Fall 2025 Term

The purpose of the AARMS Advanced Course program is to give graduate students and upper year undergraduates from AARMS Member Universities an opportunity to take courses not offered at their home institution free of charge. In Fall 2025, the courses listed below will be offered in an exclusively online format.

Students may be able to claim credit for AARMS Advanced Courses from their home institution using mechanisms similar to the AARMS Summer School. Students hoping to receive academic credit for courses in this program are strongly encouraged to consult with their home institution about this process before the start of lectures.

Both students and instructors should consult the frequently asked questions.  Please send any addition questions about this program to Andrew Irwin.

Important dates

  • August 20, 2025: Application opens for AARMS Advanced courses (applications will be accepted on a rolling basis)
  • September 20, 2025: Last deadline for students to join the class;

Registration

To register for an AARMS Advanced Course in Fall 2025 please contact the instructor directly.  Send a statement of interest to the instructor listed below indicating why you wish to take the class and listing previous courses relevant to the topic.

Dr. Jeannette Janssen
E-Mail: jeannette.c.m.janssen@gmail.com

Dr. Yorck Sommerhäuser
E-Mail: sommerh@mun.ca

 

 

Discrete Random Structures

Jeannette Janssens webDr. Jeannette Janssen, Dalhousie University

This course will cover basics of probability and stochastic processes, and then focus on areas where probability and combinatorics interact. Topics include: probabilistic method, stochastic graph models for complex networks, probabilistic algorithms. Probabilistic techniques include: expectation and concentration of random variables, stochastic processes, conditional expectation, Markov chains, martingales, branching processes. All of these concepts will be applied to random graphs and other discrete structures.

Representation Theory

Dr. Yorck Sommerhäuser (Memorial University)

A representation is the concrete realization of an abstract algebraic object by linear transformations of some vector space. If this vector space is finite-dimensional, these linear transformations can be expressed as matrices.

Representations can be studied for many algebraic objects, such as groups, both finite and infinite, associative algebras, Lie algebras,
and many others. In this course, we will concentrate on finite-dimensional representations of finite groups, with special emphasis on the symmetric group. We will begin with developing the theory of group characters, where we in particular prove their orthogonality relations and explain the notion of a character table. We will then illustrate these concepts in the case of the symmetric group, whose representations will be constructed with the help of Young tableaux. We will then compute the characters of the symmetric group with the help of various character formulas, such as the Frobenius character formula.

The textbook for the course is “The Symmetric Group” by B. Sagan, published by Springer-Verlag in the Graduate Texts in Mathematics series. Prerequisites for the course are a basic knowledge of group theory and a good understanding of linear algebra. Concepts from multilinear algebra, such as tensor products and symmetric powers, will be needed only occasionally.