# Calendar

## Yesterday

## A Problem of Bombieri for Univalent Functions

### Geometric Analysis Seminar, Debraj Chakrabarti, Central Michigan University, MATH 731

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

## The $\overline{\partial}$ Problem on Annuli

Abstract: We consider the problem of establishing $L^2$-estimates for the Cauchy-Riemann equations on annuli between pseudoconvex domains. Relating the $L^2$-Dolbeault cohomology with the Cech cohomology with respect to the sheaf of $L^2$ holomorphic functions, we show that such estimates exist for certain piecewise smooth holes. This leads to estimates for the $\overline{\partial}$-problem on piecewise smooth domains in the Sobolev space $W^1$.### 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.### Bridge to Research Seminar, Dr. Steven Dong, Purdue University, UNIV 303

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

## Modeling, Formulation and Simulations

Abstract: This talk aims to provide an overview of our research work and a discussion of potential opportunities for people interested in this area. We focus on the development of effective and efficient mathematical models and numerical techniques, and the application of such techniques to explore and illuminate fluid- and solid-related phenomena. I will first touch on several areas related to our works, and then discuss in relative detail the modeling and computational issues related to multiphase flows consisting of an arbitrary number of immiscible incompressible fluid components. Some numerical examples and test simulations will be provided.## Today

## Functional Limit Theorems for Long Memory, Heavy Tailed Processes

Abstract: We establish a functional central limit theorem for long memory stationary infinitely divisible processes with heavy tailed marginals. The class of central limit theorems we consider involves a significant interaction of probabilistic and ergodic theoretical ideas and tools. The limiting process constitutes a new class of stable processes and is expressed in terms of an integral representation involving a stable random measure, due to the heaviness of marginal tails, and the Mittag-Leffler process, due to long memory. If, in particular, the original sequence has negative dependence, the Brownian motion appears as well in the limiting process, due to the second-order cancellation property.This is joint work with Gennady Samorodnitsky (Cornell) and Paul Jung (University of Alabama).

### Department of Mathematics Colloquium, Xueyu Zhu, University of Iowa, MATH 175

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

## Fast Numerical Methods for Uncertainty Quantification in High Dimensional Problems

Abstract: Development of efficient numerical methods for the solution of problems with high-dimensional stochastic inputs has been a subject of active research in computational sciences and engineering. This is motivated by the need to reduce the computational cost of Uncertainty Quantification (UQ). In this talk, I will discuss several recently developed UQ algorithms that are particularly suitable for high dimensional large scale simulations. More specifically, we present multifidelity stochastic collocation methods. The methods combine the computational efficiency of low-fidelity models with the high accuracy of expensive high-fidelity models. The methods can be useful when the computational resources are limited. And they are non-intrusive and applicable to black-box simulation tools.Refreshments will be served in the Math Library Lounge at 4:00 p.m.

## Tomorrow

### Spectral and Scattering Theory Seminar, Antonio SaBarreto, Purdue University, MATH 731

Wednesday, Sep 28 1:30 pm - 2:30 pm

## Time Dependent Scattering on Asymptotically Hyperbolic Manifolds

Abstract: We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the fundamental solution of the wave operator on asymptotically hyperbolic manifolds. If there are no trapped geodesics, this formula is used to show that the scattering operator is a Fourier integral operator that quantizes the scattering relation.## Generalized Sylvester Forms and Equations of Rees Algebras

Abstract: The Rees algebra of an ideal I is the coordinate ring of the blowup along V(I), and contains information about the powers of I. When I is an ideal in a polynomial ring generated by forms of the same degree, the Rees algebra is also the coordinate ring of the graph of a rational map between projective spaces. It is an important problem to determine the defining equations of the Rees algebra of an ideal.Recently, there has been some success using Sylvester forms to compute these equations in special cases. I will present a generalization of Sylvester forms that can be used to find the high-degree equations of Rees algebras over the polynomial ring $k[x,y]$.

### Algebraic Geometry Seminar, Michael Temkin, Hebrew University of Jerusalem, REC 315

Wednesday, Sep 28 2:45 pm - 3:45 pm

## Topological Transcendence Degree

Abstract: my talk will be devoted to a basic theory of extensions of complete real-valued fields L/K. Naturally, one says that L is topologically-algebraically generated over K by a subset S if L lies in the completion of the algebraic closure of K(S). One can then define topological analogues of algebraic independence, transcendence degree, etc. These notions behave much wierder than their algebraic analogues. For example, there exist non-invertible continuous K-endomorphisms of the completed algebraic closure of K(x). In my talk, I will tell which part of the algebraic theory of transcendental extensions extends to the topological setting, and which part breaks down.### Informal Algebraic Geometry Seminar, Harrison Wong, Purdue University, REC 315

