# Calendar

## Next Week

### Bridge to Research Seminar, Dr. Ben McReynolds, Purdue University, UNIV 303

Monday, Aug 29 4:30 pm - 5:30 pm

## How I Learned Arithmetic in Grad School

Abstract: In this talk, I will describe how I got to graduate school and somewhat unexpectedly spent most of my time learning arithmetic. I will discuss how a book my advisor wrote had such an intriguing title that I started working with him; the book turned out to not be what I thought it was about. Time permitting, I will discuss how I spent 18 months trying to understand 14 pages in a book. Despite this abstract, there will actually be some interesting mathematics in this talk that touches on topics from algebra, geometry/topology, and number theory.### CCAM Seminar, Prof. Qinghai Zhang, Zhejiang University, China REC 114

Monday, Aug 29 4:30 pm - 5:30 pm

## Towards Fourth- and Higher-order Numerical Simulations of Incompressible Flows with Moving Boundaries

## Euler scheme for SDEs driven by fractional Brownian motions with $H > 1/2$

Abstract: The modified Euler scheme for SDEs driven by fractional Brownian motions is a natural generalization of the classical Euler scheme in the Brownian motion case. In the first part of the talk we focus on the rate of convergence and the asymptotic error distribution of this numerical scheme, and compare these results to the Brownian motion case. In the second part we consider some higher-order Euler schemes (or Taylor schemes) and their variations. Almost sure rate of convergence and $L_p$-rate of convergence are obtained for these numerical schemes, which allow us to design the best Euler-type numerical scheme for the almost sure or the $L_p$-convergence.### Informal Algebraic Geometry Seminar, Donu Arapura, Purdue University, MATH 731

Wednesday, Aug 31 2:45 pm - 3:45 pm

## The Hodge to de Rham Spectral Sequence

Abstract: This will be part of the series of preparatory talks for Ahmed Abbes's mini-course. I will try to explain in concrete terms the more homological aspects of basic Hodge theory.## $K(\pi, 1)$ spaces in Etale Topology

Abstract: This will be part of the series of preparatory talks for Ahmed Abbes's mini-course (see below). I will discuss some elementary aspects of the theory of $K(\pi, 1)$ spaces in the etale setting (after a breif review of these spaces in the usual topological setting).## A Mathematician's Introduction to Quantum Computing

Abstract: Quantum computing has been making lots of headlines lately; both locally and globally. Purdue just embarked on a massive quantum computing collaboration with Microsoft, and with the new D-Wave-2X quantum computer publicly available for purchase for under $10 million, move universities, labs, and business are using them every month. I will discuss what quantum computing is, why it is useful, how it may affect the fields of mathematics and computer science in the coming years, and what challenges its development faces. This talk will be relatively light on physics and instead will take as mathematical of a perspective to the topic as possible. To keep things full of pictures, several of my examples will come from coloring problems in combinatorial graph theory. Some material from graph theory, probability, linear algebra, computer science, and of course physics will be used, but I will introduce everything I use; no prior background needed.## Higher Order Representation Stability

### Real Algebraic Geometry Seminar, A. Gabrielov, Purdue University, MATH 431

Thursday, Sep 1 11:00 am - 12:00 pm

## Rational Functions With Real Critical Points, the Catalan Numbers, and the Schubert Calculus

Abstract: How many rational functions of degree $d$ have a given set of $2d-2$ points as their set of critical points? If we identify functions that differ by a fractional-linear transformation in the target space (all such functions have the same critical points) the answer is $u_d$, the Catalan number. This is equivalent to a problem in the Schubert calculus. How many codimension 2 affine subspaces in $C^d$ intersect affine lines tangent to the rational normal curve $\gamma(t)=(t,\dots,t^d)$ at $2d-2$ distinct points? The answer (Schubert, 1886) is $u_d$, the Catalan number.Theorem. Suppose that all $2d-2$ points are real. Then all $u_d$ equivalence classes of rational functions with these critical points are real (contain real functions). The proof is based on counting certain combinatorial objects, called nets, associated with real rational functions with real critical points.

The corresponding result in the Schubert calculus is a special case of the B. and M. Shapiro conjecture about $p$-dimensional affine subspaces in $C^d$ osculating the rational normal curve at $(p+1)(d-p)$ real points. It was proved by Mukhin, Tarasov and Varchenko using techniques developed for integrable models of quantum mechanics. There is no direct algebraic proof, even for $p=2$.

