## 2020 Diversity in Mathematics: Undergraduate Summer School Information and Registration

- Start Date: 08/04/2020
- End Date: 08/14/2020

Vancouver, BC

**Undergraduate Summer School Eligibility Requirements:**

The summer school is open to *female-identifying, non- binary and two- spririt undergraduate students* studying mathematics or a related discipline such as computer science, physics and statistics at a university in Canada or in the northwest United States, with at least one year of studies remaining in their program. Priority will be given to second and third-year students. Each participant will receive on-campus room and board and a possible allowance for travel expenses to and from Vancouver.

Please note that the purpose of the program is to introduce the undergraduate participants to a wide variety of professions and careers, in academia and in industry, where advanced mathematics is used every day with spectacular success. It is NOT a purely research-oriented or purely industry-oriented summer school, rather a sampler of different flavours of mathematics-based careers.

A new component of the program will facilitate effective engagement and interaction with high school students who are good at math, who may not have had enough opportunities to learn about the impact of advanced mathematics and who can thrive under the mentorship of bright and strong undergraduate women in STEM.

Please use the above information to assess your interest and fit for the program. Address these items adequately in your personal statement.

**Program delivery format: **

**Courses: **There will be mini-courses, running through the two weeks, taught by female instructors on the topic of their choice. The students will do group projects with presentations the last day for each course.

**Field Trips**:One day each week will be for field trips to businesses employing individuals in the Mathematical Sciences.

**Distinguished public lecture**: TBC

**Guest speakers and ****Panel discussions: **TBC

### 2020 Course Overview:

__Course 1: ____Inverse problems and images__

**Course Dates**: August 4- August 8 (inclusive)

**Course Instructor**: Tracey Balehowsky, University of Helsinki

**Brief Course Description:** Many problems which we would like to solve in the sciences can be abstractly described as follows: given our observations (measurements) of the system we seek to understand, determine the properties of the system which gave rise to the observations. Mathematically, we call this situation an inverse problem, since we know something about solutions (observations) to our model of the system, but we want to determine the coefficients of our model (which encode information about the system’s properties). In this course we will introduce inverse problems arising in imaging, such as computed tomography (CT scan) and magnetic resonance imaging (MRI). We will explore some mathematical techniques used for image construction, denoising, and sampling.

**Prerequisites**: Multivariable calculus, second year linear algebra (in particular comfortability with SVD, bases, eigenvalues and eigenspaces).

**Tech Requirements:** Access to computers with Matlab. I plan to have the student fill in some prewritten code to run.

__Course 2: ____Self-complementary graphs and cyclic hypergraph decompositions__

**Course Dates**: August 10- 14

**Course Instructors****:** Shonda Dueck, University of Winnipeg

**Prerequisites****:** Discrete Mathematics, Graph Theory, basic Group Theory is an asset (mainly Cyclic Groups).

**Course Description**: A hypergraph consists of a set of points called vertices, and a set of subsets of this vertex set called edges. A simple graph is a hypergraph in which every edge has cardinality 2. Hypergraphs are used to model many types of networks, such as transportation systems, the link structure of websites, and data organization networks. One interesting problem in hypergraph theory is that of decomposing a hypergraph into smaller subhypergraphs which all have the same structure. Such decompositions in which the subhypergraphs have desirable properties, such as high symmetry or regularity, are of special interest since they correspond to key structures in combinatorial design theory that have useful applications in cryptography.

We will begin by studying the self-complementary graphs. These are the simple graphs which are isomorphic to their complement, so a self-complementary graph and its complement together decompose the complete graph into two isomorphic subgraphs. We will determine necessary conditions on the order of the self-complementary graphs and look at some nice algebraic techniques for constructing them. The self-complementary graphs are well studied due to their relation to the graph isomorphism problem, which has unknown complexity. Next we will generalize this idea to study the self-complementary hypergraphs, using the same algebraic construction techniques we applied to graphs. We will also construct some self-complementary graphs and hypergraphs which have high symmetry using basic cyclic group theory. Finally, we will study the t-complementary hypergraphs, which are the parts in a cyclic decomposition of the complete hypergraph into t isomorphic hypergraphs. At the heart of this mini course is the study of how permutations of a given finite vertex set V act on the subsets of V, and some basic number theory will come into play.

**Tech Requirements****:** It might be helpful for students to have access to GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra. Distributed freely at https://www.gap-system.org/

**Application information**:

Interested participants are required to review the below information carefully. Application and registration to the Summer School is a two step system. Applicants must send in the information below. Once you qualify, you will receive an email from the organizers with the second step on registration and payment of the summer school fee ($100CAD). **Early applications are strongly encouraged as spaces may fill up early.**

Send an email to: diversity-ug@pims.math.ca.

Email Subject Line: 2020 DIVERSITY IN MATH: Summer School Application: Last Name, First Name

Email Contents:

a) A personal statement (300 words max) including why you would like to participate, the value of this workshop to you and how you have prepared for this summer school. Also indicate whether you will require accommodation on-campus.

b) CV

c) Informal transcript

d) Attach one letter of recommendation from your supervisor or other qualified persons. It should indicate why you are well suited to the summer school, and how you would benefit from attending.

Successfull applicants will receive:

- Accommodation at UBC and SFU dorms for the duration of the program (particpants will be housed in single rooms at the dorms)

- Some funding to defray travel costs to and from Vancouver (applicable to students outside the Vancovuer Lower Mainland)

- Coffee breaks during the summer school and a hosted lunch or dinner as part of the program.

__Dates__:

Arrivals and check-in to residence: August 3, 2020

Departures and check out: Aug 14, 2020

__Accommodation:__

Accommodation will be available for the undergraduate component only. Housing will be at the University of British Columbia dorms and at Simon Fraser University in Burnaby.

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