Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, October 8, 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, October 8, 2015

9:00 am in Illini Rooms A & B, Illini Union,Thursday, October 8, 2015

#### Corporate Forum

Abstract: The Corporate Forum will be held from 9 a.m. to 4 p.m. The Corporate Forum will be held from 9 a.m. to 4 p.m. Students majoring in Mathematics, Math/CS, Actuarial Science, and Statistics are invited to attend the 3rd Annual Mathematics Corporate Forum. Students will be able to engage with employers during this career fair/information session combination. The career fair will be held 9 am–4 pm (closed for lunch from noon–1 pm). Company presentations will be held throughout the day. See schedule at http://www.math.illinois.edu/UndergraduateProgram/math-career-fair.html

11:00 am in 241 Altgeld Hall,Thursday, October 8, 2015

#### Mollifications of the Riemann zeta-function and families of $L$-functions

###### Nicolas Robles (UIUC Math)

Abstract: We explain how by twisting the a mean value integral of the Riemann zeta-function by a suitable Dirichlet polynomial we can generate interesting results about the proportion of non-trivial zeros on the critical line. By using sieve results of Conrey, Iwaniec and Soundararajan, this mollification process can yield better results (over 50%) for certain averages of $L$ functions up to degree 3. This is joint work with Dirk Zeindler, Arindam Roy and Alexandru Zaharescu.

12:30 pm in 464 Loomis Laboratory,Thursday, October 8, 2015

#### Shape dependence and RG flow of entanglement entropy

###### Dean Carmi (Tel-Aviv Physics)

Abstract: I will describe the results of two recent papers on entanglement entropy (EE). In the first paper we study the shape dependence of EE. We start with symmetric entangling surfaces and slightly deform them, and we compute the resulting corrections to the EE. In the second paper we study EE on a sphere. We obtain a few analytical results, and discuss the connection to RG flows and c-theorems.

1:00 pm in 243 Altgeld Hall,Thursday, October 8, 2015

#### Shadows of Teichmueller discs in the curve graph

###### Robert Tang (Oklahoma Math)

Abstract: A Teichmueller disc parameterises the family of metrics obtained by performing SL(2,R)-deformations on a given flat surface. We consider several natural sets of curves associated with a Teichmueller disc from the point of view of the curve graph. We show that these sets agree up to uniform Hausdorff distance, and are all quasiconvex. Furthermore, we extend the notion of balance time along Teichmueller geodesics to Teichmueller discs, and show that it satisfies analogous projection properties to the curve graph. This talk will focus on the tools used to prove the above results. This is a joint work with Richard Webb.

2:00 pm in 347 Altgeld Hall,Thursday, October 8, 2015

#### Global homotopy theory

###### Mychael Sanchez (UIUC Math)

Abstract: I’ll talk about global homotopy theory, which can be thought of as homotopy theory for spaces with simultaneous compatible actions by compact Lie groups. I’ll define and give examples of global spaces and introduce global homology theories.

2:00 pm in 243 Altgeld Hall,Thursday, October 8, 2015

#### Embeddability of graphs into Banach spaces

###### Florent Baudier (Texas A&M)

Abstract: We will discuss several results about the bi-Lipschitz embeddability of certain families of graphs (trees, diamond graphs, Laksoo graphs, parasol graphs). Our motivation is to exhibit natural geometric properties of Banach spaces that prevent low-distortion embeddability of certain sequences of graphs. The study of the faithful embeddability of general metric spaces is motivated by some fundamental applications in theoretical computer science (Euclidean distortion of finite metric spaces) or in geometric group theory and topology (coarse embeddability of groups).

2:00 pm in 241 Altgeld Hall,Thursday, October 8, 2015

#### A generalization of the Schur-Siegel-Smyth trace problem

###### Kyle Pratt (UIUC Math)

Abstract: Let $\alpha$ be a totally positive algebraic integer, and define its absolute trace to be $\frac{Tr(\alpha)}{\text{deg}(\alpha)}$, the trace of $\alpha$ divided by the degree of $\alpha$. Elementary considerations show that the absolute trace is always at least one, while it is conjectured that for any $\epsilon >0$, the absolute trace is at least $2-\epsilon$ with only finitely many exceptions. This is known as the Schur-Siegel-Smyth trace problem. I will discuss joint work with George Shakan and Alexandru Zaharescu in which we show that the Schur-Siegel-Smyth trace problem is a special case of a more general phenomenon.

3:00 pm in 243 Altgeld Hall,Thursday, October 8, 2015

#### Algebra and Geometry of Wachspress surfaces

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

Abstract: Let $P_d$ be a convex polygon with $d$ vertices. The associated Wachspress surface $W_d$ is a fundamental object in approximation theory, defined as the image of the rational map $\mathbb{P}^2 \stackrel{w_d}{\longrightarrow} \mathbb{P}^{d-1}$ determined by the Wachspress barycentric coordinates for $P_d$. We show $w_d$ is a regular map on a blowup $X_d$ of $\mathbb{P}^2$ and if $d>4$ is given by a very ample divisor on $X_d$, so has a smooth image $W_d$. We determine generators for the ideal of $W_d$, and prove that in graded lex order, the initial ideal of $I_{W_d}$ is given by a Stanley-Reisner ideal. As a consequence, we show that the associated surface is arithmetically Cohen-Macaulay, of Castelnuovo-Mumford regularity two, and determine all the graded betti numbers of $I_{W_d}$.

4:00 pm in 245 Altgeld Hall,Thursday, October 8, 2015

#### Recent developments in the Sparse Fourier Transform

###### Anna Gilbert (University of Michigan)

Abstract: The Discrete Fourier Transform (DFT) is a fundamental component of numerous computational techniques in signal processing and scientific computing. The most popular means of computing the DFT is the Fast Fourier Transform (FFT). However, with the emergence of big data problems, in which the size of the processed data sets can easily exceed terabytes, the "Fast" in Fast Fourier Transform is often no longer fast enough. In addition, in many big data applications it is hard to acquire a sufficient amount of data in order to compute the desired Fourier transform in the first place. The Sparse Fourier Transform (SFT) addresses the big data setting by computing a compressed Fourier transform using only a subset of the input data, in time sub-linear in the data set size. The goal of this talk is to survey these recent developments, to explain the basic techniques with examples and applications in big data, to demonstrate trade-offs in empirical performance of the algorithms, and to discuss the connection between the SFT and other techniques for massive data analysis such as streaming algorithms and compressive sensing.