David Bindel, Cornell, USA, SIAG-LA Lecturer
Christoph Helmberg, Technische Universität Chemnitz, Germany
Leslie Hogben, Iowa State University, USA
Apoorva Khare, Indian Institute of Science, Bangalore, India
Igor Klep, University of Auckland, New Zealand
Gitta Kutyniok, Technische Universität Berlin, Germany
Joseph Landsberg, Texas A&M, USA, LAA Lecturer supported by Elsevier
Federico Poloni, Pisa University, Italy
Nikhil Srivastava, University of California, Berkeley, USA
Yuan Jin Yun, Universidade Federal do Paraná, Brazil
To appear
Topic: Matrix Analysis
Organizers: James Pascoe & Miklos Palfia
Topic: Frames
Organizers: Gitta Kutyniok & Deanna Needell
Topic: Matrix Equations and Matrix Inequalities
Organizers: Fuzhen Zhang & Qing-Wen Wang
Topic: Algebra and Tensor Spaces
Organizers: David Gleich & Yang Qi
Topic: Linear Algebra and Quantum Information Science
Organizers: Yiu-Tung Poon, Raymond Nung-Sing Sze & Sarah Ploskers
Topic: Combinatorial Matrix Theory
Organizers: Byan Shader, Shaun Fallat, Steve Butler & Kevin Vander Meulen
Topic: Matrix Techniques in Operator Theory and Operator Algebras
Organizer: Hugo Woerdeman
Topic: Spectral Graph Theory
Organizers: Sebastian Cioba, Jack Koolen & Leonardo Lima
Topic: Linear Algebra Education
Organizers: Sipedeh Stewart & Rachel Quinlan
Topic: Nonnegative Inverse Spectral Problems
Organizers: Raphael Loewy & Ricardo L. Soto
To appear
To appear
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.
Carlos Tomei, Pontifícia Universidade Católica, PUC-Rio, Brazil
To appear