### Automorphic Forms and Representation Theory Seminar, Professor Simon Marshall, University of Wisconsin at Madison, BRNG 1260

Thursday, Sep 1 1:30 pm - 2:30 pm

## Bounds for Maass Forms on Semisimple Groups

Abstract:Let G/Q be a semisimple group. I will explain a theorem that states that if G(R) is split or is the restriction of scalars of a complex group, then Maass forms on G of large Laplace eigenvalue have smaller sup norms than the `trivial' upper bound. On the other hand, I will also explain a theorem that shows that if G(R) is not split and R-almost simple, then there exist Maass forms on G whose sup norms grow like a power of the eigenvalue, which is unexpected on manifolds of nonpositive curvature. The second theorem is joint with Farrell Bromley.### Number Theory Seminar, Professor Edray Goins, Purdue University, MATH 731

Thursday, Sep 1 4:30 pm - 5:30 pm

## Introduction to Representation Theory

Abstract: We discuss some of the basics for representations of finite groups, including the permutation representation, the augmentation ideal, Mischke’s theorem, and Wedderburn’s theorem.## Two Weeks

### Department of Mathematics Colloquium, Leslie Hogben, Iowa State University, MATH 175

Tuesday, Sep 6 4:30 pm - 5:30 pm

## Distance Spectra

Abstract: The distance matrix of a graph G of order n is a symmetric $n \times n$ integer matrix whose ij-entry is the distance between vertices $v_i$ and $v_i$. Distance matrices was introduced by Graham and Pollak in the study of loop switching in circuits. The distance eigenvalues of G are the eigenvalues of its distance matrix, which form the distance spectrum of G. The original problem and various recent results will be described, including a proof of a 1978 conjecture of Graham and Lovasz that the coefficients of the distance characteristic polynomial are unimodal (and log-concave), the determination of distance spectra for distance regular graphs that have one positive distance eigenvalue, and a characterization of strongly regular graphs having more positive than negative distance eigenvalues.This talk is based on joint work with G. Aalipour, A. Abiad, Z. Berikkyzy, J. Cummings, J. De Silva, W. Gao, K. Heysse, F.H.J. Kenter, J.C.-H. Lin, and M. Tait.

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

### Informal Algebraic Geometry Seminar, Yong Suk Moon, Purdue University, MATH 731

Wednesday, Sep 7 2:45 pm - 3:45 pm

## An Introduction to Almost Ring Theory

Abstract: This talk will be an overview of the basics objects and results in almost ring theory. It will essentially be an overview of the main results stated in Chapter 5 of the book "The p-adic Simpson Correspondence" by Abbes-Gros-Tsuji.### Algebraic Geometry Seminar, Tong Liu, Purdue University, MATH 731

Wednesday, Sep 7 3:45 pm - 4:45 pm

## Universal $p$-adic Thickenings and Rings of Periods

### Automorphic Forms and Representation Theory Seminar, Professor Chung Pang Mok, Purdue University, BRNG 1260

Thursday, Sep 8 1:30 pm - 2:30 pm

## A Weak Form of Beyond Endoscopic Decomposition for the Stable Trace Formula of Odd Orthogonal Groups

Abstract: We show that the cuspidal component of the stable trace formula of a special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace formula, when r is the standard or the second fundamental representation of the dual group. The results are consequences of Arthur's works on endoscopic classification of automorphic representations, together with known results concerning a class of Langlands L-functions for special odd orthogonal groups.## Three Weeks

### Computational & Applied Mathematics Seminar, Dr. Kyongmin Yeo, IBM T.J. Watson Research Center, REC 114

Monday, Sep 12 4:30 pm - 5:30 pm

## TBA

### Department of Mathematics Colloquium, Richard Schoen, University of California, Irvine, MATH 175

Tuesday, Sep 13 4:30 pm - 5:30 pm

## Geometries that Optimize Eigenvalues

Abstract: When we choose a metric on a manifold we determine the spectrum of the Laplace operator. Thus an eigenvalue may be considered as a functional on the space of metrics. For example the first eigenvalue would be the fundamental vibrational frequency. In some cases the normalized eigenvalues are bounded independent of the metric. In such cases it makes sense to attempt to find critical points in the space of metrics. In this talk we will survey two cases in which progress has been made focusing primarily on the case of surfaces with boundary. We will describe the geometric structure of the critical metrics which turn out to be the induced metrics on certain special classes of minimal (mean curvature zero) surfaces in spheres and euclidean balls. The eigenvalue extremal problem is thus related to other questions arising in the theory of minimal surfaces.Refreshments will be served in the Math Library Lounge at 4:00 p.m.

