Seminars and Colloquia by Series

The Sunflower-Free Process

Series
Graph Theory Seminar
Time
Tuesday, April 28, 2026 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Amanda Priestley – UT Austin

An $r$-sunflower is a collection of $r$ sets such that the intersection of any two sets in the collection is identical. We analyze a random process which constructs a $w$-uniform $r$-sunflower free family starting with an empty family, and at each step, adding a set chosen uniformly at random from all choices that could be added without creating an $r$-sunflower with the previously chosen sets. To analyze this process, we extend results of Bennett and Bohman (arXiv:1308.3732v5 [math.CO]) who analyzed a general random process which adds one object at a time chosen uniformly at random from all objects that can be added without creating certain forbidden subsets. This talk is based on joint work with Professor Patrick Bennett.

Higher Du Bois and higher rational singularities: from Hodge theory to moduli

Series
Representation Theory, Moduli, and Physics Seminar
Time
Tuesday, April 28, 2026 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Haoming Ning – University of Washington

 A central theme in algebraic geometry is understanding how much of the well-behaved theory of smooth varieties survives in the presence of singularities. Du Bois and rational singularities are among the most important classes studied in algebraic geometry due to their nice cohomological behavior. For instance, they preserve features like the Hodge decomposition and vanishing theorems one expects for smooth varieties.
Recently, motivated by developments in Hodge theoretic methods, there has been substantial interest in studying their higher analogs. This talk will survey recent developments connecting these notions to deformation properties and moduli theory, and applications to Calabi-Yau varieties. I will also report on recent joint work with Brian Nugent extending the theory of higher Du Bois and higher rational singularities to pairs — a framework that is both essential in modern birational geometry and a natural setting for studying Hodge theory for open varieties.

The Heegaard Floer d-invariant for rational homology spheres

Series
Geometry Topology Seminar
Time
Monday, April 27, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Isabella Khan – MIT

The Heegaard Floer d-invariant is a numerical invariant of rational homology spheres which is analogous to the Frøyshov h-invariant from Instanton theory. In this talk, we use Zemke’s recent isomorphism between lattice Floer and Heegaard Floer homology to compute the d-invariant for all rational homology spheres which arise as negative definite plumbed manifolds, verifying a 20 year old conjecture of Némethi. 

Neural Networks with Local Converging Inputs for Solving the Stokes Equations Using Subdomain Data Generation

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 27, 2026 - 14:00 for 30 minutes
Location
Skiles 005
Speaker
Farjana Siddiqua – Visiting Assistant Professor, Georgia Institute of Technology –

Deep neural network–based surrogate models have recently gained traction for solving fluid-flow partial differential equations, but their reliance on global interpolation often demands large, computationally expensive architectures and extensive training data. Neural networks with local converging inputs (NNLCI) offer a contrasting strategy. By restricting attention to the local domain of dependence and using converging coarse-grid solutions as inputs, NNLCI dramatically reduces computational cost and data requirements while achieving strong generalization. In this work, we extend the NNLCI framework to the three‑dimensional Stokes equations and introduce a new subdomain data generation methodology specifically tailored for NNLCI, enabling high‑fidelity prediction while completely eliminating the need to compute fine‑grid numerical solutions on the full domain at any stage of the computing process. This innovation eliminates the most computationally intensive component of 3D simulations at its root.

Invariants of SDP Exactness in Quadratic Programming

Series
Algebra Seminar
Time
Monday, April 27, 2026 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Julia Lindberg – Georgia Institute of Technology

In this talk I will discuss a particular convex relaxation of quadratic programs called the Shor relaxation. We study the Shor relaxation of quadratic programs by fixing a feasible set and considering the space of objective functions for which the Shor relaxation is exact. I will discuss conditions under which this region is invariant under the choice of generators defining the feasible set as well as how this region reflects the symmetry in the feasible region. Finally, I will discuss applications of these results to quadratic binary programs. This is joint work with Jose Rodriguez.

