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# Linear Algebra

DMS Linear Algebra/Algebra Seminar
Dec 05, 2017 04:00 PM
Parker Hall 356

Speaker: Sima Ahsani

Title: Metrics on the manifold of positive definite matrices and matrix means

Abstract: I will talk about the set of positive definite matrices as a Riemannian manifold. Then I will introduce two metrics on this set and explain their basic properties. After describing their connection through the geometric mean of two positive definite matrices, similarities and differences between two metrics will be discussed.

DMS Linear Algebra/Algebra Seminar
Nov 28, 2017 04:00 PM
Parker Hall 356

Speaker: Samir Raouafi

Title: On the extension of the Kreiss Matrix Theorem

Abstract: Let A be a matrix with spectrum δ(A). The Kreiss Matrix Theorem (KMT), a well-known fact in applied matrix analysis, gives estimates of upper bounds for ∥An∥ if δ(A) is in the unit disc, or for ∥etA∥ if δ(A) is in the left-half plane based on the resolvent norm. In this talk, we shall discuss some extensions of this celebrated theorem to simply connected compact sets in the complex plane.

DMS Linear Algebra/Algebra Seminar
Nov 14, 2017 04:00 PM
Parker Hall 356

Speaker: Wei Gao

Title: Sign patterns that require H_n and its generalization to zero-nonzero patterns

Abstract: The refined inertia of a square real matrix is the ordered 4-tuple (n_+, n_-, n_z, 2n_p), where n_+ (resp., n_-) is the number of eigenvalues with positive (resp., negative) real part, n_z is the number of zero eigenvalues and 2n_p is the number of pure imaginary eigenvalues.

The set of refined inertias H_n=(0, n, 0, 0), (0, n-2, 0, 2), (2, n-2, 0, 0) is important for the onset of Hopf bifurcation in dynamical systems. In this talk, I will introduce some results about sign patterns, i.e., matrices whose entries are from the set {+, -, 0}, that require H_n.

Recently, Berliner et al. expend H_n to H_n* for zero-nonzero patterns, i.e., matrices whose entries are from the set {0, *}. In this talk, I will show that there is no zero-nonzero pattern that requires H_n*.​

DMS Linear Algebra/Algebra Seminar
Nov 07, 2017 04:00 PM
Parker Hall 356

Speaker: Luke Oeding

Title: Higher Order Partial Least Squares and an Application to Neuroscience.

Abstract: Partial least squares (PLS) is a method to discover a functional dependence between two sets of variables X and Y.   PLS attempts to maximize the covariance between X and Y by projecting both onto new subspaces. Higher order partial least squares (HOPLS) comes into play when the sets of variables have additional tensorial structure. Simultaneous optimization of subspace projections may be obtained by a multilinear singular value decomposition (MSVD). I'll review PLS and SVD, and explain their higher order counterparts. Finally I'll describe recent work with G. Deshpande, A. Cichocki, D. Rangaprakash, and X.P. Hu where we propose to use HOPLS and Tensor Decompositions to discover latent linkages between EEG and fMRI signals from the brain, and ultimately use this to drive Brain Computer Interfaces (BCI)'s with the low size, weight and power of EEG, but with the accuracy of fMRI.

DMS Linear Algebra/Algebra Seminar
Oct 31, 2017 04:00 PM
Parker Hall 356

Speaker: Reimbay Reimbayev

Title: Synchronization in Neuronal Networks, Part II

Abstract: In the second part of my talk I will concentrate on proving the stability of global synchronization manifold for the network of square-wave bursting neurons using semi-numerical tools and graph theoretical considerations.

DMS Linear Algebra/Algebra Seminar
Oct 24, 2017 04:00 PM
Parker Hall 356

Speaker: Huajun Huang

Title: The QR algorithm and Lie theoretical interpretation

Abstract: The QR algorithm for numerical computation of matrix eigenvalues was named by the editors of Computing in Science & Engineering as one of the top 10 algorithms in the 20th century. In this talk, I will briefly review the history and related algorithms, discuss the convergence behaviors in complex and real matrices settings, and extend the main results in the context of real semisimple Lie groups.

DMS Linear Algebra/Algebra Seminar
Oct 10, 2017 04:00 PM
Parker Hall 356

Speaker: Reimbay Reimbayev

Title: Synchronization in Neuronal Networks and more

Abstract: Synchronized neuronal firing is notoriously known to induce pathological brain states, such as epilepsy and Parkinson’s tremors. In this talk I will present my recent work published in PTRS. Using bifurcation theory and numerical simulations, I show why facilitating inhibition in a neuronal network might sometimes be counterproductive. I will also discuss a particular problem I have been interested from Graph Theory.

DMS Linear Algebar/Algebra Seminar
Oct 03, 2017 04:00 PM
Parker Hall 356

Speaker: Sunil Hans

Title: Annulus containing all the zeros of a polynomial

Abstract: As we know the properties of polynomials have been studied since the time of Gauss and Cauchy, and have played an important role in many scientific disciplines. Problems involving location of their zeros find important applications in many areas of applied mathematics. Since Abel and Ruffini proved that there is no general algebraic solution to polynomial equations of degree five or higher, the problem of finding an annulus containing all the zeros of a polynomial became much more interesting and over a period large number of results have provided in this direction.

This talk will introduce the new explicit bounds for the moduli of the zeros involving binomial coefficients, Fibonacci Numbers, Pell Numbers, Lucas Numbers and many more.

DMS Linear Algebra/Algebra Seminar
Sep 26, 2017 04:00 PM
Parker Hall 356

Speaker: Xavier Martínez-Rivera

Title: A new principal rank characteristic sequence

DMS Linear Algebra/Algebra Seminar
Sep 19, 2017 04:00 PM
Parker Hall 356

Speaker: Doug Leonard

Title: Desingularizing function fields

Abstract: I'll give a few examples of poorly coordinatized domains (and hence their function fields), and explain desingularization in terms of proper coordinatization and formal Laurent series. But, for a mostly linear algebra audience, I'll focus on what I call unimodular transformations (since they come from unimodular matrices), and how they do a better job of desingularization than sequences of blowups.

Last Updated: 08/21/2017