Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, April 28, 2016.

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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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1  2  3  4  5                   1  2    1  2  3  4  5  6  7
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Thursday, April 28, 2016

11:00 am in 241 Altgeld Hall,Thursday, April 28, 2016

#### Effective equidistribution of horocycle lifts

Abstract: We give a rate in the problem of equidistribution of lifted horocycles in the space of unimodular two-dimensional lattice translates. The ineffective version is due to Elkies and McMullen and relies on Ratner's Theorem. The approach used here builds on recent works of Strombergsson and of Browning and the author.

12:00 pm in Altgeld Hall 243,Thursday, April 28, 2016

#### Induced group actions

###### Denis Osin (Vanderbilt University)

Abstract: I will discuss the following natural extension problem for group actions: Given a group G, a subgroup H\le G, and an action of H on a metric space S, when is it possible to extend it to an action of the whole group G? When does such an extension preserve interesting properties of the original action of H? I will explain how to formalize this problem and will present a construction of the induced action which behaves well when G is hyperbolic relative to H or, more generally, H is hyperbolically embedded in G. We will also discuss some applications. This talk is based on my work in progress with C. Abbott and S. Balasubramanya.

2:00 pm in 243 Altgeld Hall,Thursday, April 28, 2016

#### Curve packing and modulus estimates

###### Katrin Fässler (University of Jyväskylä)

Abstract: The modulus of curve families is a powerful tool in the study of quasiconformal and related mappings. Quantitative lower bounds for the modulus can often be obtained if the considered curve family is of a special form, for instance if it constitutes a nice foliation, or if it consists of all possible curves connecting two nondegenerate continua. In this talk I will discuss a collection of curves that is not of this form, namely a family of planar curves that contains an isometric copy of every rectifiable curve in $\mathbb R^2$ of length one. The "worm problem" of L. Moser asks for the least area covered by the curves in such a family. J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c>0$. We strengthen Marstrand’s result by discussing the p-modulus of a Moser family for certain values of $p$. This is joint work with T. Orponen.

2:00 pm in Altgeld Hall 241,Thursday, April 28, 2016

#### Double Gauss Sums

###### Hiram Golze (UIUC)

Abstract: We will evaluate a Gauss sum where there is a binary quadratic form in the exponent. This will allow us to find the number of solutions to certain congruences of the form $ax^2+bxy+cy^2+dz^2+ezw+fw^2 \equiv k \pmod { p^n}$, where $k$ is a nonzero integer. This talk will follow the paper of Alaca, Alaca, and Williams.

3:00 pm in 243 Altgeld Hall,Thursday, April 28, 2016

#### The Weak Lefschetz property for quotients by quadratic monomials

###### Hal Schenck (UIUC Math)

Abstract: Michałek-Miró-Roig recently gave a beautiful geometric characterization of quotients by ideals generated by quadratic or cubic monomials such that the multiplication map by a general linear form fails to be injective in the first nontrivial degree. Their work was motivated by a conjecture of Ilardi connecting the failure to Laplace equations and classical results of Togliatti from the 1920's on osculating planes. We investigate the Weak Lefschetz property for quotients by quadratic monomial ideals, explaining failure of the Weak Lefschetz property for some cases not covered by previous work. This work is joint with J. Migliore and U. Nagel.

4:00 pm in 245 Altgeld Hall,Thursday, April 28, 2016

#### Spring Department Faculty Meeting

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