Department of

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for events the day of Friday, May 6, 2022.

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Friday, May 6, 2022

3:00 pm in 341 Altgeld Hall,Friday, May 6, 2022

Calculus for Algebraic Topologists

Johnson Tan (UIUC Math)

Abstract: Early on in our mathematical studies, we learn that instead of studying a problem directly it is useful to study a linearization of the problem. For example, to understand a smooth map between manifolds we can look at the resulting linear map between the tangent spaces at a point. In this talk we will be looking at a categorification of this idea through the lens of Goodwillie Calculus. In particular, given a map between sufficiently nice infinity categories we will define what it means for such a map to be "linear" and furthermore how one can approximate by such maps. Time permitting, we will explore further generalizations of this idea.