The CMS organizes three-hour mini-courses to add more value to meetings and to attract more students and researchers.

The mini-courses will be held on Friday, December 2, and include topics suitable for any interested parties. **You don’t have to be registered for the meeting in order to register for mini courses. **

**Registration fees for the mini-courses are as follows: **

| |

Student/ Postdocs (members) | $50 |

Student/ Postdocs (non-members) | $75 |

CMS Members | $100 |

CMS Non-Members | $150 |

RBC Sponsored Closing the Gap (Black, Indigenous, female-identifying, LGBTQ+, or person with disabilities; must be 15-29 years of age) – CMS student member ***Canadian citizens and permanent residents only | $25 |

## Mini-Course Schedule

#### Morning Courses : 9am – 12pm (Eastern Time)

### Introduction to Topological Data Analysis

Topological data analysis seeks to bring powerful tools from topology to bear on problems in data science, helping to elucidate the geometry and structure of diverse data sets. This minicourse will offer an introduction to relevant topological ideas and approaches, as well as demonstrating how they can be used in data science to solve real practical problems. Particular focus will be given to problems in unsupervised learning and exploratory data analysis where such tools are most effective.

Please note a version of this course was given at the 2019 Winter meeting.

### Pursuit-evasion games on graphs

In pursuit-evasion games, a set of pursuers attempts to locate, eliminate, or contain an evader in a graph. The rules, specified from the outset, greatly determine the difficulty of the questions posed above. For example, the evader may be visible, but the pursuers may have limited movement speed, only moving to nearby vertices adjacent to them. Central to pursuit-evasion games is the idea of optimizing certain parameters, such as the search number, burning number, or localization number.

In the mini-course, we will introduce several pursuit-evasion games on graphs and conjectures arising from their analysis. Finding the values, bounds, and algorithms to compute these graph parameters leads to topics intersecting graph theory, the probabilistic method, and geometry.

### Sphere packing and semidefinite programming

Packing problems can be found in mathematics, physics, computational chemistry, and coding theory, to name a few sciences. Most of them are fascinating and interesting, but also notoriously difficult. A breakthrough by Viazovska (awarded the Fields Medal this year) shows how much these problems are connected with number theory and algebraic geometry, among other parts of mathematics. The previous work of Cohn and Elkies (among others) shows that these problems are also connected with optimization, such as semidefinite programming. We shall consider the very basics of sphere packing and try some practical examples. No previous knowledge of semidefinite programming is required.

#### Afternoon Courses : 1pm – 4pm (Eastern Time)

### Instructional skills for new instructors

This mini course is open to everyone but is intended for novice mathematics instructors interested in developing and enhancing their instructional skills and practices, and their identities as instructors. The specific foci of the mini-course will depend on the people participating in the course – participants will focus on what matters to them! By the end of the mini-course, participants will be equipped with instructional practices that reflect their teaching philosophy and goals.

The mini course will make extensive use of participatory learning. Participants will design and deliver several mini-lessons and/or learning activities, and critically reflect on their experiences.

### Introduction to discrete quantum walks

Discrete quantum walks are motivated by search problems—one of the best known

quantum algorithms, Grover’s search, is a discrete quantum walk on the complete graph with loops. From an algebraic perspective, a discrete quantum walk is determined by a unitary matrix representation of some graph, and—just like the adjacency matrix and the Laplacian matrix—its spectrum contains important information about the graph, which can be used to study the behaviour of the walk.

In this mini-course, I will give an overview of different models of discrete quantum walks, and explore the relation between properties of these walks and properties of the underlying graphs. With the theory we developed, we will then treat problems such as quantum search, quantum state transfer, and simulations using continuous quantum walks.

This mini-course is based on the book, Discrete Quantum Walks on Graphs and Digraphs, by Chris Godsil and Hanmeng Zhan. The main tool for this course is linear algebra, and no knowledge of quantum physics is required.

### Machine Learning from the Perspective of Data Science

The purpose of this mini course is to provide beginners and advanced students/researchers with some general framework for facing real data-driven problems. We will use two case studies to provide some insights into the machine learning process from the perspective of data science. In our first case “Relevant features for Airbnb listing prices”, we will introduce a relatively comprehensive walkthrough of an exploratory data analysis process on an unfamiliar dataset. We will learn how to systematically approach investigating an unknown dataset while maintaining creativity to look for insights. In our second case “Prediction of fair market prices of used cars”, we will discuss the challenges of feature engineering in order to implement regression in real-world contexts and we will look at neural networks as an alternative to explicit feature engineering. This mini course is appropriate for both beginners and advanced students/researchers from different fields.

##### Friday, December 2

###### 1:00pm – 4:00pm (Eastern Time)

**Instructor: **Alexandre Odesski (Brock University)

### Multiplication kernels

Commutative associative multiplications on a space of functions can be defined in terms of multiplication kernels which are an infinite-dimensional analog of structure constants of multiplication in finite-dimensional case. Associativity constrain gives an integral equation for multiplication kernel. I will explain various ways of dealing with this integral equation in purely algebraic terms. In particular, connections with integrable systems will be discussed and a lot of examples will be constructed.

The course will be based on the paper:

M. Kontsevich, A. Odesskii, Multiplication kernels, Lett. Math. Phys. 111 (2021), no. 6, Paper No. 152, 59 pp.

The course will be accessible for graduate and even for strong undergraduate students. Moreover, I will describe a lot of hot open problems suitable for them to start work on.