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Haggai Liu

Simon Fraser University
Moduli Spaces of Weighted Stable Curves and their Fundamental Groups

February 25, 2025

ESB 4133 (PIMS library)

The Deligne-Mumford compactification, $\overline{M_{0,n}}$, of the moduli space of $n$ distinct ordered points on $\mathbb{P}^1$, has many well understood geometric and topological properties. For example, it is a smooth projective variety over its base field. Many interesting properties are... Read more

Discrete mathematics

Alexis Kaminski

UC Berkeley
Fluxes and mixing of reacting biogeochemical scalars in stratified shear layers

February 24, 2025

MATX 1100 and Zoom

Turbulent mixing is a key physical process in the ocean, impacting the distributions of momentum, heat, salt, and other important tracers. The latter includes biogeochemical (BGC) scalars, representing many different species of plankton and nutrients that play an important role in marine... Read more

Sabin Cautis

UBC
Abelian Hall categories

February 24, 2025

Math 126, Dept. of Mathematics, UBC

We will explain how, to any quiver, one can associate a finite length abelian category which categorifies the corresponding K-theoretic Hall algebra. The simples in this category provide a (dual) canonical basis of the Hall algebra. In particular, if the quiver is affine, this provides a basis... Read more

Algebra and Algebraic geometry

Kyle McKee

MIT
Circulation and Transport in Hele-Shaw Flows

February 13, 2025

CEME 2202 and Zoom

Viscously-dominated flow between two closely spaced plates is described by two-dimensional potential flow according to the standard Hele-Shaw approximation. When driven exclusively by pressure, the class of realizable potential flows is highly restricted: only flows with exactly zero circulation... Read more

Emily Casey

University of Washington
Boundary regularity of planar domains and the Carleson epsilon-function

February 12, 2025

2207 Main Mall

A longstanding conjecture of Carleson stated that the tangent points of the boundaries of certain planar domains can be characterized by the behavior of the Carleson $\varepsilon$ -function. This conjecture, which was fully resolved by Jaye, Tolsa, and Villa in 2021, established that having... Read more

Harmonic Analysis and Fractal Geometry

Jonathan Hermon

UBC
Relaxing, mixing and cutoff for random walks on nilpotent groups

February 12, 2025

The mixing time and spectral gap of a random walk on the symmetric group can sometimes be understood in terms of its low dimensional representations (e.g., Aldous' spectral gap conjecture). It turns out that under a mild degree condition involving the step of the group, the same holds for... Read more

Probability

Thomas Karam

University of Oxford
Adapting some basic matrix rank properties to the ranks of tensors

February 11, 2025

Zoom

Tensors are higher-dimensional generalisations of matrices, and likewise the main notion of complexity on matrices - their rank - may be extended to tensors. Unlike in the matrix case however, there is no single canonical notion of rank for tensors, and the most suitable notion often depends on... Read more

Discrete mathematics

Federico Scavia

CNRS and Universite Sorbonne Paris Nord
Galois representations modulo p that do not lift modulo p^2

February 10, 2025

Math 126, Dept. of Mathematics, UBC

For every finite group H and every finite H-module A, we determine the subgroup of negligible classes in H^2(H,A), in the sense of Serre, over fields with enough roots of unity. As a consequence, we show that for every odd prime p and every field F containing a primitive p-th root of unity,... Read more

Algebra and Algebraic geometry

Deanna Needell

UCLA
Fairness and Foundations in Machine Learning

February 7, 2025

ESB 2012

In this talk, we will address areas of recent work centered around the themes of fairness and foundations in machine learning as well as highlight the challenges in this area. We will discuss recent results involving linear algebraic tools for learning, such as methods in non-negative matrix... Read more

Tom Chandler

University of Wisconsin-Madison
Fluid–structure interactions in active complex fluids

February 6, 2025