Department of

Mathematics


Seminar Calendar
for events the day of Friday, November 17, 2017.

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     October 2017          November 2017          December 2017    
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  1  2  3  4  5  6  7             1  2  3  4                   1  2
  8  9 10 11 12 13 14    5  6  7  8  9 10 11    3  4  5  6  7  8  9
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Friday, November 17, 2017

4:00 pm in 345 Altgeld Hall,Friday, November 17, 2017

Canceled

4:00 pm in 241 Altgeld Hall,Friday, November 17, 2017

Riemannian Popcorn, the Heat Kernel in Geometric Analysis

Aubrey Laskowski (UIUC)

Abstract: The heat kernel is the fundamental solution to the heat equation $(\partial_t-\Delta)u=0$ on a specified domain. The heat equation has shown up in geometry in unexpected ways, such as in a proof of the Atiyah-Singer index theorem. Varadhan and Norris each provided asymptotic relationships between the heat kernel and the Riemannian distance function. We will be discussing these results among others at a high level, without in-depth proofs. If time allows, we will discuss the natural connections of the heat kernel to probability theory. Some background in analysis will be useful, but not necessary.