# Calendar

## Tomorrow

Refreshments served in the Library Lounge

### Student Commutative Algebra Seminar, Mr. Vinh Nguyen, Purdue University, UNIV 103

Monday, Sep 25 3:30 pm - 4:20 pm

## How Integral Closures Arise

### Geometry/Geometric Analysis Seminar, Gabriel Khan, Ohio State University, MATH 731

Monday, Sep 25 3:30 pm - 4:20 pm

## Estimates on the Principle Eigenvalue of a Hermitian Manifold

Abstract: One of the central questions in complex geometry seeks to understand the moduli space of complex structures on a given manifold. In this talk, we consider a modified version of this problem, where we first specify a Riemannian metric and then study the moduli space of the complex structures compatible with it. Under some assumptions, we can derive a lower bound on the principle eigenvalue of the complex Laplacian using the Riemannian geometry alone, independent of the particular choice of complex structure. Along the way, we encounter non-self-adjoint drift Laplacians and show how the classic Li-Yau estimate can be adapted to this setting.## Representing primes by quadratic forms; a motivation for the Langlands' program

Abstract: In this talk, we will give an introduction to the ideas of the Langlands' program. We will focus on some classical results about representing primes by quadratic forms, and will say a few words about how this lead to some of the ideas of the Langlands' program.## Next Week

### Operator Algebras Seminar, Paul McKenney, Miami University, UNIV 319

Tuesday, Sep 26 2:30 pm - 3:20 pm

## Set theory and automorphisms of corona algebras

Abstract: In the 70's, Shelah found a model of set theory where every homeomorphism of the Cech-Stone remainder of the natural numbers is induced by a bijection between cofinite sets of natural numbers. In the late 2000's, Farah showed that there is a model where every automorphism of the Calkin algebra is inner. I will discuss to what extent these results find a common generalization for coronas of separable C*-algebras. This discussion will lead to some interesting connections to other areas of operator algebra. No knowledge of set theory will be assumed, beyond the very basics.Refreshments served in the Library Lounge

### Probability Seminar, Maylis Varveene, Universite de Toulouse , UNIV 101

Wednesday, Sep 27 1:30 pm - 2:20 pm

## Rate of convergence to equilibrium for discrete-time stochastic dynamics with memory

We are interested in a general class of recursive discrete dynamics : ${\scriptsize X_{n+1}=F(X_n,\Delta_{n+1})}$ where ${\scriptsize (\Delta_n)_{n\in \mathbb{Z}}}$ is an ergodic stationary Gaussian sequence. We can think for instance of fractional Brownian motion increments. First, we will see how it is possible to define invariant distributions in this a priori non-Markovian setting. Then, after proving existence of such a distribution, we will get a uniqueness result and a rate of convergence to this invariant distribution in total variation distance. The proof is based on a coupling method (with a step which is specific to this non-Markovian framework) first implemented by M.Hairer in a continuous time setting. This method was also used by J. Fontbona and F. Panloup, as well as A. Deya, F. Panloup and S. Tindel in order to extend M. Hairer's results.Refreshments served in the Library Lounge

### Automorphic Forms and Representation Theory Seminar, Prof. Xinyi Yuan, UC Berkeley, BRNG 1260

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

## Height formulas on Shimura curves

Abstract: The goal of this talk is to summarize three different height formulas on Shimura curves for quaternion algebras over totally real fields: the Gross--Zagier formula, the formula for the height of a CM point, and the formula for the modular height of the Shimura curve. While the heights and the L-functions involved in different formulas are very different, the proofs of the formulas lie in the same framework.### 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