### Algebraic Geometry Seminar, Ahmed Abbes (CNRS and IHES), MATH 731

Wednesday, Sep 14 3:00 pm - 4:30 pm

## The Hodge-Tate Spectral Sequence

Abstract: In this course, I will review the construction of the Hodge-Tate spectral sequence following Faltings' approach and I will show that it bears a certain analogy with the conjugate spectral sequence in characteristic p. I will focus on one of the main ingredients, namely, Faltings' fundamental comparison theorem which is the basis of all comparison theorems between the p-adic etale cohomology and other p-adic cohomologies. The course is based on a joint work with Michel Gros (http://arxiv.org/abs/1509.03617).### Automorphic Forms and Representation Theory Seminar, Professor Ahmed Abbes, CNRS and IHES, BRNG 1260

Thursday, Sep 15 1:30 pm - 3:00 pm

## The Hodge-Tate Spectral Sequence

Abstract: This will be the second lecture in the mini-course, and a continuation of the first lecture. For more information see https://www.math.purdue.edu/~patel471/abbes_course.htm## September

### Computational & Applied Mathematics Seminar, Professor Wei Cai, UNC at Charlotte, REC 114

Monday, Sep 19 4:30 pm - 5:30 pm

## TBA

### Algebraic Geometry Seminar, Ahmed Abbes (CNRS and IHES), MATH 731

Wednesday, Sep 21 3:00 pm - 4:30 pm

## The Hodge-Tate Spectral Sequence

Abstract: This will be a continuation of the mine-course.### Automorphic Forms and Representation Theory Seminar, Professor Baiying Liu, Purdue University, BRNG 1260

Thursday, Sep 22 1:30 pm - 2:30 pm

## On the Local Converse Theorem for p-adic GL(n)

Abstract: In this talk, I will introduce a complete proof of a standard conjecture on the local converse theorem for generic representations of GLn(F), where F is a non-archimedean local field. This is a joint work with Prof. Herve Jacquet. (http://arxiv.org/abs/1601.03656)### Computational & Applied Mathematics Seminar, Professor Zhenning Cai, DUKE, REC 114

Monday, Sep 26 4:30 pm - 5:30 pm

## Surface Hopping Gaussian Beam Method for Hyperbolic Systems With Applications to Quantum-Classical Liouville Equations

Abstract: The surface hopping method is widely used in chemistry for mixed quantum-classical dynamics. In this talk, we will discuss the understanding of the surface hopping method based on a class of hyperbolic equations with stiff source terms. An algorithm combining the Gaussian beam method and the surface hopping method is proposed for such systems, and the algorithm can be applied to the quantum-classical Liouville equations to solve high-dimensional problems.### Department of Mathematics Colloquium, Xueyu Zhu, University of Iowa, MATH 175

Tuesday, Sep 27 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.## October

### Computational & Applied Mathematics Seminar, Professor Makram Hamouda, Indiana University, REC 114

Monday, Oct 3 4:30 pm - 5:30 pm

## TBA

### Department of Mathematics Colloquium, Ernie Croot, Georgia Institute of Technology, MATH 175

Tuesday, Oct 4 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Special Department of Mathematics Colloquium, Professor Ken Ono, Emery University, BRNG 2280

Friday, Oct 7 4:30 pm - 5:30 pm

## TBA

### CCAM Seminar, Professor Jorge Velasco-Hernandez, UNAM, Juriquilla, REC 114

Monday, Oct 10 4:30 pm - 5:30 pm

## TBA

### Department of Mathematics Colloquium, Jared Wunsch, Northwestern University, MATH 175

Tuesday, Oct 18 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Department of Mathematics Colloquium, Professor Bo Guan, Ohio State University, MATH 175

Tuesday, Oct 25 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.## November

### CCAM Distinguished Seminar, Professor Roger Temam, Indiana University, LWSN 1142

Monday, Nov 7 4:30 pm - 5:30 pm

## TBA

## TBA

### CCAM Seminar, Professor Meerschaert, Michigan State University, REC 114

Monday, Nov 14 4:30 pm - 5:30 pm

## TBA

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Spectral and Scattering Theory Seminar, Semyon Dyatlov, MIT, MATH 731

Wednesday, Nov 16 1:30 pm - 2:30 pm

## Dynamical Zeta Functions and Topology for Negatively Curved Surfaces

Abstract: For a negatively curved compact Riemannian manifold (or more generally, for an Anosov flow), the Ruelle zeta function is defined by $$ \zeta(s)=\prod_\gamma (1-e^{-s\ell_\gamma} ),\quad \Re s\gg 1, $$ where the product is taken over all primitive closed geodesics $\gamma$ with $\ell_\gamma>0$ denoting their length. Remarkably, this zeta function continues meromorphically to all of $ \mathbb C$.Using recent advances in the study of resonances for Anosov flows and simple arguments from microlocal analysis, we prove that for an orientable negatively curved surface, the order of vanishing of $\zeta(s)$ at $s=0$ is given by the absolute value of the Euler characteristic. In constant curvature this follows from the Selberg trace formula and this is the first result of this kind for manifolds which are not locally symmetric. This talk is based on joint work with Maciej Zworski.

### Graduate Student Invited Colloquium, Peter Sarnak, Princeton University, MATH 175

Tuesday, Nov 22 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Department of Mathematics Colloquium, Professor Ragnar Buchweitz, University of Toronto, MATH 175

Tuesday, Nov 29 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.## December

### Department of Mathematics, Professor Andrew Putman, University of Notre Dame, MATH 175

Tuesday, Dec 6 4:30 pm - 5:30 pm