Wednesday, Sep 28 3:45 pm - 4:45 pm

## Grothendieck Topologies

### Student Colloquium, Mr. Yingwei Wang, Purdue University, REC 307

Wednesday, Sep 28 4:30 pm - 5:30 pm

## An Introduction to Muntz Polynomials with Applications to Numerical Solutions for Differential Equations

Abstract: In general, solutions to the Laplacian equation enjoy relatively high smoothness. However, they can exhibit singular behaviors at domain corners or points where boundary conditions change type. In this talk I will focus on the mixed Dirichlet-Neumann boundary conditions for Laplacian equation, and discuss how singularities in this case adversely affect the accuracy and convergence of standard numerical methods. Then, starting from the celebrated Weierstrass theorem on polynomial approximation, I will describe the approximation theory related to the so called Muntz polynomials, which can be viewed as a generalization of usual polynomials. Additionally, I will illustrate the idea of Muntz-Galerkin methods, and show that how they can overcome the difficulties to achieving high order accuracy for the problems with singularities.## Thursday

## Boundary Bubbling Analysis of Approximate Harmonic Maps Under Weak Anchoring Condition in Dimension Two

Abstract: We consider a sequence of weakly convergent, approximate harmonic maps $u_k$ from a two dimensional domain $\Omega$ into a compact Rimenanian manifold $(N,h)$ under a weak anchoring condition $g:\partial\Omega\to N$, which can be viewed as critical points of $$ 1/2\int_\Omega (|Du|^2+\langle\tau, u\rangle)+w/2\int_{\partial\Omega}|u-g|^2 $$ where $\tau$ is a given tension field. Under mild conditions on $\tau_k$ and $g_k$, we obtain a global energy quantization result, which accounts for the loss of energy by a finite number of harmonic $2$ spheres.### Foundations of Math Seminar, Ben McReynolds, Purdue University, BRNG B230

Thursday, Sep 29 4:00 pm - 5:30 pm

## What Is An Algebra?

Abstract: This seminar is a revamped version of the seminar previously known as the "Secret Seminar". The talks will be informal and educational. Each topic will be covered for as long as there is interest and need for further discussion. The first topic will focus on simple and semisimple algebras over fields. We will focus first on examples of such algebras and some of the basic structure theory of Artin and Wedderburn. Topics I plan on touching on through the entire lecture series will be Brauer groups, Skolem-Noether Theorem, subfields of simple algebras, involutions on simple/semisimple, and the local-to-global properties of simple algebras over number fields. I will also, when relevant, discuss where these objects arise in context to geometric and algebro-geometric objects. I anticipate that the lecture series will last for 2-4 lectures.### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Sep 29 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Number Theory Seminar, Mr. Jeremy Fuller, Purdue University, MATH 731

Thursday, Sep 29 4:30 pm - 5:30 pm

## Induced Characters and Frobenius Reciprocity

Abstract: We discuss Chapter 19.3 of Summit and Foote’s Abstract Algebra.## Friday

## What Can Computational Models Tell Us About How the Brain Automatizes Sequence Production?

ABSTRACT: Most behaviors unfold in time and include a sequence of sub-movements or cognitive activities. In addition, most behaviors are automatic and repeated daily throughout life. Yet, relatively little is known about the neurobiology of automatic sequence production. Past research suggests a gradual transfer from the associative striatum to the sensorimotor striatum, but a number of more recent studies challenge this role of the basal ganglia in automatic sequence production. In this article, we propose a new neurocomputational model of automatic sequence production in which the main role of the basal ganglia is to train cortical-cortical connections within the premotor areas that are responsible for automatic sequence production. The new model is used to simulate four different data sets from human and non-human animals, including (1) behavioral data (e.g., response times), (2) electrophysiology data (e.g., single-neuron recordings), (3) macro-structure data (e.g., transcranial magnetic stimulation), and (4) neurological circuit data (e.g., inactivation studies). We conclude with a comparison of the new model with existing models of automatic sequence production and discuss a possible new role for the basal ganglia in automaticity.## Next Week

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

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

## The Primitive Equations on Bounded Domains: Theoretical and Numerical Applications

Abstract: We will consider in this talk some singular perturbations and boundary layers related to the Primitive Equations, mode by mode and then globally. In the presence of boundaries, the behavior of the solutions to the Primitive Equations at small viscosity will be studied. Furthermore, we also investigate a Hybrid Finite Volume method adapted to the boundary layer profile. This is a simple preview of this method applied to the barotropic mode.### Department of Mathematics Colloquium, Ernie Croot, Georgia Institute of Technology, MATH 175

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

## New Applications of the Polynomial Method to Problems in Combinatorics

Abstract: In this talk, based on work joint with Peter Pach and Seva Lev, I will present some new results on applying algebra to showing that subsets of $(Z/4Z)^n$ of size at least about $3.62^n$ (for n sufficiently large) contain three-term arithmetic progressions. I will also discuss extensions of this work to $Fp^n$, due to Ellenberg and Gijswijt.Refreshments will be served in the Math Library Lounge at 4:00 p.m.

