**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**