Mathematics Seminar at ICTP - Monday, 21 November 2016, at 16:00

[Math Section]

M A T H E M A T I C S   S E M I N A R S  2016


Monday, 21 November, at 16.00 hrs.



Kiyokazu Nagatomo(Osaka University)


Title:
Curiosity at 164/5 and 236/7

Abstract:
I would not really like to tell you the meaning of the two rational 
numbers in the title, I would rather like to keep them mysterious until 
the occasion of my talk. However, I must give some ingredients of my 
talk, otherwise you might not come to the seminar, maybe.
One of the main ingredients is conformal field theories. As you may 
know, conformal field theories involve many mathematical aspects, for 
instance, vertex operator algebras, moduli spaces of algebraic curves, 
modular forms, linear differential equations with regular singularities, 
and so on. In my research on classifying rational conformal field 
theories, these two numbers appeared naturally. On my way to deal with 
these numbers, I needed the notion of modular tensor categories which 
include the concepts of quantum dimensions and global dimensions.
What I did, and will explain in this talk, is that I first find 
solutions of linear differential equations with regular singularities 
whose spaces of solutions are invariant under the slash 0 action, and 
get the exact form of S-matrices corresponding to the S-transformation. 
Then the theory of modular tensor categories allows us to compute 
quantum dimensions and then global dimensions. By contrast, the theory 
of vertex operator algebra gives us different global dimensions, which 
means such conformal field theories do not exist.
Because I use many mathematical tools including modular forms on the 
congruence groups (which you know very well), I decided to use slides to 
give you enough information and make the talk self-contained. In fact, 
every notion which appears in my talk will be explained. A prior 
knowledge is not required.



VENUE:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)