Department of

Mathematics


Seminar Calendar
for events the day of Thursday, October 24, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, October 24, 2019

11:00 am in 241 Altgeld Hall,Thursday, October 24, 2019

Non-vanishing of Dirichlet L-functions

Rizwanur Khan (University of Mississippi)

Abstract: $L$-functions are fundamental objects in number theory. At the central point $s = 1/2$, an $L$-function $L(s)$ is expected to vanish only if there is some deep arithmetic reason for it to do so (such as in the Birch and Swinnerton-Dyer conjecture), or if its functional equation specialized to $s = 1/2$ implies that it must. Thus when the central value of an $L$-function is not a "special value", and when it does not vanish for trivial reasons, it is conjectured to be nonzero. In general it is very difficult to prove such non-vanishing conjectures. For example, nobody knows how to prove that $L(1/2, \chi)$ is nonzero for all primitive Dirichlet characters $\chi$. In such situations, analytic number theorists would like to prove 100% non-vanishing in the sense of density, but achieving any positive percentage is still valuable and can have important applications. In this talk, I will discuss work on establishing such positive proportions of non-vanishing for Dirichlet $L$-functions.

1:00 pm in 464 Loomis Laboratory,Thursday, October 24, 2019

Simple holographic models of black hole evaporation

Chris Akers (Berkeley Physics)

Abstract: Several recent papers have shown a close relationship between entanglement wedge reconstruction and the unitarity of black hole evaporation in AdS/CFT. The analysis of these papers however has a rather puzzling feature: all calculations are done using bulk dynamics which are essentially those Hawking used to predict information loss, but applying ideas from entanglement wedge reconstruction seems to suggest a Page curve which is consistent with information conservation. In this note we present a new pair of models which clarify this situation. Our first model gives a holographic illustration of unitary black hole evaporation, in which the analogue of the Hawking radiation purifies itself as expected, and this purification is reproduced by the entanglement wedge analysis. Moreover a smooth black hole interior persists until the last stages the evaporation process. Our second model gives an alternative holographic interpretation of the situation where the bulk evolution leads to information loss: unlike in the models proposed so far, this bulk information loss is correctly reproduced by the entanglement wedge analysis. In both models no bulk quantum corrections need to be considered: classical extremal surfaces are enough to do the job. We argue that our first model is a better analogy for what actually happens to evaporating black holes, but we also emphasize that any complete resolution of the information problem will require an understanding of non-perturbative bulk dynamics.

2:00 pm in 347 Altgeld Hall,Thursday, October 24, 2019

Branching Processes Part 2

Peixue Wu (UIUC Math)

Abstract: The first part of this talk is very introductory, I will talk about the basic ideas of branching mechanism (originated from random walk) and some generalizations of the simple branching process, e.g., age-dependent processes, multi-type branching process. ​I will focus on the limit theorem of branching processes.​ ​In the second part, I will talk about the superprocess (which is measure-valued branching processes) and some recent works about it.

3:00 pm in 347 Altgeld Hall,Thursday, October 24, 2019

Some algebraic combinatorics arising in CR Geometry

John P. D'Angelo   [email] (University of Illinois at Urbana-Champaign )

Abstract: We will define and discuss infinitely many triangles of integers that share many properties with Pascalís triangle. The rows correspond to coefficients of invariant polynomials arising in CR geometry. One special case yields polynomials $f_{p,q}(x,y)$ that satisfy $f_{p,q}(x,y)$ is congruent to $x^p + y^p$ mod $(p)$ if and only if $p$ is prime or $p=1$. The talk will be accessible to beginning graduate students but will glimpse research directions.

4:00 pm in 245 Altgeld Hall,Thursday, October 24, 2019

Disability Allyship and DRES Information

Rachel Jackson Green (University of Illinois Disability Resources and Educational Services (DRES))

Abstract: This workshop is meant for all faculty and TAs - everyone who teaches courses in the Mathematics Department. Rachel Jackson Green will discuss disability allyship as it pertains to instruction. She will cover both the logistics of DRES accommodations for students as well as ways to make instruction as accessible as possible for all students, whether they are using DRES accommodations or not.