Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, March 6, 2019.

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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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Wednesday, March 6, 2019

3:00 pm in 2 Illini Hall,Wednesday, March 6, 2019

#### Abelian Varieties in Positive Characteristic

###### Ravi Donepudi (Illinois Math)

Abstract: This talk will be an introduction to the theory of abelian varieties over fields of positive characteristic. The presence of the non-separable Frobenius automorphism in this context gives the theory a flavor entirely different from over the complex numbers. An important question in this area is to characterize which abelian varieties (with extra data) arise as Jacobians of smooth curves. Much of the progress on this problem has been through studying some stratifications of moduli spaces of abelian varieties. We will introduce these moduli spaces and stratifications, and survey interesting results in this area.

3:00 pm in 243 Altgeld Hall,Wednesday, March 6, 2019

#### To Be Announced

###### Ben Vega Westhoff (University of Illinois, Atmospheric Sciences)

3:00 pm in 341 Altgeld Hall,Wednesday, March 6, 2019

#### Abstract systems of congruences

###### Spencer Unger (Tel Aviv University)

Abstract: Abstract systems of congruences provide a different perspective for viewing geometrical paradoxes from the early 20th century. Consider partitioning a space into $n$ pieces $A_1, A_2, \dots, A_n$. An abstract system of congruences is a collection of statements (called congruences), like $A_2 \cup A_6$ is isometric to $A_{17}$. Such a system is satisfied by a particular partition if each congruence is satisfied. We survey some recent results and some open problems.