## Seminars and Colloquia by Series

### The pants complex and More-s

Series
Geometry Topology Student Seminar
Time
Wednesday, March 8, 2023 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Roberta ShapiroGeorgia Tech

The pants complex of a surface has as its 0-cells the pants decompositions of a surface and as its 1-cells some elementary moves relating two pants decompositions; the 2-cells are disks glued along certain cycles in the 1-skeleton of the complex. In "Pants Decompositions of Surfaces," Hatcher proves that this complex is contractible.

During this interactive talk, we will aim to understand the structure of the pants complex and some of the important tools that Hatcher uses in his proof of contractibility.

### Uniqueness results for meromorphic inner functions

Series
Analysis Seminar
Time
Wednesday, March 8, 2023 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Burak HatinogluGeorgia Tech

A meromorphic inner function is a bounded analytic function on the upper half plane with unit modulus almost everywhere on the real line and a meromorphic continuation to the complex plane. Meromorphic inner functions and equivalently meromorphic Herglotz functions play a central role in inverse spectral theory of differential operators. In this talk, I will discuss some uniqueness problems for meromorphic inner functions and their applications to inverse spectral theory of canonical Hamiltonian systems as Borg-Marchenko type results.

### Reconfiguring List Colorings

Series
Time
Tuesday, March 7, 2023 - 15:45 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Daniel CranstonVirginia Commonwealth University

A \emph{list assignment} $L$ gives to each vertex $v$ in a graph $G$ a
list $L(v)$ of
allowable colors.  An \emph{$L$-coloring} is a proper coloring $\varphi$ such that
$\varphi(v)\in L(v)$ for all $v\in V(G)$.  An \emph{$L$-recoloring move} transforms
one $L$-coloring to another by changing the color of a single vertex.  An
\emph{$L$-recoloring sequence} is a sequence of $L$-recoloring moves.  We study
the problem of which hypotheses on $G$ and $L$ imply that for that every pair
$\varphi_1$ and $\varphi_2$ of $L$-colorings of $G$ there exists an $L$-recoloring
sequence that transforms $\varphi_1$ into $\varphi_2$.  Further, we study bounds on
the length of a shortest such $L$-recoloring sequence.

We will begin with a survey of recoloring and list recoloring problems (no prior
background is assumed) and end with some recent results and compelling
conjectures.  This is joint work with Stijn Cambie and Wouter Cames van
Batenburg.

### The linear stability of weakly charged and slowly rotating Kerr-Newman family of charged black holes

Series
PDE Seminar
Time
Tuesday, March 7, 2023 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lili HeJohns Hopkins University

I will discuss the linear stability of weakly charged and slowly rotating Kerr-Newman black holes under coupled gravitational and electromagnetic perturbations. We show that the solutions to the linearized Einstein-Maxwell equations decay at an inverse polynomial rate to a linearized Kerr-Newman solution plus a pure gauge term. The proof uses tools from microlocal analysis and a detailed description of the resolvent of the Fourier transformed linearized Einstein-Maxwell operator at low frequencies.

### PL surfaces and genus cobordism

Series
Geometry Topology Seminar
Time
Monday, March 6, 2023 - 14:00 for 1 hour (actually 50 minutes)
Location
006
Speaker
Hugo ZhouGeorgia Tech

Every knot in S^3 bounds a PL (piecewise-linear) disk in the four ball. But this is no longer true for knots in other three manifolds, as demonstrated first by Akbulut, who constructed a knot which does not bound any PL disk in a specific contractible four manifold. Then Levine showed that there exist knots that do not bound a PL disk in any homology four ball. What happens if we relax the condition of bounding PL disk to bounding a PL surface with some given genus? I will discuss the joint work with Hom and Stoffregen, where we proved that for each n, there exists a knot K_n in an integer homology sphere that does not bound a PL surface of genus n in any homology four ball. This talk is meant to be accessible to a broad audience.

