Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, November 19, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, November 19, 2015

11:00 am in 241 Altgeld Hall,Thursday, November 19, 2015

#### Recent progress on extreme central values of $L$-functions

###### Bob Hough (IAS)

Abstract: Soundararajan's resonance method is a first moment method for demonstrating the existence of large central values of $L$-functions within natural families. In recent work I have supplemented the resonance method to study the angle distribution of the large values found. Also, recent work of Bondarenko and Seip has introduced a new combinatorial argument which strengthens the estimate obtained for extreme values of the Riemann zeta function on the half line. I will describe some of the new ideas in these arguments.

1:00 pm in 243 Altgeld Hall,Thursday, November 19, 2015

#### Fibrations, subsurfaces and triangulations

###### Yair Minsky (Yale University)

Abstract: When a hyperbolic 3-manifold fibers over the circle, the stable/unstable laminations of its monodromy map give us a model for its geometric structure. The features of this model are determined by the projections of these laminations into arc complexes of subsurfaces of the fiber. The quality of this model depends on the topological type of the fiber, and we do not have a good global understanding of how this structure behaves for arbitrary fibrations. As a kind of laboratory for testing such questions we consider the (typically infinitely many) different ways that a given 3-manifold can fiber over the circle, as organized by Thurston's norm. It turns out that, using Agol's veering triangulations, we can obtain some more precise answers. This is joint work with Sam Taylor.

1:00 pm in 167 Everitt Lab,Thursday, November 19, 2015

#### Non-archimedean abelian Polish groups and their actions

###### Su Gao (University of North Texas)

Abstract: Non-archimedean abelian Polish groups are precisely closed subgroups of countable products of countable discrete abelian groups. In this talk I will give some characterizations of such groups which are tame, i.e., whose orbit equivalence relations are always Borel. These are generalizations of a result of Solecki. We also consider orbit equivalence relations generated by non-archimedean abelian Polish groups in the Borel reducibility hierarchy and give some upper bounds for the actions of tame groups and locally compact groups.

2:00 pm in 347 Altgeld Hall,Thursday, November 19, 2015

#### Representability of Algebraic Vector Bundles in the $\mathbb A^1$ Homotopy Category

###### Daniel Carmody   [email] (UIUC Math)

Abstract: I'll begin by reviewing results about representability of topological vector bundles and recalling some typical applications of representability. Then I'll state the representability theorem of Asok, Hoyois, and Wendt and describe some applications analogous to those in the topological setting. I'll end by sketching a proof of the theorem.

2:00 pm in 241 Altgeld Hall,Thursday, November 19, 2015

#### On certain methods for finding higher degree L-functions

###### Patrick Kuehn (University of Zurich)

Abstract: L-functions are analytic functions connected to certain mathematical objects, and they usually have many applications to number theory, mathematical physics and cryptography. By an L-function, we generally mean a Dirichlet series with a functional equation and an Euler product. In this talk I will describe a method to recover numerically the Dirichlet coefficients of a general L-function of degree d up to a certain precision. This method will be used to implement an algorithm that “scans” new, primitive L-functions on the space of the spectral parameters of dimension d-1.

3:00 pm in 243 Altgeld Hall,Thursday, November 19, 2015

#### Hilbert functions and minimal free resolutions for sets of points in $\mathbb{P}^1\times \mathbb{P}^1$

###### Eliana Duarte (UIUC Math)

Abstract: In the 90’s, Giuffrida, Maggioni and Ragusa (GMR) classified arithmetically Cohen-Macaulay (aCM) sets of points in $\mathbb{P}^1\times \mathbb{P}^1$. These are points whose distribution on the rulings of $\mathbb{P}^1\times \mathbb{P}^1$ determines their bigraded Hilbert function and minimal free resolution. In recent years progress has been made to understand sets of points in $\mathbb{P}^1\times \mathbb{P}^1$ which are not aCM but the picture is far from being complete. In this talk I will present the classification of aCM sets of points due to GMR and some recent results by L. Marino for more general configurations of points.

3:00 pm in 259 Altgeld Hall (DGS office),Thursday, November 19, 2015

#### Résumé feedback: drop-in session

###### Jennifer Kim (UIUC Graduate Career Development)

Abstract: Drop in between 3:00 and 4:30pm with your résumé, and get feedback and advice. Also, you can ask questions about careers in business, industry and government (BIG).

4:00 pm in 245 Altgeld Hall,Thursday, November 19, 2015

#### Skinning maps and gluing problems for hyperbolic 3-manifolds

###### Yair Minsky (Yale)

Abstract: In the 1970's Bill Thurston introduced a number of geometric and analytical tools for studying hyperbolic structures on 3-manifolds, and the ways in which these structures can be deformed and fitted together. Among these is his Skinning Map, a holomorphic map of Teichmuller spaces induced by the relationship between a hyperbolic 3-manifold and the covering spaces associated to its boundary. The properties of this map remain fascinating, and are relevant to improving our quantitative understanding of the interaction between topology and geometry in 3 dimensions. We will sketch some of this story, some open questions, some answers, and some work in progress.