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PDEs & Applications Seminar

Friday, April 4, 2025

Time: 10:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Gieri Simonett (Vanderbilt University)

Title: On magnetoviscoelastic fluids in 3D

Abstract: I will introduce a thermodynamically consistent model for a magnetoviscoelastic fluid in 3D. Existence, uniqueness, and asymptotic behavior of strong solutions is studied in the framework of quasilinear parabolic systems and maximal regularity in L_p-spaces. It will be shown that the critical points of the entropy functional with prescribed energy correspond exactly to the equilibria of the system. Constant equilibria are normally stable: solutions that start close to a constant equilibrium exist globally and converge exponentially fast to a (possibly different) constant equilibrium. Moreover, it will be shown that the negative entropy serves as a strict Lyapunov functional and that every solution that is eventually bounded in the topology of the natural state space exists globally and converges to the set of equilibria.

Math & Stats Department Colloquium
Friday, April 4, 2025

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Gieri Simonett (Vanderbilt University)

Title: Fluid flow on surfaces

Abstract: I will consider the motion of a viscous, incompressible fluid on a surface (or, more generally, on a Riemannian manifold with or without boundary). In this context, one might think of an aqua planet. The fluid motion is described by the surface Navier-Stokes equations. What are these equations, and how does the fluid evolve? Interestingly, there is an intriguing connection between the long-time behavior of solutions and the existence of Killing vector fields. Numerical simulations will be shown to underscore theoretical predictions.

Math & Stats Number Theory Seminar
Friday, March 28th, 2025

Time: 9:30 a.m.  Place: Jeffery Hall, Room 202

Speaker: Sebastien Darses (Aix-Marseille University / IRC-CRM Montreal)

Title: Approximation problems and identities related to the zeta function

Abstract: One of the seemingly innocent reformulations of the Riemann hypothesis is the Nyman-Beurling criterion: an approximation problem in L2 concerning dilations of the fractional part function, which has a nice geometric interpretation. Randomizing these dilations generates new criteria and structures. These ones are related to a variety of objects and problems: e.g. period functions associated to some Eisenstein series, power moment problems in measure theory, higher moments of zeta. The talk could drift depending on the audience's interests.

Math & Stats Department Colloquium
Friday, March 28, 2025

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Nathalie Moon (University of Toronto)

Title: Meaningful Learning Through Equitable Assessment in Statistics Education

Abstract: The landscape of statistics education assessment has transformed dramatically in recent years, influenced by both the COVID-19 pandemic and the rapid adoption of Large Language Models. This talk explores how principles of equitable assessment can create more meaningful learning experiences in statistics courses. Drawing from recent classroom experiences, I'll share strategies that promote iteration, reflection, and authentic engagement with statistical concepts—including structured feedback/revision cycles and activities that model professional statistical workflows. I'll also address practical challenges such as balancing flexibility with accountability and managing logistical constraints. By designing assessments with these principles in mind, we can create learning environments where students feel empowered to take risks, persist through challenges, and ultimately surprise us with their insights.

This colloquium is sponsored by the Canadian Statistical Sciences Institute (CANSSI Ontario) through the Student PhD And Research networK (SPARK) Program.

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PDEs & Applications Seminar

Friday, March 28, 2025

Time: 10:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Kodjo Raphael Madou (McGill University)

Title: On the supercritical fractional diffusion equation with Hardy-type drift

Abstract: The subject of this talk is the heat kernel of the supercritical fractional diffusion equation with a drift in the critical Hölder space. One way to address such drifts in the non-local setting is to introduce certain desingularizing weights and apply Nash's method in a weighted space. We show that such a drift can have point irregularities strong enough to make the heat kernel vanish at a point for all t>0. The talk is based on joint work with D. Kinzebulatov and Yu A. Semenov.

Math & Stats Algebra & Geometry Seminar
Monday, March 31, 2025

Time: 4:30 p.m.  Place: Jeffery Hall, Room 116

Speaker: Federico Galetto (Cleveland State University)

Title: Principal jets of monomial ideals

Abstract: The study of jets originates in differential geometry and has found applications to a range of topics from birational geometry to motivic integration. After showing how to construct the jets of an affine scheme, I will discuss connections with monomial ideals and combinatorics, specifically with clutters or simple hypergraphs. I will then present some results on principal jets of monomial ideals from joint work with Nicholas Iammarino and Teresa Yu.

Math & Stats Algebra & Geometry Seminar
Monday, March 24, 2025

Time: 4:30 p.m.  Place: Jeffery Hall, Room 116

Speaker: Patricia Klein (Texas A&M University)

Title: Algebra and geometry of ASM weak order

Abstract: The central objects of study in this talk will be Schubert varieties in the complete flag variety. These Schubert varieties are indexed by permutations, which we will identify with permutation matrices. Schubert varieties can be studied via affine varieties called matrix Schubert varieties, introduced by Fulton. One can associate an arbitrary intersection of matrix Schubert varieties to what is called an alternating sign matrix (ASM). In this talk, we will review the role of matrix Schubert varieties - and their unions and intersections - in Schubert calculus and describe classical uses of permutation matrices and strong Bruhat order in encoding algebro-geometric invariants. We will then describe new work giving relationships between algebro-geometric invariants of unions and intersections of matrix Schubert varieties and ASMs under weak Bruhat order. No prior knowledge of strong or weak Bruhat order will be assumed for this talk. This is joint work with Laura Escobar and Anna Weigandt.

Math & Stats Department Colloquium
Friday, March 21, 2025

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Cy Maor (Hebrew University of Jerusalem)

Title: Non-Euclidean Elasticity - From the Shapes of Leaves to (Almost) Isometric Immersions and Back

Abstract: Non-Euclidean elasticity concerns elastic bodies that are strained even in the absence of external forces. While its origins trace back to the 1950s, the field gained renewed attention in the 21st century as a framework for understanding the shapes of leaves, molecular structures, and other systems undergoing inhomogeneous growth. Mathematically, it studies the question of how to immerse 3D Riemannian manifolds in ℝ^3 "as isometric as possible" (in a precise sense). In this talk, I will introduce the model and discuss the mathematical questions it raises—some resolved, many still open. There will be pictures, there will be theorems, and, hopefully, even a live experiment.