Seminars and Colloquia by Series

On scaling properties for two-state problems

Series
Math Physics Seminar
Time
Friday, September 12, 2025 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bogdan Raita – Georgetown University –

We study differential inclusions of the type $A v=0$ and $v \in K$, where $v$ is a vector field satisfying a linear PDE system $A$ and $K$ is a compact set. We are particularly interested in the case when $K$ consists of two vectors (\textit{two-state problem}). We consider Dirichlet boundary conditions for $v$, in which case the differential inclusion typically has no solutions. We study a suitable relaxation of the system, in which we penalize the surface energy required to switch between the two states. We study the asymptotics of the regularized energy integral. We show that the asymptotics depend polynomially on the regularization parameter with a quantification which — somewhat surprisingly — depends on the order of the linear PDE system $A$. Joint work with A. R\”{u}land, C. Tissot, A. Tribuzio.

Computationally efficient reductions between some statistical models

Series
Stochastics Seminar
Time
Thursday, September 11, 2025 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mengqi Lou – Georgia Institute of Technology

Average-case reductions establish rigorous connections between different statistical models, allowing us to show that if one problem is computationally hard, then another must be as well. Reductions from the planted clique problem have revealed statistical-to-computational gaps in many statistical problems with combinatorial structure. However, several important models remain beyond the reach of existing reduction techniques—for example, no reduction-based hardness results are currently known for sparse phase retrieval.

In this talk, we introduce a computationally efficient procedure that approximately transforms a single observation from certain source models with continuous-valued sample and parameter spaces into a single observation from a broad class of target models. I will present several such reductions and highlight their applications in computational lower bounds, including universality results and hardness in sparse generalized linear models. I will also discuss a potential application in transforming one differentially private mechanism into another.

This is joint work with Guy Bresler and Ashwin Pananjady. Part of the talk is based on the paper: https://arxiv.org/abs/2402.07717.

A cobordism map for linearized Legendrian contact homology

Series
Geometry Topology Student Seminar
Time
Wednesday, September 10, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tom Rodewald – Georgia Tech

In order to distinguish Legendrians with the same classical invariants, Chekanov and Eliashberg separately defined the Chekanov-Eliashberg DGA. Chekanov further defined a linearized version. Ekholm, Honda, and Kalman showed an exact Lagrangian cobordism between two Legendrians induces a DGA map on their respective DGAs. We show how to adapt this map to the linearized version. Time permitting, we will use this map to obstruct invertible concordances between negative twist knots. This is joint work with Sierra Knavel.

Scattering for Nonlinear Schrödinger Equations with a potential

Series
PDE Seminar
Time
Tuesday, September 9, 2025 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Gavin Stewart – Arizona State University –

Please Note: TBA

In this talk, I'll discuss the asymptotics of the cubic nonlinear Schrödinger equation with potential in dimension 1 for small, localized initial data. In the case when the potential is equal to 0, it has been known for some time that solutions exhibit modified scattering. Due to additional complications introduced by the potential, the case with V nonzero has not been addressed until recently. 

 

Here, we present a method to obtain asymptotics for this problem.  The main ingredients are  (1) a new linear identity, which allows us to relate certain vector field-like quantities for the problem with a potential to those for the problem with no potential, and (2) an adaptation of the method of testing with wave packets introduced by Ifrim and Tataru. Compared to previous results, this method can handle potentials with slower decay at infinity.

Coloring Graphs With No Totally Odd Clique Immersion

Series
Graph Theory Seminar
Time
Tuesday, September 9, 2025 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Caleb McFarland – Georgia Tech –

We prove that graphs that do not contain a totally odd immersion of $K_t$ are $\mathcal{O}(t)$-colorable. In particular, we show that any graph with no totally odd immersion of $K_t$ is the union of a bipartite graph and a graph which forbids an immersion of $K_{\mathcal{O}(t)}$. Our results are algorithmic, and we give a fixed-parameter tractable algorithm (in $t$) to find such a decomposition.

Regular Lagrangians in Lefschetz fibrations

Series
Geometry Topology Seminar
Time
Monday, September 8, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Joe Breen – University of Alabama

Giroux and Pardon conjectured that a Lagrangian L in a Weinstein manifold W is regular (that is, compatible with the Weinstein structure in a natural sense) if there is a Lefschetz fibration p: W \to \C such that p(L) is a ray. In this talk, I will discuss forthcoming joint work with A. Roy and L. Wang, which establishes this conjecture. As an application of the proof, we show how all fillings of the rainbow closures of a positive braid can be described by manipulations of arcs in the base of an appropriate Lefschetz fibration.

Power flow, toric deficiency, and strata-confined polyhedral homotopies

Series
Algebra Seminar
Time
Monday, September 8, 2025 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tianran Chen – Auburn University at Montgomery

Please Note: There will be a pre-seminar 10:55-11:15 in Skiles 005.

Power-flow equations model the intricate balancing conditions in electric power grids and are central to analysis and control.  They can be reformulated as Laurent polynomial systems, which makes algebraic and polyhedral techniques applicable.  In this talk, we first explore different ways in which this can be done.

However, certain algebraic formulations may be deficient: the actual number of isolated solutions (counting multiplicity) may fall below the Bernshtein–Kushnirenko–Khovanskii (BKK) bound predicted from Newton polytopes.  By choosing a proper parametrization one uncovers that this deficiency exhibits a certain toric structure.  Recognizing that structure reframes the deficit as a geometric feature rather than a numerical anomaly.  In the second part of this talk, we explore variations of polyhedral homotopy methods designed to respect and exploit this structure.

====(Below is the information on the pre-talk.)====

Title: Mixed volume, mixed cells, and stable self intersections

Abstract: This talk provides an introduction to mixed volume, mixed cells, and their connections to the Bernshtein–Kushnirenko–Khovanskii bound, as well as stable intersections of tropical hypersurfaces.

ε-series by Logan Post, Jasper Seabold, and Adri Wessels

Series
Combinatorics Seminar
Time
Friday, September 5, 2025 - 15:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Logan Post, Jasper Seabold, and Adri Wessels – Georgia Tech

Three fifteen-minute talks by local speakers.

Logan Post: Almost all even-parity binary words are shuffle squares

Jasper Seabold: Using Grid Graphs to Study Hypergraph Ramsey Questions

Adri Wessels: 

An introduction to Margulis' inequalities

Series
CDSNS Colloquium
Time
Friday, September 5, 2025 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 311
Speaker
Asaf Katz – Georgia Tech

Margulis inequalities and Margulis functions (a.k.a Foster-Lyapunov stability) have played a major role in modern dynamics, in particular in the fields of homogeneous dynamics and Teichmuller dynamics.
Moreover recent exciting developments in the field of random walks over manifolds give rise to related notions and questions in a much larger geometrical content, largely motivated by recent work of Brown-Eskin-Filip-Rodriguez Hertz.

I will explain what are Margulis functions and Margulis inequalities and describe the main lemma due to Eskin-Margulis (“uniform expansion”) that allows one to prove such an inequality. I will also try to sketch some interesting applications.

No prior knowledge is needed, the talk will be self-contained and accessible.

Zoom Link: https://gatech.zoom.us/j/94689623118?pwd=Ie8Ir2bExulIP4joQbcmZiwsxpIq75.1 Meeting ID: 946 8962 3118 Passcode: 910355

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