Courses

Algebraic cycles and Hodge theory, I
These lectures form an expanded version of a series of lectures delivered by Lewis during 13-19 August 2000 at the Instituto de …
Last updated on Aug 6, 2024 external
A Primer to Arithmetic Statistics
In the past 25 years or so, the subject of “Arithmetic Statistics”, beginning with the work of Bhargava’s success in …
Last updated on Feb 20, 2025 ongoing
Advanced studies in Theoretical and Computational Biology

The purpose of this graduate course is to equip graduate students with cutting-edge techniques in data-driven mathematical and …

Last updated on Feb 20, 2025 ongoing
Algebraic Topology
The course is a first semester of algebraic topology. Broadly speaking, algebraic topology studies spaces and shapes by assigning …
Last updated on Feb 20, 2025 ongoing
Analytic and diophantine number theory with applications to arithmetic geometry
This course provides an introduction into analytic number theoretic methods with applications to arithmetic geometry. We will study …
Last updated on Feb 20, 2025 ongoing
Extremal Combinatorics

This course covers classical problems and modern techniques in extremal combinatorics. The first part of the course is on extremal …

Last updated on Feb 20, 2025 past
Fundamental models in fluid dynamics
The course will be an introduction to the behaviour of fluids (liquids and gases) from an applied math perspective, starting with an …
Last updated on Feb 20, 2025 ongoing
Introduction to Cohomology of Arithmetic Groups
The most basic example of an arithmetic group is $\Gamma=SL_n(Z),$ and understanding the cohomology of this group (and its close …
Last updated on Feb 20, 2025 past
Mathematical Classical Mechanics
This course presents classical mechanics to a mixed audience of mathematics and physics undergraduate and graduate students. It is …
Last updated on Feb 20, 2025 ongoing
Mathematical Ecology - Nonlinear PDE Models
In this course we are learning to build and analyse nonlinear differential equation models. The focus of the course will be models of …
Last updated on Feb 20, 2025 ongoing
Spectral Methods for PDEs
Spectral methods are numerical methods for solving PDEs. When the solution is analytic, the convergence rate is exponential. The first …
Last updated on Feb 20, 2025 ongoing
Stochastic Analysis-Stochastic Differential Equations
This is a one semester three credit hour course. We shall first briefly introduce some basic concepts and results on stochastic …
Last updated on Feb 20, 2025 ongoing
Topics in Mathematical Biology: biological image data and shape analysis
Advances in imaging techniques have enabled the access to 3D shapes present in a variety of biological structures: organs, cells, …
Last updated on Feb 20, 2025 past
Translation Surfaces
Translation surfaces and their moduli spaces have been the objects of extensive recent study and interest, with connections to widely …
Last updated on Mar 25, 2025 upcoming
Algebraic and probabilistic techniques in combinatorics
The course will provide an introduction to algebraic and probabilistic techniques in combinatorics and graph theory. The main topics …
Last updated on May 23, 2024 past
Algebraic Number Theory

This will be a standard graduate number theory course. Topics will include:

  • Number fields, rings of integers, ideals and unique …
Last updated on May 23, 2024 past
Computer Algebra
A course on algorithms for algebraic computation and tools for computing with multivariate polynomials, polynomial ideals, exact linear …
Last updated on Jan 29, 2024 past
Ergodic Theory
Ergodic theory is the study of measure-preserving transformations. These occur naturally in an array of areas of mathematics (e.g. …
Last updated on May 23, 2024 past
Formalization of Mathematics
The last few years have seen amazing advances in interactive proof assistants and their use in mathematics. For example, Lean’s …
Last updated on Jan 29, 2024 past
Hodge theory, Deligne cohomology and algebraic cycles
Students taking this course will be exposed to the latest developments in the field of regulators algebraic cycles. This course was …
Last updated on May 23, 2024 past