Program

To appear

Invited Mini-Symposia

Matrix Analysis
James Pascoe & Miklos Palfia

Frames
Gitta Kutyniok & Deanna Needell

Matrix Equations and Matrix Inequalities
Fuzhen Zhang & Qing-Wen Wang

Algebra and Tensor Spaces
David Gleich & Yang Qi

Linear Algebra and Quantum Information Science
Yiu-Tung Poon, Raymond Nung-Sing Sze & Sarah Plosker

Combinatorial Matrix Theory
Bryan Shader, Shaun Fallat, Steve Butler & Kevin Vander Meulen

Matrix Techniques in Operator Theory and Operator Algebras
Hugo Woerdeman

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

Linear Algebra Education
Sipedeh Stewart & Rachel Quinlan

Nonnegative Inverse Spectral Problems
Raphael Loewy & Ricardo L. Soto

 

Contributed Mini-Symposia

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

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

Cocliques and colourings
Gabriel Coutinho & Chris Godsil

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

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

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

From operator systems to non-commutative graphs
Ivan G. Todorov & Andreas Winter

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

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

Matrices over elementary divisor domains
Froilan Cesar Martinez Dopico & Vanni Noferini

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

Spectral inequalities
Enide Andrade, Maria Robbiano Bustamante & Geird Dahal

To appear

MC 1: Graph Theory and Quantum Walks

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

Krystal Guo, Simons Institute for the Theory of Computing

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.

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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