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for events the day of Thursday, September 12, 2019.

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Thursday, September 12, 2019

11:00 am in 241 Altgeld Hall,Thursday, September 12, 2019

Moments of half integral weight modular L–functions, bilinear forms and applications

Alexander Dunn (Illinois Math)

Abstract: Given a half-integral weight holomorphic newform $f$, we prove an asymptotic formula for the second moment of the twisted L-function over all primitive characters modulo a prime. In particular, we obtain a power saving error term and our result is unconditional; it does not rely on the Ramanujan-Petersson conjecture for the form $f$. This gives a very sharp Lindelöf on average result for L-series attached to Hecke eigenforms without an Euler product. The Lindelöf hypothesis for such series was originally conjectured by Hoffstein. In the course of the proof, one must treat a bilinear form in Salié sums. It turns out that such a bilinear form also has several arithmetic applications to equidistribution. These are a series of joint works with Zaharescu and Shparlinski-Zaharescu.

12:00 pm in 243 Altgeld Hall,Thursday, September 12, 2019

Weil-Petersson translation length and manifolds with many fibered fillings.

Chris Leininger (Illinois Math)

Abstract: In this talk, I will discuss joint work with Minsky, Souto, and Tayor in which we prove that any mapping torus of a pseudo-Anosov mapping class with bounded normalized Weil-Petersson (WP) translation length contains a finite set of “vertical and horizontal closed curves”, and drilling out this set of curves results in one of a finite number of cusped hyperbolic 3–manifolds (depending only on the normalized WP length bound). This echoes an earlier result, joint with Farb and Margalit, for the Teichmuller metric. We also prove new estimates for the WP translation length of compositions of pseudo-Anosov mapping classes and arbitrary powers of a Dehn twist.

1:00 pm in 464 Loomis,Thursday, September 12, 2019


Vishnu Jejjala (University of Witwatersrand)

Abstract: Identifying patterns in data enables us to formulate questions that can lead to exact results. Since many of the patterns are subtle, machine learning has emerged as a useful tool in discovering these relationships. We show that topological features of Calabi–Yau geometries are machine learnable. We indicate the broad applicability of our methods to existing large data sets by finding relations between knot invariants, in particular, the hyperbolic volume of the knot complement and the Jones polynomial.

2:00 pm in 347 Altgeld Hall,Thursday, September 12, 2019

Introduction to Random Planar Maps part 2

Grigory Terlov (UIUC Math)

Abstract: The main focus of the second part of this talk is to discuss bisections between random bipartite planar maps and decorated Galton Watson trees. Then if time permits we will continue connecting this model with other areas of probability that audience might be familiar with and/or interested in exploring.

4:00 pm in 245 Altgeld Hall,Thursday, September 12, 2019

Non-Smooth Harmonic Analysis

Palle Jorgensen   [email] (University of Iowa)

Abstract: While the framework of the talk covers a wider view of harmonic analysis on fractals, it begins with a construction by the author of explicit orthogonal Fourier expansions for certain fractals. It has since branched off several directions, each one dealing with aspect of the wider subject. The results presented cover (among other papers) joint work with Steen Pedersen, then later, with Dorin Dutkay. Fractals. Intuitively, it is surprising that any selfsimilar fractals in fact do admit orthogonal Fourier series. And our initial result generated surprised among members of the harmonic analysts community. The theme of Fourier series on Fractals has by now taken off in a number of diverse directions; e.g., (i) wavelets on fractals, or frames; (ii) non-commutative analysis on graph limits, to mention only two. Two popular question are: “What kind of fractals admit Fourier series?” “If they don’t, then what alternative harmonic analysis might be feasible?”