## Gene Expression Data Analysis Using the Gene Ontology

Current technologies for biological systems give scientists the ability to record thousands of measurements for each biomolecule, including genes, proteins and metabolites. Domain enhanced analysis (DEA) uses the Gene Ontology (GO) to guide analysis of such data with a goal of increased interpretability. DEA uses a "top-down" approach to perform domain aggregation by first combining gene expressions related to each GO term using the Partial Least Squares (PLS) procedure. The first scores from the PLS procedure applied to each GO term are used to test for differentially expressed patterns using a standard t test. We find the general t test inadequate for adjusting for the number of genes within each GO term. New tests are proposed by finding a more appropriate null distribution for each PLS score, a distribution that is adjusted for the size of the GO term. We also discuss the impact of using different two-class classification response variables, namely 0/1 or -1/1. Refreshments will precede the talk in the MATH Library Lounge at 3 pm.### Special Basic Skills Workshop, Dr. Thomas Backing, System and Technology Research, MATH Library Lounge

Friday, Sep 29 2:15 pm - 3:15 pm

## Working in Industry Q&A

An informal question and answer session with Dr. Thomas Backing who graduated with his PhD from Purdue University in Mathematics in 2016 and is currently working at System and Technology Research. He will give some general advice about working in industry as well as provide information about potential full-time and summer internship positions at System and Technology Research.Refreshments served in the Library Lounge

## Two Weeks

### Geometry/Geometric Analysis Seminar, Gabor Szekelyhidi, University of Notre Dame, MATH 731

Monday, Oct 2 3:30 pm - 4:20 pm

## Degenerations of C^n and Calabi-Yau metrics

I will describe a new family of complete Calabi-Yau metrics on C^n, with Euclidean volume growth. Similar constructions have also been given by Yang Li and Conlon-Rochon recently. A related construction, generalizing work of Hein-Naber, yields Calabi-Yau metrics on germs of certain isolated singularities, whose tangent cones have singular cross sections.## Spectral Indicator Method with Cayley Transformation for Eigenvalue Problems

Recently, a non-classical eigenvalue solver, called RIM, was proposed to compute (all) eigenvalues in a region on the complex plane. Without solving any eigenvalue problem, it tests if a region contains eigenvalues using an approximate spectral projection. Regions that contain eigenvalues are subdivided and tested recursively until eigenvalues are isolated with a specified precision. This makes RIM an eigensolver distinct from all existing methods. Furthermore, it requires no a priori spectral information. In this paper, we propose an improved version of RIM for non-Hermitian eigenvalue problems. Using Cayley transformation and Krylov subspace methods, the computation cost is reduced significantly. Effectiveness and efficiency of the new method are demonstrated by numerical examples and compared with 'eigs' in Matlab.Refreshments served in the Library Lounge prior to Colloquium.

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

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

## TBD

### Probability Seminar, Ibrahim Ekren, Michigan State University, UNIV 101

Wednesday, Oct 4 1:30 pm - 2:20 pm

## TBA

Refreshments served in the Library Lounge

### Basic Skills Workshop, Dr. Philip Mummert, Purdue University, REC 121

Thursday, Oct 5 10:30 am - 11:20 am

## Getting a Job at a Small College

What are liberal arts colleges looking for? What should job applicants expect? How do applications get noticed? What's really going on at each step of the hiring process? Dr. Phil Mummert, Assistant Department Head, will share some advice and field questions. He attended Cedarville University (a small liberal arts college) for undergrad, completed his PhD at Purdue (not a small school) in 2007, worked at Taylor University (small liberal arts college) from 2007-2014, and at Butler University for one year, where he also served on an employment search committee.Refreshments served in the Library Lounge

## Efficient Spectral and Spectral-Element Methods for Transformation Electromagnetics

In this talk, we present efficient spectral/spectral-element methods for acoustic and ectromagnetic wave scattering problems arisen from transformation electromagnetics (or optics). We advocate the use of Dirichlet-to-Neumann (DtN) transparent boundary conditions to reduce the unbounded problem to an equivalent boundary value problem. We provide semi-analytic techniques to seamlessly integrate global DtN boundary conditions with local spectral elements in both 2D and 3D by using special elemental transformations of curved elements. We also introduce a novel non-reflecting absorbing layer from the concept of inside-out (or inverse) invisibility cloak. We highlight the applications of the solvers for the simulations of electromagnetic cloaks.## Three Weeks

