Date
Friday October 10, 2025Location
Jeffrey Hall, Room 234Math & Stats Department Colloquium
Speakers: Summer undergraduate students
Title: Summer Research Undergraduate Presentations
Abstract: Some of the undergraduate students who worked on research projects during the summer will present their results.
Date
Monday October 6, 2025Location
Jeffery Hall, Room 422Speaker: Alexandre (Sasha) Zotine (McMaster University)
Title: Dynamics of Projectivized Toric Vector Bundles
Abstract:
Understanding the dynamics (self-maps) of a variety can often reveal information about its geometry. For example, the only curves with non-trivial surjective endomorphisms are of genus zero or one. In this talk, I will discuss the dynamics of projectivized vector bundles, where a similar classifying phenomenon seems to arise: the existence of non-trivial surjective endomorphisms suggests that the bundle splits into a direct sum of line bundles. This is joint work with Javier González Anaya and Brett Nasserden.
Date
Monday September 22, 2025Location
Jeffery Hall, Room 319Speaker: David Miyamoto (Queen's University)
Title: The smooth structure of a Lie group and its quotients
Abstract:
Given a Lie group G and a closed normal subgroup H, the quotient G/H is a Lie group with Lie algebra Lie(G)/Lie(H). When H is not closed (e.g. H could be dense), then G/H is no longer a manifold, and its quotient topology could even be trivial. I will discuss how, by instead viewing G/H as a diffeological space, we may always treat this quotient group as a smooth group with the expected Lie algebra. Specifically: G/H is a quasifold group, meaning it is locally modeled by quotients of R^n by countable affine actions (joint with Yi Lin), and it is elastic, meaning we have a Lie functor for which Lie(G/H) = Lie(G)/Lie(H) (invoking results of Christian Blohmann). Time permitting, I will indicate how this generalizes to the case of infinite-dimensional Banach Lie groups.
Date
Monday October 6, 2025Location
Jeffery Hall, Room 319Speaker: Abdul Zalloum (Queen's University)
Title: Injective metric spaces
Abstract:
A metric space is said to be injective if it is an injective object in the category of metric spaces with respect to 1-Lipshitz maps. In other words, X is injective if for any 1-Lipshitz map f: Y→X and any isometric embedding i: Y→Z, there is a 1-Lipshitz map f':Z -->X with f'i= f. I’ll start my talk with the above definition, then, from the definition alone, I’ll derive a series of striking properties of injective metric spaces—so strong that, at first glance, they make such spaces seem almost too good to exist. I will then show you that they are all over the place: every metric space admits an equivariant isometric embedding into an injective space.
Date
Wednesday September 24, 2025Location
Room 222, Jeffery HallSpeaker: Kamryn Spinelli
Affiliation: Queen's University
Title: An introduction to tautological systems
Abstract: A tautological system is a type of holonomic D-module constructed to govern periods of Calabi-Yau families. For periods of Calabi-Yau complete intersections or double covers of a fixed compact complex manifold X, Lian and Yau gave a recipe to write down the tautological system governing the canonically normalized period integrals discussed in the last talk. One great advantage is that when X is a homogeneous variety G/P, the tautological system has a tactile description in terms of the representation theory of G. In this talk we will give a tour of the theory of tautological systems, with examples.
Date
Wednesday September 10, 2025Location
Room 222, Jeffery HallSpeaker: Kamryn Spinelli
Affiliation: Queen's University
Title: Constructing volume forms on Calabi-Yau complete intersections
Abstract: The integrals of volume forms of Calabi-Yau manifolds, called periods, are of fundamental importance in mirror symmetry and the study of complex moduli. In 2012, Lian and Yau showed how to canonically construct a section of the Hodge bundle on moduli spaces of CY complete intersections of a fixed manifold X through the notion of a CY bundle. By descending forms from the CY bundle to X, one can canonically resolve the ambiguities in the choice of volume form. In this first talk of the seminar, we will summarize the results of the first half of Lian and Yau's article, with an eye toward examples.
Date
Thursday October 9, 2025Location
Jeffery Hall, Room 319Speaker: Abdullah Zubair
Affiliation: Queen's University
Title: Jeu de taquin. Introduction to words and transformations.
Abstract: We will review the product operation introduced in the first lecture. We then introduce the process of rectification, and use it to construct an alternative product operation of young tableaux. Finally, we give an introduction to words and elementary transformations.
Date
Monday September 22, 2025Location
Room 422, Jeffery HallSpeaker: Portia Anderson (Queen's University)
Title: Commutative Properties of Schubert Puzzles with Convex Polygonal Boundary Shapes
Abstract: Schubert puzzles are combinatorial gadgets that perform computations in Schubert calculus, i.e. they compute the structure constants of the cohomology ring of the Grassmannian. While Schubert puzzles are classically triangular, in this talk we generalize them to include puzzles of other convex polygonal shapes. We present theorems on the commutative properties of these convex polygonal puzzles, which generalize the basic commutative property of triangular puzzles.
Date
Friday October 3, 2025Location
Room 235, Jeffery HallTitle: Combinatorics of even-valent graphs on Riemann surfaces
Speaker: Roozbeh Gharakhloo
Affiliation: University of California, Santa Cruz
Abstract:
Let $\mathscr{N}_g(\mu,j)$ denote the number of connected labeled $\mu$-valent graphs with $j$ vertices that can be embedded in a compact Riemann surface of minimal genus~$g$. For example, $\mathscr{N}_0(4,1)=2$ and $\mathscr{N}_1(4,1)=1$, which can be verified by drawing connected labeled $4$-valent graphs with a single vertex on the sphere and on the torus. The problem of determining $\mathscr{N}_g(\mu,j)$ for fixed $g, j,$ and $\mu$ arose in models of two-dimensional quantum gravity and has since inspired a rich body of work, involving both combinatorial methods and techniques from random matrix theory.
After reviewing the connections with random matrices, orthogonal polynomials and Riemann-Hilbert problems, I will present existing results for $\mathscr{N}_g(\mu,j)$ as a function of $j$ when $g$ and $\mu$ are both fixed. I will then describe recent progress on obtaining explicit formulae for $\mathscr{N}_g(2\nu,j)$, viewed as a function of both $j$ and $\nu$ for fixed $g$. If time permits, I will also discuss new developments on the combinatorics of mixed-valent graphs.
This talk is based on joint works with A. Barhoumi (Grinnell), P. Bleher (IU), N. Hayford (KTH), T. Lasic Latimer (UCSC), and K. McLaughlin (Tulane).
Date
Monday September 15, 2025Location
Room 422, Jeffery HallSpeaker: Khoa Nguyen (Queen's University)
Title: Indecomposable non-weight modules over sl(m|1)
Abstract:
In this talk we present a family of indecomposable non-weight sl(m|1)-modules obtained as pullbacks of exponential D(m|1)-modules
E(g)=C[x_1,...,x_m,ξ]e^g(x_1,...,x_m)
along the homomorphisms Φ_S: U(sl(m|1))→D(m|1) indexed by S ⊆{1,...,m}.The resulting sl(m|1)-modules lie in the category M_{sl(m|1)}(k|k) of U(h)-free U(sl(m|1))-modules of rank k in each parity. We establish an isomorphism theorem for this family and give an indecomposability criterion.
This is based on joint work with I. Dimitrov, C. Paquette, and D. Wehlau.
