CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Professor Antun Milas, RPI 

Time:          Wednesday, October 8, at 4:30pm 

Place:         Earth Sciences Bldg. Room 152A, Univ. at Albany 

Title:         Modular Forms, Partitions and Conformal Field Theory 
 


Abstract:

There is a long history of interest in the theory of partitions.
The first discoveries in this theory were made by Euler in the 18th
century who studied combinatorial identities by using generating
functions (or infinite q--series) for partitions. It turns out that many
generating functions exhibit modular properties and this fact links them
with the theory of modular forms and modern number theory.

Independently, by using ideas from the theory of infinite-dimensional  
Lie algebras Macdonald reinterpreted many properties of q-series
and combinatorial identities in a completely new fashion. However,
Macdonald's work did not explain why certain q--series associated
to representations of infinite-dimensional Lie algebras exhibit modular
properties. Surprisingly, the answer to this question came from physics
(more precisely from string theory and conformal field theory).

In the first part of my talk I will give a friendly introduction to
the theory of partitions, explain what is the Dedekind eta function
and briefly explain notions such as modular invariance, modularity, etc.
In the second part I shall explain (at least in informal way) why the
conformal field theory provides understanding of the mysterious
relationship between representation theory of infinite-dimensional Lie
algebra and modular forms. I will finish with a few applications
based on my recent work.


Refreshments at 4:15 pm in ES 152.