### Probability Seminar, David Sivakoff, Ohio State University, UNIV 101

Wednesday, Oct 11 1:30 pm - 2:20 pm

## TBA

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

## October

Refreshments served in the Library Lounge

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

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

## How Nonlocal Formulations are Changing the Modeling and Simulation Landscape at Sandia National Laboratories

Nonlocal formulations have continued to gain momentum due to a number of attractive features: they naturally handle discontinuities, inherently improve signal-to-noise ratios, and simplify discretization of complex domains. This talk will provide an overview of several application areas in which nonlocal formulations have been used to greatly extend modeling and simulation capabilities at Sandia. These areas include image processing, digital image correlation, hydraulic fracture modeling, and manufacturing process simulation and design. The talk will conclude with some remaining challenges to using nonlocal formulations more effectively. The goal of this talk is to get the audience to consider using nonlocal formulations, contribute to their development, and potentially work towards addressing some of these challenges. Full seminar abstractRefreshments served in the Library Lounge prior to Colloquium.

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

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

## TBA

### Probability Seminar, Anirban DasGupta, Purdue University, UNIV 101

Wednesday, Oct 18 1:30 pm - 2:20 pm

## The randomly deleted factorial and lacunary series

Refreshments served in the Library Lounge

### 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.Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

### CCAM Seminar, Dr. Aihua Wood, Air Force Institute of Technology, UNIV 103

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

## TBD

### Special Automorphic Forms and Representation Theory Seminar, Prof. Chandrasheel Bhagwat, IISER, BRNG 1260

Tuesday, Oct 24 1:30 pm - 2:20 pm

## TBA

Note the special date and time.Refreshments served in the Library Lounge prior to Colloquium.

### Probability Seminar, Tal Orenshtein, UniversitÅ½ de Lyon 1, UNIV 101

Wednesday, Oct 25 1:30 pm - 2:20 pm

## TBA

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

### Department of Statistics Research Colloquium, Philip Protter, Columbia University, GRIS 103

Friday, Oct 27 10:30 am - 11:30 am

## TBA

### CCAM Lunch Seminar, Prof. Guang Cheng, Purdue University, LWSN B134

Friday, Oct 27 11:30 am - 12:20 pm

## TBA

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

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

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

## TBD

Refreshments served in the Library Lounge prior to Colloquium.

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

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

## November

Refreshments served in the Library Lounge

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

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

## Title: TBA

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge prior to Colloquium.

### Department Colloquium, Prof. Kasso Okoudjou, University of Maryland, MATH 175

Tuesday, Nov 7 3:30 pm - 4:20 pm

## TBA

## TBA

Refreshments served in the Library Lounge

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

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

## Title: TBA

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

## 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.Refreshments served in the Library Lounge prior to Colloquium.

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

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

## TBD

## TBA

Refreshments served in the Library Lounge

### 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

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

## TBD

Refreshments served in the Library Lounge

### CCAM Seminar, Dr. Xiu Yang , Pacific Northwest National Lab, UNIV 103

Monday, Nov 27 4:30 pm - 5:20 pm

## Alternating direction method for enhancing sparsity of the representation of uncertainty

Abstract: Compressive sensing has become a powerful tool for uncertainty quantification when only limited data is available. We provide a general framework using alternating direction method to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion. This method identifies new sets of random variables through iterative rotations such that the new representation of the uncertainty using these variables is sparser. Consequently, we increase both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. We demonstrate the effectiveness of this method with applications in analyzing uncertainties in high-dimensional complex systems.Refreshments served in the Library Lounge prior to Colloquium.

Refreshments served in the Library Lounge

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

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

## Title: TBA

Refreshments served in the Library Lounge

## December

### CCAM Lunch Seminar, Prof. David Gleich, Purdue University, LWSN B134

Friday, Dec 1 11:30 am - 12:20 pm

## TBD

### CCAM Seminar, Prof. Padmanabhan Seshaiyer , National Science Foundation, UNIV 103

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

Refreshments served in the Library Lounge prior to Colloquium.

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge