# Calendar

## Yesterday

### Automorphic Forms and Representation Theory Seminar, Prof. Manish Patnaik, University of Alberta, UNIV 317

Thursday, Feb 22 1:30 pm - 2:20 pm

## Metaplectic covers of Kac-Moody groups and Whittaker functions

We will describe how to construct metaplectic covers of Kac-Moody groups, generalizing a classical construction of Matsumoto. In the case of non-archimedean local fields, we will then explain how to formulate Whittaker functions on such groups, and compute them via a Casselman-Shalika type formula. Joint work with with A. Puskas.### PDE Seminar, Prof. Alex Misiats, Virginia Commonwealth University, REC 121

Thursday, Feb 22 3:30 pm - 4:20 pm

## Convex Duality in Nonconvex Variational Problems.

We consider the minimization problem related to modeling materials with memory, e.g. shape memory alloys. I will start my presentation with a visual illustration of shape memory effect. Physical experiments suggest that if two distinct phases of such material are present at opposite sides of a rectangular sample, a zig-zag pattern is formed. Our goal is to understand if this pattern is energy minimizing. The mathematical model of this phenomenon involves the minimization of singularly perturbed elastic energy. I my talk I will review classic minimization approach via convex duality. Despite the fact that the problem is highly nonconvex, in my talk, I will describe a relaxation method which allows to use the convex duality technique for the purpose of obtaining a sharp lower bound.

### Mathematics Society, Prof. Steve Bell, Purdue University, REC 108

Thursday, Feb 22 6:00 pm - 7:00 pm

## Fourier Series are Music to My Ears

Most people think that Fourier series were invented by J. B. Fourier to study heat flow in a wire. They were really invented years earlier by Johann Bernoulli, in competition with his brother, Jacob, to study the motion of a vibrating string. I will explain how understanding Fourier series leads to a deeper understanding of music.

I will also reveal how this subject lured me away from Acoustical Engineering as an undergraduate at University of Michigan to pure math as a PhD student at MIT, and how it still reverberates in my present research.

## Next Week

### Geometric Analysis Seminar, Robert Hardt, Rice University, MATH 731

Monday, Feb 26 3:30 pm - 4:30 pm

## A Linear Isoperimetric Inequality for Algebraic and Analytic Varieties

Abstract: In R^n, the classical n dimensional isoperimetric inequality bounds the volume of any smooth region U by c_n [H^{n-1}(BdryU)]^{n/(n-1)}, where c_n is the constant giving equality with U being an n ball. In higher codimension, any integral k-1 dimensional cycle B in R^n with k < n , is the boundary of some k chain T with mass(T) \leq c_k mass(B)^ {k/(k-1)}. The proof by Federer and Fleming in 1960 generalized to an ambient space X like a compact Riemannian manifold, a polyhedron, or more generally a Euclidean Lipschitz neighborhood retract, with the constant $C_X$ depending on X. However, this relation may fail for various singular spaces X such as algebraic varieties. With T. DePauw (Paris VII), we prove a {\it linear} isoperimetric inequality valid for cycles of any dimension in a compact set X defined by polynomial or real analytic equalities or inequalities. This generalizes earlier work on codimension one boundaries by L.Bos -P.Milman and B.Hua-FH.Lin.</p>### CCAM Seminar, Haizhao Yang, National University of Singapore, REC 308

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

## A Unified Framework for Oscillatory Integral Transform: When to use NUFFT or Butterfly Factorization?

This talk introduces a nearly optimal fast algorithm for the matvec $g=Kf$ for $K\in \mathbb{C}^{N\times N}$, which is the discretization of the oscillatory integral transform $g(x) = \int K(x,\xi) f(\xi)d\xi$ with a kernel function $K(x,\xi)=\alpha(x,\xi)e^{2\pi i\Phi(x,\xi)}$, where $\alpha(x,\xi)$ is a smooth amplitude function , and $\Phi(x,\xi)$ is a piecewise smooth phase function with $O(1)$ discontinuous points in $x$ and $\xi$. A unified framework is proposed to compute $Kf$ with $O(N\log N)$ time and memory complexity via the non-uniform fast Fourier transform (NUFFT) or the butterfly factorization (BF), together with an $O(N)$ fast algorithm to determine whether NUFFT or BF is more suitable. This framework works for two cases: 1) explicite formulas for the amplitude and phase functions are known; 2) only indirect access of the amplitude and phase functions are available. Especially in the case of indirect access, our main contributions are: 1) an $O(N\log N)$ algorithm for recovering the amplitude and phase functions is proposed based on a new low-rank matrix recovery algorithm; 2) a new stable and nearly optimal BF with amplitude and phase functions in form of a low-rank factorization (IBF-MAT) is proposed to evaluate the matvec $Kf$. Numerical results are provided to demonstrate the effectiveness of the proposed framework.

### Algebraic Geometry seminar, Christine Berkesch, University of Minnesota, MATH 731

Wednesday, Feb 28 3:25 pm - 4:25 pm

## Parametric behavior of A-hypergeometric solutions.

Abstract: A-hypergeometric systems are the D-module counterparts of toric ideals, and theirbehavior is linked closely to the combinatorics oftoric varieties. I will discuss recent work that aims to explain the behavior of the solutions of these systems as their parameters vary. In particular, we stratify the parameter space so that solutions are locally analytic within each (connected component of a) stratum. This is joint work with Jens ForsgÃ¥rd and Laura Matusevich.### Automorphic Forms and Representation Theory Seminar, Dr. Qing Zhang, Sun Yat-sen University, UNIV 317

Thursday, Mar 1 1:30 pm - 2:20 pm

## Local converse theorem for unitary groups

Local converse theorem says that an irreducible generic representation of a classical group over a p-adic field should be determined by its various local gamma factors twisting with GL_n. In this talk, I will describe a sketch of a proof of local converse theorems for quasi-split unitary groups. A main ingredient of the proof is certain properties of partial Bessel functions developed by Cogdell-Shahidi-Tsai.