Path partitions in regular (directed) graphs

Series
Combinatorics Seminar
Time
Friday, April 24, 2026 - 15:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Akif Yildiz – Centrum Wiskunde & Informatica –

As a generalization of Hamiltonicity problems, one may consider partitioning the vertices of a (directed) graph into as few paths (or cycles) as possible. Ore's classical theorem gives a tight upper bound on the number of paths needed to cover an n-vertex graph, with imbalanced bipartite graphs showing that the bound is best possible. A conjecture of Magnant and Martin (2009) suggests that Ore's bound can be significantly improved for regular graphs. This is also connected to the famous linear arboricity conjecture and has attracted considerable attention in recent years, including a very recent result establishing the conjecture up to a factor of two. In this talk, I will discuss directed and oriented variants of this conjecture and present some results in these settings. Based mostly on joint work with Allan Lo and Viresh Patel.

On Spectral Gap Stability for 2D AKLT Models

Series
Math Physics Seminar
Time
Friday, April 24, 2026 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Amanda Young – University of Illinois Urbana-Champaign –

The classification of quantum phases of matter is a fundamental topic in the study of quantum many-body systems. One main question in this study is whether or not there is a nonvanishing spectral gap above the ground state energy and, if so, whether or not this gap is stable under sufficiently short-range perturbations. In their seminal work, Affleck, Kennedy Lieb and Tasaki (AKLT) conjectured the existence of a spectral gap for the model they defined on the hexagonal lattice. Significant evidence supporting this long-standing claim was only recently achieved and naturally leads to the question of whether or not this gap is stable. In this talk, we review this and other recent progress on proving gaps for AKLT models and then turn to the question of whether these gaps are stable. One avenue for establishing gap stability pioneered by Bravyi, Hastings and Michalakis is to prove that the finite volume ground states are sufficiently indistinguishable by local observables in the bulk - a property known as Local Topological Quantum Order. We discuss a forthcoming work which uses cluster expansion techniques to prove that the ground states of the AKLT model on the hexagonal lattice and Lieb lattice satisfy LTQO. This talk is based on joint work with Thomas Andrew Jackson and Bruno Nachtergaele.

Random Plane Graphs: A Different Theory of Random Graphs

Series
Other Talks
Time
Friday, April 24, 2026 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 249
Speaker
Adam Sheffer – CUNY

The study of random graphs is a rich and well-developed field. However, the standard tools of this field break down when forbidding edge intersections. Our current understanding of random non-intersecting graphs is based on different methods, such as charging schemes. 

 

This talk is an introduction to this rather different theory of random graphs. We will survey the current best results (some by the speaker), applications, and common tools. 

On Spectral Gap Stability for 2D AKLT Models

Series
Math Physics Seminar
Time
Friday, April 24, 2026 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Amanda Young – University of Illinois, Urbana-Champagne –

The classification of quantum phases of matter is a fundamental topic in the study of quantum many-body systems. One main question in this study is whether or not there is a nonvanishing spectral gap above the ground state energy and, if so, whether or not this gap is stable under sufficiently short-range perturbations. In their seminal work, Affleck, Kennedy Lieb and Tasaki (AKLT) conjectured the existence of a spectral gap for the model they defined on the hexagonal lattice. Significant evidence supporting this long-standing claim was only recently achieved and naturally leads to the question of whether or not this gap is stable. In this talk, we review this and other recent progress on proving gaps for AKLT models and then turn to the question of whether these gaps are stable. One avenue for establishing gap stability pioneered by Bravyi, Hastings and Michalakis is to prove that the finite volume ground states are sufficiently indistinguishable by local observables in the bulk - a property known as Local Topological Quantum Order. We discuss a forthcoming work which uses cluster expansion techniques to prove that the ground states of the AKLT model on the hexagonal lattice and Lieb lattice satisfy LTQO. This talk is based on joint work with Thomas Andrew Jackson and Bruno Nachtergaele.

Geometry and spectrum of graphs: regularity of the spectral measure

Series
School of Mathematics Colloquium
Time
Thursday, April 23, 2026 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Charles Bordenave – Institut de Mathématiques de Marseille –

The spectrum of the discrete Laplacian on a infinite graph, or of its random perturbations such as the Anderson tight-binding model, encodes a rich information about the structure of that space. While natural questions abound (nature of the spectrum, localization of eigenfunctions, behavior of the spectral measure), few admit complete answers outside of very specific cases. In this talk, we will briefly survey some of the main open questions in the area. We will then present an elementary geometric criterion that provides control over the  regularity of the spectral measure.

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