Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 23, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, October 23, 2020

4:00 pm in Zoom (email ruiyuan at illinois for info),Friday, October 23, 2020

#### On the Pila-Wilkie Theorem

###### Neer Bhardwaj (UIUC Math)

Abstract: We prove Pila and Wilkie’s Counting theorem, following the original paper, but exploit cell decomposition more thoroughly to simplify the deduction from its main ingredients. Our approach in particular completely avoids ‘regular’ or $C^1$ smooth points, and related technology; which also allows simplifications around Pila’s ‘block family’ refinement of the result.

4:00 pm in Altgeld Hall,Friday, October 23, 2020

#### Index theory through loop spaces

###### Gayana Jayasinghe

Abstract: I'll present some ideas in Atiyahs paper, "Circular symmetry and stationary phase approximation", where he goes through Wittens argument for a proof of the Index theorem by applying the Duistermaat-Heckman formula on loop spaces.