## Splendor in the Graphs

## Two Weeks

### Geometric Analysis Seminar, Chika Mese, Johns Hopkins University, MATH 731

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

Title: Harmonic maps into CAT(1) spaces

The pioneering works of Gromov-Schoen and Korevaar-Schoen established the theory of harmonic maps into NPC spaces, i.e. complete metric space of non-positive curvature. In this talk, we will discuss harmonic map theory when we relax the curvature assumption and consider metric spaces with curvature bounded from above.

### Math is Key Lecture, Dr. Eugenia Cheng, School of the Art Institute of Chicago

Tuesday, Mar 6 3:30 pm - 4:20 pm

## How To Bake Pi: making abstract mathematics palatable

Why does mathematics inspire love in some people and fear in others? Why do some people think mathematics is important for everyone while others think it is a collection of gibberish touching little of the world beyond the brains of some rare geniuses? Why do some think it is a creative art akin to poetry and music, while others think it is a boring tool for producing answers? In this talk I will present mathematics as a way of thinking, and not just about numbers. I will use a variety of unexpectedly connected examples including music, juggling and baking, as in the title of my recent book. My aim is to show that math can be made fun, intriguing and relevant for people of all ages, by means of hand-on activities, examples that everyone can relate to, and peculiar anecdotes. I will present surprisingly high level mathematics including some advanced abstract algebra usually only seen by maths undergraduates or PhD students, yet show how to make it accessible even to children. My message is relevant to those who wish to spread their love of math, as well as those who wish to overcome their fear of it. There will be a distinct emphasis on edible examples.## March

### CCAM Seminar, Prof. Jie Liang, University of Illinois, Chicago, REC 308

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

## TBA

## A partial Laplacian as an infinitesimal generator on the Wasserstein space

We study stochastic processes on the Wasserstein space, together with their infinitesimal generators. One of these processes plays a central role in our work. Its infinitesimal generator defines a partial Laplacian on the space of Borel probability measures, and we use it to define heat flow on the Wasserstein space. We verify a distinctive smoothing effect of this flow for a particular class of initial conditions. To this end, we will develop a theory of Fourier analysis and conic surfaces in metric spaces. We note that the use of the infinitesimal generators has been instrumental in proving various theorems for Mean Field Games, and we anticipate they will play a key role in future studies of viscosity solutions of PDEs in the Wasserstein space.

### Automorphic Forms and Representation Theory Seminar, Prof. Shiang Tang, University of Utah, UNIV 317

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

### Department Colloquium, Prof. Cristina Villalobos, University of Texas, Rio Grande Valley, MATH 175

Tuesday, Mar 27 3:30 pm - 4:20 pm

## TBD

### Automorphic Forms and Representation Theory Seminar, Dr. Fan Gao, Purdue University, UNIV 317

Thursday, Mar 29 1:30 pm - 2:20 pm

## TBA

### Mathematics Society, Prof. Donatella Danielli, Purdue University, REC 108

Thursday, Mar 29 6:00 pm - 7:00 pm

## April

### Department Colloquium, Prof. Dinakar Ramakrishnan, California Institute of Technology, MATH 175

Tuesday, Apr 3 3:30 pm - 4:20 pm

## TBD

### Automorphic Forms and Representation Theory Seminar, Prof. Mark Van Hoeij, Florida State University, UNIV 317

Thursday, Apr 5 1:30 pm - 2:30 pm

### Automorphic Forms and Representation Theory Seminar, Prof. Melissa Emory, University of Missouri, REC 113 (Note Special Day/Time/Location)

Friday, Apr 6 1:30 pm - 2:30 pm

### Department Colloquium, Prof. Frank Thorne, University of South Carolina, MATH 175

Tuesday, Apr 10 3:30 pm - 4:20 pm

## TBD

### Automorphic Forms and Representation Theory Seminar, Prof. Ravi Ramakrishna, Cornell University, UNIV 317

Thursday, Apr 12 1:30 pm - 2:20 pm

## TBA

### Automorphic Forms and Representation Theory Seminar, Prof. Adriana Salerno, Bates College, REC 113 (Note Special Day/Time/Location)

Friday, Apr 13 1:30 pm - 2:30 pm

### Department Colloquium, Prof. Matt Gursky, University of Notre Dame, MATH 175

Tuesday, Apr 17 3:30 pm - 4:20 pm

## TBD

### Automorphic Forms and Representation Theory Seminar, Dr. Cris Negron, MIT, UNIV 317

Thursday, Apr 19 1:30 pm - 2:20 pm

## TBD

### CCAM Lunch Seminar, Prof. Georgios Karagiannis, Durham University, REC 303

Friday, Apr 20 11:30 am - 12:30 pm

## TBA

### CCAM Seminar, Dr. Andrew Hill, Centers for Disease Control and Prevention, REC 308

Monday, Apr 23 4:30 pm - 5:30 pm