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<p class="MsoPlainText"><span style="font-size:11.0pt">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:<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:11.0pt">Speaker: David Morrison – University of California, Santa Barbara<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:11.0pt">Date: Thursday, March 6, 2012<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:11.0pt">Time: 4:30 PM<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:11.0pt">Place: Cockins Hall, Room 240<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:11.0pt">Title: Riemann surfaces, conformal blocks, and supersymmetric quantum field theories: from Physics conjecture to Mathematics theorem <o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:11.0pt">Abstract: <o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Georgia","serif"">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.<br>
<br>
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.<br>
<br>
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.<br>
<br>
The focus of talk will be on the interplay between physics and mathematics which led to these results.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Georgia","serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Georgia","serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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