Special Physics & Math Department Combined Colloquium Today, March 8, 2012 at 4:30 pm in Cockins Hall, Room 240

[Tate, Arnay]

Please take note of Special Physics & Math Department Combined Colloquium taking place today, Thursday, March 6, 2012 at 4:30 PM in Cockins Hall, Room 240. Details concerning the talk are as follows:



Speaker:               David Morrison - University of California, Santa Barbara

Date:                     Thursday, March 6, 2012

Time:                    4:30 PM

Place:                    Cockins Hall, Room 240

Title:                     Riemann surfaces, conformal blocks, and supersymmetric quantum field theories: from Physics conjecture to Mathematics theorem

Abstract:


The work of Seiberg and Witten in the mid-1990's on a class of supersymmetric quantum field theories was important for both physics and mathematics.  In physics, it pointed the way to the study of non-perturbative aspects of a variety of quantum field theories and string theories, and led fairly directly to the so-called ``second superstring revolution'' of 1995.  In mathematics, the work had remarkable consequences for topology in four dimensions, leading to the rapid solution of many long-standing problems.

In 2009, Davide Gaiotto re-invigorated this area of physics with a new construction for these supersymmetric theories.  Gaiotto's construction is based on a punctured Riemann surface assembled out of   ``pair of pants'' pieces.  Soon afterwards, Alday, Gaiotto, and Tachikawa looked for a correspondence between Gaiotto's four-dimensional quantum field theories, and an older class of two-dimensional quantum field theories associated to punctured Riemann surfaces, in which the key physical ingredient is known as a ``conformal block.''  Their ``AGT conjecture'' specifies a precise relationship between those physical theories.

When translated into mathematics, the AGT conjecture becomes a statement about geometric representation theory.  That statement has now been proven, first by Maulik and Okounkov, with a second proof by Schiffmann and Vasserot.

The focus of talk will be on the interplay between physics and mathematics which led to these results.



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