Seminars and Colloquia by Series

Oriented Matroids and Combinatorial Neural Codes

Series
Algebra Seminar
Time
Monday, February 17, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Zvi RosenFlorida Atlantic University

A combinatorial neural code is convex if it arises as the intersection pattern of convex open subsets of Euclidean space. We relate the emerging theory of convex neural codes to the established theory of oriented matroids, both categorically and with respect to feasibility and complexity. By way of this connection, we prove that all convex codes are related to some representable oriented matroid, and we show that deciding whether a neural code is convex is NP-hard.

Spaces of trees and fatgraphs for string topology and moduli spaces

Series
Geometry Topology Seminar
Time
Monday, February 17, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kate PoirierCUNY - City College of Technology

Spaces of fatgraphs have long been used to study a variety of topics in math and physics. In this talk, we introduce two spaces of fatgraphs arising in string topology—one which parameterizes operations on chains of the free loop space of a manifold and one which parametrizes operations on Hochschild cochains of a “V-infinity” algebra. We present a conjecture relating these two spaces to one another and to the moduli space of Riemann surfaces. We also introduce polyhedra called “assocoipahedra” which generalize Stasheff’s associahedra to algebras with a compatible co-inner product. Assocoipahedra are used to prove that the dioperad governing V-infinity algebras satisfies certain algebraic properties. 

Structure-Preserving Numerical Method for Stochastic Nonlinear Schrodinger Equation

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 17, 2020 - 13:50 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Cui, JianboGeorgia Tech math

It's know that when discretizing stochastic ordinary equation with non-globally Lipschitz coefficient, the traditional numerical method, like
Euler method, may be divergent and not converge in strong or weak sense. For stochastic partial different equation with non-globally Lipschitz
coefficient, there exists fewer result on the strong and weak convergence results of numerical methods. In this talk, we will discuss several numerical schemes approximating stochastic Schrodinger Equation.  Under certain condition, we show that the exponential integrability preserving schemes are strongly and weakly convergent with positive orders.

Algebraic definitions for string topology

Series
Geometry Topology Seminar Pre-talk
Time
Monday, February 17, 2020 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kate PoirierCUNY - City College of Technology

String topology studies various algebraic structures given by intersecting loops in a manifold, as well as those on the Hochschild chains or homology of an algebra. In this preparatory talk, we survey a collection of such structures and their relationships with one another.

A rigorous proof of Batchelor's law for passive scalar turbulence

Series
CDSNS Colloquium
Time
Monday, February 17, 2020 - 11:15 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alex BlumenthalUniversity of Maryland and Georgia Tech

Batchelor's law describes the power law spectrum of the turbulent regime of passive scalars (e.g., temperature or a dilute concentration of some tracer chemical) advected by an incompressible fluid (e.g., the Navier-Stokes equations at fixed Reynolds number), in the limit of vanishingly low molecular diffusivity. Predicted in 1959, it has been confirmed empirically in a variety of experiments, e.g. salinity concentrations among ocean currents. On the other hand, as with many turbulent regimes in physics, a true predictive theory from first principles has been missing (even a non-rigorous one), and there has been some controversy regarding the extent to which Batchelor's law is universal. 

 

In this talk, I will present a program of research, joint with Jacob Bedrossian (UMD) and Sam Punshon-Smith (Brown), which has rigorously proved Batchelor's law for passive scalars advected by the Navier-Stokes equations on the periodic box subjected to Sobolev regular, white-in-time body forces. The proof is a synthesis of techniques from dynamical systems and smooth ergodic theory, stochastics/probability, and fluid mechanics. To our knowledge, this work constitutes the first mathematically rigorous proof of a turbulent power law spectrum. It also establishes a template for predictive theories of passive scalar turbulence in more general settings, providing a strong argument for the universality of Batchelor's law. 

Clustering a Mixture of Gaussians

Series
ACO Student Seminar
Time
Friday, February 14, 2020 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
He JiaCS, Georgia Tech

We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussian are well-separated or their covariances are well-separated. Our algorithm and analysis extend naturally to robustly clustering mixtures of well-separated logconcave distributions. The mean separation required is close to the smallest possible to guarantee that most of the measure of the component Gaussians can be separated by some hyperplane (for covariances, it is the same condition in the second degree polynomial kernel). Our main tools are a new identifiability criterion based on isotropic position, and a corresponding Sum-of-Squares convex programming relaxation.

Replica Symmetry Breaking for Random Regular NAESAT

Series
School of Mathematics Colloquium
Time
Thursday, February 13, 2020 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Allan SlyPrinceton University

Ideas from physics have predicted a number of important properties of random constraint satisfaction problems such as the satisfiability threshold and the free energy (the exponential growth rate of the number of solutions).  Another prediction is the condensation regime where most of the solutions are contained in a small number of clusters and the overlap of two random solutions is concentrated on two points.  We establish this phenomena for the random regular NAESAT model.

Introduction to algebraic graph theory

Series
Graph Theory Working Seminar
Time
Wednesday, February 12, 2020 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
James AndersonGeorgia Tech
In this introductory talk, we explore the first 5 chapters of Biggs's Algebraic Graph Theory. We discuss the properties of the adjacency matrix  of graph G, as well as the relationship between the incidence matrix of G and the cycle space and cut space. We also include several other small results. This talk will be followed by later talks in the semester continuing from Biggs's book.
 

The Frohman-Kania-Bartoszynska invariant is the 3D index

Series
Geometry Topology Seminar
Time
Wednesday, February 12, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
S. GaroufalidisSUSTECH and MPI Bonn
We prove that a power series invariant of suitable ideal triangulations, defined by Frohman-Kania-Bartoszynska coincides with the power series invariant of Dimofte-Gaiotto-Gukov known as the 3D index. In partucular, we deduce that the FKB invariant is topological, and that the tetrahedron weight of the 3D index is a limit of quantum 6j symbols. Joint work with Roland van der Veen.

TBA by Stavros Garoufalidis

Series
Geometry Topology Student Seminar
Time
Wednesday, February 12, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker

Please Note: This is an ordinary research Geometry/Topology seminar: https://math.gatech.edu/seminars-colloquia/series/geometry-topology-seminar/s-garoufalidis-20200212

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