Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, May 2, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
April 2019              May 2019              June 2019
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1  2  3  4  5  6             1  2  3  4                      1
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30

Thursday, May 2, 2019

11:00 am in 241 Altgeld Hall,Thursday, May 2, 2019

#### The Distribution of log ζ(s) Near the Zeros of ζ

###### Fatma Cicek (Rochester Math)

2:00 pm in 147 Altgeld Hall,Thursday, May 2, 2019

#### Supnorm estimates for $\bar\partial$ in $\mathbb{C}^n$

###### Martino Fassina (Illinois Math)

Abstract: Let $\Omega$ be a domain in $\mathbb{C}^n$ and $f$ a $\bar\partial$-closed form on $\Omega$. A fundamental question in complex analysis is to establish the existence of solutions to the inhomogeneous Cauchy-Riemann equations $\bar\partial u=f$ that satisfy a norm estimate in $\Omega$. Whether such solutions exist depends both on the geometry of $\Omega$ and the regularity of $f$. In this talk, we consider the case where $\Omega$ is a polydisc. We establish the existence of weak solutions to $\bar\partial$ satisfying an $L^{\infty}$ estimate on $\Omega$ whenever the datum $f$ is in $L^{\infty}(\Omega)$, thus answering an old question of Kerzman and Stein. The talk is based on joint work with Yifei Pan.

3:00 pm in 347 Altgeld Hall,Thursday, May 2, 2019

#### Cell Decompositions for Rank Two Quiver Grassmannians

###### Dylan Rupel (Michigan State University)

Abstract: The (partial) flag varieties are among the most well-understood geometric objects. Essential to this understanding are the Schubert decompositions of these varieties. In this talk, I will recall two constructions of the Schubert decompositions of ordinary vector subspace Grassmannians and explain how analogues of these constructions combine to give rise to cell decompositions for Grassmannians of subrepresentations in (truncated) preprojective representations of acyclic quivers with two vertices. Depending on time I will describe some of the combinatorics underlying this geometry and discuss open problems and conjectures. This is a report on joint work with Thorsten Weist.