### Spectral and Scattering Theory Seminar, Ting Zhou, Northeastern University, MATH 731

Wednesday, Oct 5 1:30 pm - 2:30 pm

## Inverse Problems for Nonlinear Wave Equations with a Null Form

Abstract: We consider inverse problems for semilinear wave equations on Lorentzian manifolds with a quadratic form satisfying the classical null condition. Under some assumptions on the quadratic form, we prove that from the source-to-solution map, one can determine the Lorentzian metric up to diffeomorphisms. If the metric is known a priori, some information about the quadratic term can also be determined. This is a joint work with Dr. Yiran Wang.### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Oct 6 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Special Department of Mathematics Colloquium, Professor Ken Ono, Emery University, BRNG 2280

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

## TBA

## Two Weeks

### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Oct 13 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.## Three Weeks

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

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

## Diffraction in Spectral and Scattering Theory

Abstract: The diffraction of waves is a phenomenon whose study dates back to at least the 17th century, but remains a challenge for rigorous analysis. I will discuss some recent work on the phenomenon of diffraction by conic singularities, and its application to the analysis of the spectrum of the Laplace operator and the distribution of resonances in scattering theory. We expect that an acoustic wave striking the exterior of a polygon should cause prolonged ringing ("resonance") which would not be present for a smooth obstacle, and I will present some results to substantiate this claim.Refreshments will be served in the Math Library Lounge at 4:00 p.m.

### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Oct 20 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.## October

### CCAM Seminar, Prof. Yingda Cheng, Michigan State University, REC 114

Monday, Oct 24 4:30 pm - 5:30 pm

## A Sparse Grid Discontinuous Galerkin Method for High-Dimensional Transport Equations

Abstract: In this talk, we present a sparse grid discontinuous Galerkin (DG) scheme for transport equations and applied it to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG schemes for hyperbolic problems and is proven to be $L^2$ stable and convergent. A major advantage of the scheme lies in its low computational and storage cost due to the employed sparse finite element approximation space. This attractive feature is explored in simulating Vlasov and Boltzmann transport equations. We also discuss extension of the scheme to adaptive sparse grid methods.### 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.### Automorphic Forms and Representation Theory Seminar, Professor Matthias Strauch, Indiana University, BRNG 1260

Thursday, Oct 27 1:30 pm - 3:00 pm

## TBA

### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Oct 27 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.## November

### Department of Mathematics Colloquium, Professor Andreas Seeger, University of Wisconsin, Madison, MATH 175

Tuesday, Nov 1 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Automorphic Forms and Representation Theory Seminar, Dr. Hansheng Diao, Princeton University, BRNG 1260

Thursday, Nov 3 1:30 pm - 3:00 pm

## TBA

### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Nov 3 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### CCAM Distinguished Seminar, Professor Roger Temam, Indiana University, LWSN 1142

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

## TBA

### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Nov 10 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.## 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.

### Automorphic Forms and Representation Theory Seminar, Professor Yifeng Liu, Northwestern University, BRNG 1260

Thursday, Nov 17 1:30 pm - 3:00 pm

## TBA

### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Nov 17 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Computational & Applied Mathematics Seminar, Professor Greg Beylkin, University of Colorado at Boulder, REC 114

Monday, Nov 21 4:30 pm - 5:30 pm

## TBA

https://amath.colorado.edu/faculty/beylkin/### 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.### OFFICIAL UNIVERSITY HOLIDAY, ALL OFFICES ARE CLOSED IN OBSERVANCE OF THANKSGIVING

Thursday, Nov 24 - Saturday, Nov 26

### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Nov 24 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Joint CS Colloquium and CCAM Seminar, Professor Jonathan Weare, University of Chicago, LWSN 3201

Monday, Nov 28 3:30 pm - 4:30 pm

## TBA

### 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

### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

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

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Department of Mathematics, Professor Andrew Putman, University of Notre Dame, MATH 175

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

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Dec 8 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Dec 15 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Dec 22 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Dec 29 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.## 2017

### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Jan 5 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Jan 12 4:30 pm - 5:30 pm

## Fastest Algorithms for Structured Matrices via Algebra

Abstract for the Talk: We show that in many instances, at the heart of a problem in numerical computation sits a special 3-tensor, the structure tensor of the problem that uniquely determines its underlying algebraic structure. Any decomposition of the structure tensor into rank-1 terms gives an explicit algorithm for solving the problem. The rank of the structure tensor measures the speed of the fastest possible algorithm for the problem, whereas the nuclear and spectral norms quantify the numerical stability of the stablest algorithm for the problem. We will determine the fastest algorithms for the basic operation underlying Krylov subspace methods --- the structured matrix-vector products for sparse, banded, triangular, symmetric, circulant, Toeplitz, Hankel, Toeplitz-plus-Hankel, BTTB matrices --- by analyzing their structure tensors. This is joint work with Ke Ye.### Real Algebraic Geometry Seminar, Lek-Heng Lim, University of Chicago, REC 112

Thursday, Jan 19 4:30 pm - 5:30 pm