# Calendar

## Today

### Department Colloquium, Prof. A. Raghuram, Indian Institute of Science Education and Research, MATH 175

Tuesday, Aug 22 3:30 pm - 4:30 pm

## From Calculus to Number Theory (via Cohomology)

Abstract: I will begin by recalling some very classical series that we usually come across in a first course in Calculus. When recast using arithmetic terminology in vogue, these series provide examples of special values of L-functions. An L-function is a function of a complex variable s attached to some interesting arithmetic or geometric data, and the special values of the L-function give structural information of the data to which it is attached. (A classical example to drive home this point would be Dirichlet's theorem that a certain L-function admitting a nonzero value when evaluated at s=1 implies that there are infinitely many primes in arithmetic progressions.) My aim in this talk will be to give a general idea of the governing conjectures and results in this field. Using some illustrative low-dimensional examples, I will discuss some recent results which use geometric techniques involving the cohomology of locally symmetric spaces to study the arithmetic properties of the special values of L-functions.## Thursday

### Automorphic Forms and Representation Theory Seminar, Prof. Kai-Wen Lan, University of Minnesota, BRNG 1260

Thursday, Aug 24 1:30 pm - 2:20 pm

## Local systems over Shimura varieties: a comparison between two constructions

Given a Shimura variety X associated with some algebraic group G, and some finite-dimensional algebraic representation V of G^c (which is quotient of G by the maximal Q-anisotropic R-isotropic subtorus of the center), we can define two kinds of vector bundles with integrable connections, over X. The first one is based on the classical complex analytic construction using double quotients, while the second one is a new p-adic analytic construction based on the p-adic Riemann-Hilbert correspondence in the recent work by Ruochuan Liu and Xinwen Zhu. We know how to relate these two when X is of Hodge type, using the relative cohomology of some family of abelian varieties over X. But what should we do when X is a general Shimura variety, in which case no convenient family of algebraic varieties (or, rather, "motives") are available? In this talk, we shall review the background materials and formulate the problem more precisely, and give an answer._## Friday

## Kolmogorov’s Spectral Energy Dynamics in Thermoacoustic Turbulence

Periodic heating and cooling of a gas results in the generation of acoustic waves. In thermoacoustically unstable systems, sound waves drive such thermodynamic cycle, resulting in spontaneous generation and exponential self-amplification. In the talk I will discuss what happens when thermoacoustic instability is driven to the limit of shock-wave formation in highly nonlinear broadband acoustic perturbations. Before reaching such extreme conditions, single-frequency harmonic waves grow in amplitude and distort, generating higher frequencies, thereby smaller wavelengths, until the viscous limit is reached: the shock-wave thickness. The same spectral energy dynamics are observed, for example, in a boundary layer undergoing laminar-to-turbulent transition. In this case, Tollmien-Schlichting waves grow exponentially due to hydrodynamic instabilities, generating large eddies, which initiate an energy cascade, feeding progressively smaller eddies. The cascade ends when the eddy size reaches the viscous limit: the Kolmogorov length scale. Gupta, Lodato and Scalo, AIAA (2017) have revealed for the first time the design of a device capable of generating self-sustaining thermoacoustic shock waves exhibiting spectral energy transfer dynamics identical to the ones predicted by Kolmogorov’s theory for turbulent flows. High-order unstructured fully compressible Navier-Stokes simulations reveal the presence of three regimes: (i) Monochromatic harmonic growth, governed by linear thermoacoustics; (ii) Hierarchical spectral broadening, marking the early and late stages of the energy cascade; (iii) Shock-wave dominated limit cycl}, where energy production is balanced by dissipation occurring at the captured shock-thickness scale. A companion time-domain nonlinear acoustic model has been developed to demonstrate the effect of macrosonic interactions between pressure and heat-flux fluctuations, responsible for saturation and thermodynamic asymmetries. Upon onset of energy cascade, k-th overtone of thermoacoustically amplified mode grows at rate k+1 times the thermoacoustic growth rate. Frequency power spectrum at the shock-dominated limit cycle exhibits -5/2 logarithmic slope, confirmed by a dimensional analysis inspired by Kolmogorov's theory of the hydrodynamic turbulent energy cascade.## Next Week

