Mathematics

The Study of Wave Turbulence: A Meeting Ground for Mathematical Techniques

Speaker: 
Gigliola Staffilani
Date: 
Thu, Oct 15, 2026
Location: 
Online
Zoom
Conference: 
PIMS Network Wide Colloquium
Abstract: 

Wave turbulence theory is a rich and expansive field, aiming to provide a framework for understanding how waves interact across different settings. Wave interactions occur over a wide range of scales and media—spanning from gravitational waves in the cosmos to ripples on the ocean’s surface, from the swirling patterns in a morning cup of coffee to quantum particles behaving as wave packets. Despite their ubiquity, these phenomena pose significant challenges to rigorous mathematical analysis. Yet, it is precisely this difficulty that has inspired mathematicians to develop powerful and elegant interdisciplinary methods. In this talk I will explore some of these approaches, highlighting both the remarkable progress achieved and the intriguing open questions that continue to drive research in this area.

Class: 
Scientific
Subject: 
Mathematics

A filtered basis for Haiman ideals

Speaker: 
Josh Turner
Date: 
Wed, Oct 14, 2026
Location: 
PIMS, University of British Columbia
Online
Zoom
Conference: 
Emergent Research: The PIMS Postdoctoral Fellow Seminar
Abstract: 

We will talk about the ideal $J$ generated by antisymmetric polynomials in two sets of variables and its powers, and discuss how these Haiman ideals are connected to link homology, geometry, and other combinatorial objects of interest. We will then show how to reinterpret recursions for computing link homology into a method for constructing a free, filtered basis for $J^d$ over $C[y]$.

Class: 
Scientific
Subject: 
Mathematics

There is one mathematics

Speaker: 
Lior Silberman
Date: 
Fri, Oct 9, 2026
Location: 
PIMS, University of British Columbia
Online
Zoom
Conference: 
UBC Mathematics Department Colloquium
Abstract: 

In this metamathematical talk I shall argue that we genuinely belong
under one roof: that no matter how we self-identify, in an important
sense we all do the same thing. Recent developments have made the
question "what is it that we do?" even more important.

The mathematical vehicle carrying the metamathematics will be problems
that start in mathematical physics, but reach numerical methods, number
theory, and even mathematical logic.

Most of the talk should be accessible to undergraduate students.

Class: 
Scientific
Subject: 
Mathematics

Topological methods for Artificial Intelligence

Speaker: 
Gunnar Carlsson
Date: 
Thu, Oct 8, 2026
Location: 
Online
Zoom
Conference: 
PIMS Network Wide Colloquium
Abstract: 

The recent striking developments in artificial intelligence underscore the idea that we need to (a) understand better what goes on inside neural networks, (b) thereby gain more control over them and (c) develop methods that are less expensive and apply directly to specialized situations. In this talk, I will talk about work on methods using topological methods to address these three problems. In particular, I will include numerous examples.

Class: 
Scientific
Subject: 
Mathematics

A quantum walk in a park

Speaker: 
Hermie Monterde
Date: 
Wed, Oct 7, 2026
Location: 
PIMS, University of Regina
Online
Zoom
Conference: 
Emergent Research: The PIMS Postdoctoral Fellow Seminar
Abstract: 

A network of interacting qubits, usually subatomic particles, can be modelled by a connected weighted undirected graph G. A quantum walk on G is a deterministic process that describes the propagation of quantum states in the network represented by G. In this talk, we give a gentle introduction to the theory continuous quantum walks and explore the many interesting types of quantum state transfer that occur in a graph. Throughout, we endeavour to highlight the tools imported from algebraic graph theory and combinatorial matrix analysis. If time permits, then we also discuss several open problems. This is joint work with two groups, the first one is with Dr. Karen Meagher and Dr. Tung Nguyen, and the second one is a project with Joy Cooper, Homer de Vera, Alireza Talebpour and Ruth Wang that emanated from the PIMS First Year Interest Group on Continuous Quantum Walks.

Class: 
Scientific
Subject: 
Mathematics

Studying equivariant structures using transfer systems and Rubin functors

Speaker: 
Danika Van Niel
Date: 
Tue, Sep 15, 2026
Location: 
PIMS, University of British Columbia
Abstract: 

Transfer systems are combinatorial objects that encode information about equivariant operations. More precisely, a transfer system encodes the transfers (or wrong-way maps) carried by algebras over certain equivariant operads. Thus, transfer systems allow us to use combinatorial tools to study equivariant homotopy theory. Compatible pairs of transfer systems, which are a pair of transfer systems satisfying certain conditions, correspond to multiplicative structures compatible with an underlying additive structure. In particular, compatible pairs are closely related to $N_\infty$-operads which encode commutative structures in equivariant homotopy theory.

In this talk we introduce transfer systems, compatible pairs, and discuss how Rubin functors significantly aid our study of said transfer systems and their pairs. The work discussed in this talk is from two separate projects, the first is joint with DeMark, Hill, Kamel, Niu, Stoeckl, and Yan, and the second is joint with Darnall, Klanderman, Lewis, Shibata, and Trimble.

Class: 
Scientific
Subject: 
Mathematics

Minicourse on model categories - Lecture 2 of 3

Speaker: 
Inna Zakharevich
Date: 
Mon, Jun 22, 2026
Location: 
PIMS, University of Regina
Conference: 
Summer School on Homotopy Colimits
Abstract: 

This is the second of a three lecture course on model categories from the Summer School on Homotopy Colimits, held at the University of Regina.

Class: 
Scientific
Subject: 
Mathematics
Topology

Minicourse on model categories - Lecture 1 of 3

Speaker: 
Inna Zakharevich
Date: 
Mon, Jun 22, 2026
Location: 
PIMS, University of Regina
Conference: 
Summer School on Homotopy Colimits
Abstract: 

This is the first of a three lecture course on model categories from the Summer School on Homotopy Colimits, held at the University of Regina.

Class: 
Scientific
Subject: 
Mathematics
Topology

Equivariant homotopy theory - Lecture 3 of 3

Speaker: 
Anna Marie Bohmann
Date: 
Thu, Jun 25, 2026
Location: 
PIMS, University of Regina
Conference: 
Summer School on Homotopy Colimits
Abstract: 

This is the third of a three lecture course on equivariant homotopy theory from the Summer School on Homotopy Colimits, held at the University of Regina.

Class: 
Scientific
Subject: 
Mathematics
Topology

Equivariant homotopy theory - Lecture 2 of 3

Speaker: 
Anna Marie Bohmann
Date: 
Wed, Jun 24, 2026
Location: 
PIMS, University of Regina
Conference: 
Summer School on Homotopy Colimits
Abstract: 

This is the second of a three lecture course on equivariant homotopy theory from the Summer School on Homotopy Colimits, held at the University of Regina.

Class: 
Scientific
Subject: 
Mathematics
Topology

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