Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, April 3, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, April 3, 2019

3:00 pm in 243 Altgeld Hall,Wednesday, April 3, 2019

#### To Be Announced

###### Alfredo Wetzel (University of Wisconsin-Madison, Mathematics)

3:00 pm in 2 Illini Hall,Wednesday, April 3, 2019

#### Intersection Theory II

###### Yidong Chen (Illinois Physics)

Abstract: In this talk, I'll follow chapter 2 of Fulton's book and talk about divisors, pseudo-divisors, and how to intersect with divisors. As an application, I'll discuss Chern class of line bundles. With time permitting, I'll move towards the definition of Chern class of vector bundles, but will most definitely leave the actual work to the next speaker.

3:00 pm in 341 Altgeld Hall,Wednesday, April 3, 2019

#### Hurewicz' theorem (1930) on uncountable sets — a variant approach

###### Robert Kaufman (UIUC Math)

Abstract: In the theorem below, $C(K)$ is the space of continuous functions on the Cantor space $K$ and $C^*(K) \subseteq C(K)$ is the set of functions with uncountable range.

Theorem. For any analytic set $A$ in a metric space $M$, there is a continuous map $\varphi$ of $M$ into $C(K)$ such that $\varphi^{-1}(C^*(K)) = A$.

The argument uses only classical analysis; an important role is played by the notion of ultrametric space. A few minutes will be devoted to the representation of analytic sets as "projective" sets.