Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, March 1, 2018.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, March 1, 2018

11:00 am in 241 Altgeld Hall,Thursday, March 1, 2018

#### Monotonicity properties of L-functions

###### Paulina Koutsaki (University of Illinois)

Abstract: In this talk, we discuss some monotonicity results for a class of Dirichlet series. The fact that $\zeta'(s)$ is in that class presents a first example of an arithmetic function for which the associated Dirichlet series is completely monotonic, but not logarithmically completely monotonic. Moreover, we will see how our methods give rise to another formulation of the Riemann Hypothesis for the L-function associated to the Ramanujan-tau function. Based on joint work with S. Chaubey and A. Zaharescu.

2:00 pm in 241 Altgeld Hall,Thursday, March 1, 2018

#### Spectral Theory on the Modular Surface

###### Hadrian Quan   [email] (UIUC)

Abstract: Many questions about number fields can be recast as questions regarding Laplace eigenvalues on certain manifolds. In this talk I’ll discuss some ideas and results related to Selberg’s trace formula, how partial results towards Selberg’s $\frac{1}{4}$-conjecture have immediate applications, and why number theorists might care about the analysis of Laplacians to begin with.

3:00 pm in 2 Illini Hall,Thursday, March 1, 2018

#### Subword Complexes, Alternating Sign Matrices, and Prism Tableaux

###### Anna Weigandt (UIUC)

Abstract: Subword complexes were introduced by A. Knutson and E. Miller to study Schubert polynomials. The pipe dream formula for Schubert polynomials has a natural interpretation as a sum over the facets of a subword complex. In this talk, we will discuss a generalization of subword complexes, defined by alternating sign matrices (ASMs). The geometry of these complexes is governed by the poset structure of ASMs. Prism tableaux were introduced in joint work with A. Yong to study Schubert polynomials. There is a map from prism tableaux of a fixed shape to a generalized subword complex. Restricting to a distinguished set of prism tableaux produces a bijection with the top dimensional facets of this complex.