Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 28, 2017.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2017           September 2017          October 2017
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1  2  3  4  5                   1  2    1  2  3  4  5  6  7
6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
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Thursday, September 28, 2017

11:00 am in 241 Altgeld Hall,Thursday, September 28, 2017

#### Equations of hyperelliptic Shimura curves

###### Yifan Yang (National Chiao Tung University)

Abstract: Because of the lack of cusps on Shimura curves, there are few methods to construct modular forms on them. As a result, it is very difficult to determine equations of Shimura curves. In a recent work, we devised a systematic method to construct Borcherds form. Together with Schofer's formula for values of Borcherds forms at CM-points, this enabled us to determine equations of all hyperelliptic Shimura curves. This is a joint work with Jia-Wei Guo.

12:00 pm in 243 Altgeld Hall,Thursday, September 28, 2017

#### Effective Twisted Conjugacy Separability of Nilpotent Groups

###### Mark Pengitore (Purdue Math)

Abstract: There has been a recent interest in providing effective proofs of separability properties such as residual finiteness and conjugacy separability. Unlike residual finiteness, conjugacy separability does not respect finite extensions. Thus, we introduce twisted conjugacy separability, originally defined by Fel'shtyn, in order to study effective conjugacy separability of finite extensions of conjugacy separable groups. In joint work with Jonas Dere, we provide an effective proof of twisted conjugacy separability of finitely generated nilpotent groups. That, in turn, provides an effective bound for conjugacy separability of all finite extensions of a fixed nilpotent group in terms of the asymptotic behavior of conjugacy separability of the base nilpotent group.

12:30 pm in 222 Loomis,Thursday, September 28, 2017

#### Conformal field theories and three point functions

###### Subham Dutta Chowdhury (Indian Institute of Science, Bangalore)

Abstract: Conformal invariance allows additional unique parity-odd tensor-structures for three-point functions involving the stress tensor, T, and a conserved U(1) current, j, in 2+1 dimensional conformal field theories that violate parity, apart from the usual parity even structures. Following the conformal collider physics setup of Hofman and Maldacena, we put constraints on the parity violating as well as parity preserving parameters of a general CFT in d=3. We find that large N Chern-Simons theories coupled to a fundamental fermion/boson saturate the bounds that we have derived. An application of the conformal collider bounds is observed in the form of sum rules which puts constraints on spectral densities of any CFT at finite temperature. We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general $d\geq 3$ dimensions. We show that the sum rule can be written in terms the parity even Hofman-Maldacena variables $t_2$, $t_4$ which determine the three point function of the stress tensor. We then use collider constraints and obtain bounds on the sum rule which are valid in any CFT.

2:00 pm in 241 Altgeld Hall,Thursday, September 28, 2017

#### Extreme values of zeta and $L$-functions

###### Siegfred Baluyot (UIUC)

Abstract: One of the most important problems in the theory of the Riemann zeta-function is to determine how large the modulus of zeta can be on the critical line. In this talk, we will first outline the history of this problem. Then we will discuss the versatile `resonance method' of Soundararajan for detecting large values of zeta and other $L$-functions. We then complete our discussion with the recent breakthrough of Bondarenko and Seip that significantly improves the resonance method for zeta by using estimates for greatest common divisor sums.

3:00 pm in 345 Altgeld Hall,Thursday, September 28, 2017

#### W-Operators and Combinatorial Hurwitz Numbers

###### Hao Sun (University of Illinois)

Abstract: We will introduce the W-operator and show some interesting combinatorial properties about the W-operator. Then, we will show how the W-operator relates to the study of combinatorial Hurwitz numbers.

4:00 pm in 245 Altgeld Hall,Thursday, September 28, 2017

#### Fall Department Faculty Meeting

Abstract: The Fall Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception in 239 Altgeld Hall.