### CCAM Seminar, Prof. Jinqiao Duan , Illinois Institute of Technology, UNIV 103

Monday, Aug 28 4:30 pm - 5:30 pm

## TBD

### Special Seminar, Prof. Dohyeong Kim, University of Michigan, BRNG 1260

Tuesday, Aug 29 1:30 pm - 2:30 pm

## Arithmetic Chern-Simons Theory

Abstract: The analogy between number fields and 3-manifolds dates back to at least 1970's when it was popularized by an article by Mazur. A collection of ideas rooted at this analogy is called arithmetic topology. The title of the talk refers to the number theoretic counterpart of the Chern-Simons theory, as proposed by Minhyong Kim. We will review the arithmetic Chern-Simons functional, around which the theory is centered. The functional will be evaluated at some special points, showing that the functional is not constant. As a by-product, we find obstructions to some unramified Galois embedding problems. On the other hand, arithmetic linking numbers will be defined and related to the partition functions of the theory. This is based on the joint works with H. Chung, M. Kim, G. Pappas, J. Park, and H. Yoo.### Department Colloquium, Prof. Christopher Miller, Ohio State University, MATH 175

Tuesday, Aug 29 3:30 pm - 4:30 pm

## A modern approach to some classical asymptotic analysis

Abstract: (Joint work with O. Costin and R. Costin, Ohio State.) The general subject is the interplay between special functions, asymptotic analysis, differential algebra and real-analytic geometry. As a concrete motivational example, for $s>1$, let $F_s$ be the restriction to the real line of the entire function $\prod_{n>0}(1+z/n^s)$. The asymptotic behavior of the $F_s$ at $+\infty$ is documented rather extensively in the classical literature, but generally only as individual functions, not as a family of potentially interacting functions. Our most basic question: If $S$ is a subset of $(1,+\infty)$, then what can be said about the asymptotics of functions from the differential ring generated over $R[x]$ by $\{F_s: s \in S\}$? (The existing literature is remarkably sparse on this.) We are particularly interested in knowing whether no nontrivial function from this ring has infinitely many positive zeros. Our search for answers leads us from classical real and complex analysis to modern summability theory and o-minimality (a wide-ranging generalization of semialgebraic geometry). The talk will be accessible to a general mathematical audience.### Automorphic Forms Seminar, Prof. Chung Pang Mok, Purdue University, BRNG 1260

Thursday, Aug 31 1:30 pm - 2:20 pm

## The spectral side of stable local trace formula for real groups

Abstract: In this talk, we will recall the local trace formula of Arthur, and its stabilization. In the archimedean case, we can give explicit expressions for the spectral side of the stable local trace formula, in terms of Langlands parameters. Joint work with Zhifeng Peng.## TBD

## Two Weeks

### Automorphic Forms and Representation Theory Seminar, Mr. Abhishek Parab, Purdue University, BRNG 1260

Thursday, Sep 7 1:30 pm - 2:20 pm

## Title: TBA

## Three Weeks

### CCAM Seminar, Professor Jan Hesthaven, Ecole Polytechnique Federale de Lausanne (EPFL), UNIV 103

Monday, Sep 11 4:30 pm - 5:30 pm

### Department Colloquium, Prof. Gui-Qiang Chen (University of Oxford), MATH 175

Tuesday, Sep 12 3:30 pm - 4:30 pm

## September

### Graduate Student Invited Colloquium Speaker, Prof. Ilse Ipsen, North Carolina State University, MATH 175

Tuesday, Sep 19 3:30 pm - 4:30 pm

## Randomized Algorithms for Matrix Computations

The emergence of massive data sets, over the past fifteen or so years, has lead to the development of Randomized Numerical Linear Algebra. Fast and accurate randomized matrix algorithms are being designed for applications like machine learning, population genomics, astronomy, nuclear engineering, and optimal experimental design. We give a flavour of randomized algorithms for the solution of least squares/regression problems and, if time permits, for the computation of logdeterminants. Along the way we illustrate important concepts from numerical analysis (conditioning and pre-conditioning) and statistics (sampling and leverage scores).### Automorphic Forms and Representation Theory Seminar, Prof. Xinyi Yuan, UC Berkeley, BRNG 1260

