#
Geometric perspectives in mathematical quantum field theory

April 8 to April 12, 2013
at the

American Institute of Mathematics,
San Jose, California

organized by

Ambar Sengupta and Jonathan Weitsman

## Original Announcement

This workshop will be devoted to
mathematical challenges in quantum field theory.
In the late 1980's, just as classical constructive quantum field theory, with its goal of understanding the mathematics underlying modern physics, was reaching this peak, intuitive but non-mathematical functional integral methods originating in physics assumed, through the work of quantum field theorists led by Witten, an increasing importance in geometry, topology, and other areas of mathematics. Results obtained in ths way could
often be stated as mathematically precise conjectures, and often rigorously proved as theorems, giving rise to entirely new and unexpected ideas and even
entirely new fields of mathematics. Nevertheless,
the mathematics underlying Witten's methods was not generally
amenable to classical methods of constructive quantum field theory, or, for that matter, to any currently known form of mathematical analysis.
As a pseudo-historical analogy one
might imagine a page of exercises from a calculus book drifting into an ancient Greek academy. The results on this page could be stated and
verified by geometric methods; underlying them would be undiscovered ideas which made these results into mere exercises.
We are similarly in the presence of a gift from fairyland whose nature we have not been able to comprehend; even reasonable conjectures would be a very
valuable contribution.

The main focus of the mathematics community during this era has been on
independent development of the many mathematical fields arising
from Physics. Nevertheless, many workers in various areas have tried
over the years various approaches to understanding the mathematics underlying
quantum field theory, and later, string theory. The purpose of this
conference is to bring together the multivariegated group of workers
in this field and to create an opportunity for them to learn of others'
approaches and build on them.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

### Notes from workshop discussions

Wednesday afternoon discussion
Thursday afternoon discussion

Handwritten notes from
D. Pickrell's discussion

Papers arising from the workshop: