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Speaker: 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.

Speaker: 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.

Speaker: 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.

Title: 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).

Speaker: 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.

Title: Differentials and differential operators

Speaker: Claudia Miller 

Affiliation: Syracuse University

Abstract:
In the first part, I will describe Kähler differentials and derivations and some of the history behind the classic Lipman-Zariski Conjecture, as well as a generalized question proposed by Graf. Together with Vassiliadou, we give a partial answer to Graf’s question for a certain class of varieties.

In the second portion, we turn our attention to higher order differential operators, finding explicit generators and free resolutions in some low orders for these for the hypersurfaces studied by Bernstein-Gel’fand-Gel’fand and Vigué. This is joint work with Diethorn, Jeffries, Packauskas, Pollitz, Rahmati, and Vassiliadou.

No specific algebraic or geometric background is required.

Title: Estimation and Model Selection in General Spatial Dynamic Panel Data Models

Speaker: Yuehua Wu 

Affiliation: Department of Mathematics and Statistics, York University

Additional Information:
This is a CANSSI Ontario STatistics Seminar
See event on the website.

Abstract:
Common methods for estimating parameters of spatial dynamic panel data models include two-stage least squares, quasi-maximum likelihood, and generalized moments. In this talk, we present a method that uses the eigenvalues and eigenvectors of a spatial weight matrix to directly construct consistent least squares estimators of parameters of general spatial dynamic panel data models for both undirected and directed networks. Our method is conceptually simple and effective, and easy to implement. Results show that our parameter estimators are consistent and asymptotically normally distributed under mild conditions. We demonstrate the superior performance of our method through extensive simulation studies. We also provide two real data examples.

 

Math & Stats Algebra & Geometry Seminar
Monday, September 8, 2025

Time: 4:45 p.m.  Place: Jeffery Hall, Room 422

Speaker: Kaveh Mousavand (Okinawa Institute of Science and Technology)

Title: Pairwise Hom-orthogonal Modules and Some Open Conjectures

Abstract: Let A be an associative algebra and S={X_1,X_2,…,X_m} be a set of finitely generated (left) A-modules. We say that S is a set of pairwise Hom-orthogonal modules of size m if, for every distinct pair of i and j, there is no nonzero A-module homomorphism from X_i to X_j; that is, Hom_A(X_i,X_j)=0. This naturally leads to the following (still open) question: Given an algebra A, is there an upper bound on the size of such sets of pairwise Hom-orthogonal A-modules?

Motivated by some challenging conjectures in modern representation theory, we recently investigated the above problem in the setting of finite-dimensional associative algebras. In particular, we approached the question through the study of bricks, namely, those modules whose endomorphism algebras are division algebras (also known as Schur representations). In fact, using a range of algebraic and geometric techniques, we show that a full answer to the question follows directly from an open conjecture I proposed in 2019 -- now referred to as theSecond Brick–Brauer–Thrall Conjecture (2nd bBT). Our perspective not only connects this question to several central themes in contemporary research -- such as stability conditions and \tau-tilting theory -- but also leads to reformulations of stronger versions of both the 2nd bBT and our earlier results. In particular, we achieve a significant reduction of several open conjectures, now expressible in the more elementary language of pairwise Hom-orthogonal modules. To make the key problems and results in this talk more accessible, I will, for the most part, assume only a basic familiarity with elementary module theory. This talk is based on joint work with Charles Paquette.