Thursday, Sep 28 1:30 pm - 2:20 pm

## Title: TBA

### Jean Rubin Memorial Lecture (Colloquium), Prof. Jacqueline M. Hughes-Oliver, North Carolina State University, MATH 175

Thursday, Sep 28 3:30 pm - 4:30 pm

## TBA

## October

## TBD

### Department Colloquium, Prof. Phil Gressman, University of Pennsylvania, MATH 175

Tuesday, Oct 3 3:30 pm - 4:30 pm

## TBD

### CCAM Seminar, Dr. Danial Zack Turner, Sandia National Laboratory, UNIV 103

Monday, Oct 16 4:30 pm - 5:30 pm

## TBD

### Department Colloquium, Prof. Joachim Schwermer, Universitat Wien, MATH 175

Tuesday, Oct 17 3:30 pm - 4:30 pm

## TBA

### Automorphic Forms and Representation Theory Seminar, Prof. Allen Moy, Hong Kong University of Science and Technology, BRNG 1260

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

## An Euler-Poincare formula for a depth zero Bernstein projector

Work of Bezrukavnikov-Kazhdan-Varshavsky uses an equivariant system of trivial idempotents of Moy-Prasad groups to obtain an Euler-Poincare formula for the r-depth Bernstein projector. We establish an Euler-Poincare formula for the projector to an individual depth zero Bernstein component in terms of an equivariant system of Peter-Weyl idempotents of parahoric subgroups P associated to a block of the reductive quotient P. This work is joint with Dan Barbasch and Dan Ciubortau.### CCAM Seminar, Dr. Aihua Wood, Air Force Institute of Technology, UNIV 103

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

## TBD

### Departmental Colloquium, Prof. Guy Henniart, University of Paris-Sud, MATH 175

Tuesday, Oct 24 3:30 pm - 4:30 pm

## TBA

### CCAM Seminar, Prof. Xiaochuan Cai , Univ. of Colorado at Boulder, UNIV 103

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

## TBD

### Department Colloquium, Prof. Craig Sutton, Dartmouth College, MATH 175

Tuesday, Oct 31 3:30 pm - 4:30 pm

## November

### Automorphic Forms and Representation Theory Seminar, Prof. Francesc Castella, Princeton University, BRNG 1260

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

## Title: TBA

### Automorphic Forms and Representation Theory Seminar, Prof. Shunsuke Yamana, Kyoto University, BRNG 1260

Thursday, Nov 9 1:30 pm - 2:20 pm

## Title: TBA

## Blind deconvolution by Optimizing over a Quotient Manifold

## Blind deconvolution is to recover two unknown signals from their convolution. We formulate this problem as a nonconvex optimization problem on a quotient manifold and propose Riemannian optimization algorithms for solving the problem. The proposed algorithm is proven to recover the exact solution with high probability when the number of measurements is (up to log-factors) slightly larger than the information-theoretical minimum, which is the same as the state-of-the-art results. The quotient structure in our formulation yields a simpler penalty term in the cost function when compared to the state-of-the-art nonconvex method. This simplifies the convergence analysis to some extent and yields a natural implementation. Empirically, the algorithm has the best performance in the sense that compared to state-of-the-art methods, i) it needs least number of various operations, such as DFT, to reach a similar accuracy, and ii) it has the highest probability of successful recovery. This is joint work with Paul Hand at Rice university.

### Department Colloquium, Prof. Sandra Cerrai, University of Maryland, MATH 175

Tuesday, Nov 14 3:30 pm - 4:30 pm

## TBD

### Automorphic Forms and Representation Theory Seminar, Dr. Ozlem Edjer, Colorado State University, BRNG 1260

Thursday, Nov 16 1:30 pm - 2:20 pm

## Title: TBA

### Department Colloquium, Prof. Sandra Cerrai, University of Maryland at College Park, MATH 175

Tuesday, Nov 21 3:30 pm - 4:30 pm

## TBA

### Automorphic Forms and Representation Theory Seminar, Prof. Aaron Pollack, Duke University, BRNG 1260

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