### Optimal Transport for Averaged Control

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 6, 2023 - 14:00 for 1 hour (actually 50 minutes)
Location
Skile 005 and https://gatech.zoom.us/j/98355006347
Speaker
Dr. Daniel Owusu AduUGA

We study the problem of designing a robust parameter-independent feedback control input that steers, with minimum energy, the average of a linear system submitted to parameter perturbations where the states are initialized and finalized according to a given initial and final distribution. We formulate this problem as an optimal transport problem, where the transport cost of an initial and final state is the minimum energy of the ensemble of linear systems that have started from the initial state and the average of the ensemble of states at the final time is the final state. The by-product of this formulation is that using tools from optimal transport, we are able to design a robust parameter-independent feedback control with minimum energy for the ensemble of uncertain linear systems. This relies on the existence of a transport map which we characterize as the gradient of a convex function.

### Saturating the Jacobian ideal of a line arrangement via rigidity theory

Series
Algebra Seminar
Time
Monday, March 6, 2023 - 10:20 for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
Michael DiPasqualeUniversity of South Alabama

A line arrangement is a collection of lines in the projective plane.  The intersection lattice of the line arrangement is the set of all lines and their intersections, ordered with respect to reverse inclusion.  A line arrangement is called free if the Jacobian ideal of the line arrangement is saturated.  The underlying motivation for this talk is a conjecture of Terao which says that whether a line arrangement is free can be detected from its intersection lattice.  This raises a question - in what ways does the saturation of the Jacobian ideal depend on the geometry of the lines and not just the intersection lattice?  A main objective of the talk is to introduce planar rigidity theory and show that 'infinitesimal rigidity' is a property of line arrangements which is not detected by the intersection lattice, but contributes in a very precise way to the saturation of the Jacobian ideal.  This connection builds a theory around a well-known example of Ziegler.  This is joint work with Jessica Sidman (Mt. Holyoke College) and Will Traves (Naval Academy).

### No Seminar - Admitted Students Day

Series
Geometry Topology Working Seminar
Time
Friday, March 3, 2023 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker

### Anderson Localization in dimension two for singular noise, part two

Series
Mathematical Physics and Analysis Working Seminar
Time
Friday, March 3, 2023 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker

We will continue our discussion of the key ingredients of a multi-scale analysis, namely resolvent decay and the Wegner type estimate. After briefly discussing how the Wegner estimate is obtained in the regime of regular noise, we will discuss the strategy used in Bourgain-Kenig (2005) and Ding-Smart (2018) to obtain analogues thereof using some form of unique continuation principle.

From here, we'll examine the quantitative unique continuation principle used by Bourgain-Kenig, and the lack of any even qualitative analogue on the two-dimensional lattice. From here, we'll discuss the quantitative probabilistic unique continuation result used in Ding-Smart.

### Large-graph approximations for interacting particles on graphs and their applications

Series
Stochastics Seminar
Time
Thursday, March 2, 2023 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Wasiur KhudaBukhshUniversity of Nottingham

Zoom link to the talk: https://gatech.zoom.us/j/91558578481

In this talk, we will consider stochastic processes on (random) graphs. They arise naturally in epidemiology, statistical physics, computer science and engineering disciplines. In this set-up, the vertices are endowed with a local state (e.g., immunological status in case of an epidemic process, opinion about a social situation). The local state changes dynamically as the vertex interacts with its neighbours. The interaction rules and the graph structure depend on the application-specific context. We will discuss (non-equilibrium) approximation methods for those systems as the number of vertices grow large. In particular, we will discuss three different approximations in this talk: i) approximate lumpability of Markov processes based on local symmetries (local automorphisms) of the graph, ii) functional laws of large numbers in the form of ordinary and partial differential equations, and iii) functional central limit theorems in the form of Gaussian semi-martingales. We will also briefly discuss how those approximations could be used for practical purposes, such as parameter inference from real epidemic data (e.g., COVID-19 in Ohio), designing efficient simulation algorithms etc.