Ryan Tully-Doyle, University of New Haven, in mini-symposium Matrix Analysis

Xuemei Chen, New Mexico State University, in mini-symposium Frame Theory and Data Science

Austin Reilley BensonCornell University, in mini-symposium Algebra and Tensor Spaces 

John SinkovicUniversity of Waterloo, in mini-symposium Combinatorial Matrix Theory

Pietro PaparellaUniversity of Washington, in mini-symposium Nonnegative Inverse Spectral Problems

MS1 – Algorithms for rank-structured matrices and low-rank approximation
Paola Boito, Gianna M. Del Corso, Yuli Eidelman & Luca Gemignani

MS2 – Cocliques and colourings
Gabriel Coutinho & Chris Godsil

MS3 – Combinatorial Matrix Theory
Bryan ShaderShaun FallatSteve Butler & Kevin Vander Meulen

MS4 – Evolution Algebras and non associative algebraic structures
Yolanda Cabrera Casado, Maria Inez Cardoso Gonçalves, Pablo Martín Rodríguez & Paula Cadavid

MS5 – Frame Theory and Data Science
Gitta Kutyniok & Deanna Needell

MS6 – Linear Algebra Education
Sepideh Stewart & Rachel Quinlan

MS7 – Linear Algebra and Quantum Information Science
Yiu-Tung PoonRaymond Nung-Sing Sze & Sarah Plosker

MS8 – Matrices over elementary divisor domains
Froilán M. Dopico & Vanni Noferini

MS9 – Matrix Analysis
James Pascoe & Miklos Palfia

MS10 – Matrix Equations and Matrix Inequalities
Fuzhen Zhang, Qing-Wen Wang & Tin-Yau Tam

MS11 – Matrix Techniques in Operator Theory and Operator Algebras
Hugo Woerdeman

MS12 – M-matrices and Inverse M-matrices: Applications and Generalizations
Minerva Catral & K.C. Sivakumar

MS13 – Multilinear Algebra and Tensor Spaces
David Gleich & Yang Qi

MS14 – Nonnegative Inverse Spectral Problems
Raphael Loewy & Ricardo L. Soto

MS15 – Numerical Approaches for Solving Large-Scale Sparse Systems
Xiao-Chuan Cai, Marcus Sarkis & Daniel Szyld

MS16 – Perturbations of matrix eigenstructures
Andrii Dmytryshyn, Stefan Johansson, Alexei Mailybaev & Amaury A. Cruz

MS17 – Solving large linear systems from oil reservoir simulation
Luiz Mariano Carvalho, Paulo Goldfeld & Michael Souza

MS18 – Spectral Graph Theory
Sebastian Cioaba, Jack Koolen & Leonardo de Lima

MS19 – Spectral inequalities
Enide Andrade, Maria Robbiano Bustamante & Geir Dahl

MS20 – Symbolic-numeric methods in Matrix Theory
Yao Sun, Dingkang Wang & Yang Zhang

MS21 – Zero Forcing, Propagation, Throttling: Variations and Applications
Mary Flagg, Jesse Geneson & Leslie Hogben

CT1 – APPLICATIONS OF LINEAR ALGEBRA
CT2 – COMBINATORICS AND MATRICES
CT3 – GRAPHS AND MATRICES
CT4 – MATRIX THEORY
CT5 – NUMERICAL LINEAR ALGEBRA
CT6 – POLYNOMIALS AND MATRICES
CT7 – THEORY OF OPERATORS
CT8 – TOPICS IN LINEAR ALGEBRA

MC 1: Graph Theory and Quantum Walks

Gabriel Coutinho, Universidade Federal de Minas Gerais, UFMG, Brazil

Chris Godsil, University of Waterloo, Canada

Abstract: The study of quantum walks is a relatively new field with relations to Graph Isomorphism, quantum search algorithms and implementation of gate-based quantum algorithms. It is an area which has seen many successful applications of methods in linear algebra and graph theory, especially eigenvalue techniques in graphs. In this mini-course, we will cover basic definitions and properties of discrete and continuous time quantum walks on graphs. In the first lecture, we will talk about state transfer in graphs. In the second lecture, we will talk about the average mixing matrix which would be the analogue of a stationary distribution of a random walk. In the third, we will present the well-known Grover search algorithm as a quantum walk on a graph. In the last lecture, we will discuss many graph invariants given by quantum walks, some of which have inspired possible Graph Isomorphism algorithms. We will not assume any prior knowledge of quantum physics.


MC 2: Nonlinear techniques in matrix theory

Carlos Tomei, Pontifícia Universidade Católica, PUC-Rio, Brazil 

Tiago Pereira, Universidade de São Paulo, São Carlos, Brazil

Abstract: Some fundamental objects in Linear Algebra are hardly linear. In this short course, we present examples of the interplay between nonlinear techniques and aspects of spectral theory.  We apply differential equations, some Lie algebra reasoning, topological degree theory, some basic representation theory  to issues related to the (numerical or explicit) computation of eigenvalues, to inverse spectral problems and to the contextualizing of some familiar spectral properties.  Pre-requisites are minimal – one should be at ease with the standard material in undergraduate courses.

To appear