Tuesday, October 09, 2012

Higgs Hunter

Last 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 Mixed anomalies of chiral algebras compactified to smooth quasi-projective surfaces and the slides uploaded at the researchmap database. 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.

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 the MSJ official website. 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.

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.

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.

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).

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.

In the good-old-days of Greek geometry, mathematicians can naively and Platonically quote "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.""

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".

I hope I can keep my trial on the recovery of academic value in the calculation-based financial society.