example. a taiwanian woman gave me a detailed map of the subway. Mr S. of my laboratory also informed me that I misundersttod the conference hall. It was not the Fields Institute (where I have to register at 8.30 am tomorrow) but the Medical Sciences Auditorium.

Anyway, I got close to the Fields Institute; I mean, to the Seven-Eleven on the College Street. And now I am cooking my dryed rice and coffee by boiled water. So maybe I can manage to survive in this environment.

Sunday, July 10, 2005

This is what Movable Type 3 supplies

Start the web-log for the travel


Dear all;

I start the web-log for the travel for one month. Now I prepare for the suitcase as well as the poster presentation at the Fields Institute in the Strings 2005. I hope you'll enjoy this page.

The picture is where I stayed at Trieste in Italy. It was March before I presented the 2d / 7d Hitchin systems at the JPS.