Seminars and Colloquia by Series

Balian-Low theorems for subspaces

Series
Analysis Seminar
Time
Tuesday, September 29, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
online seminar
Speaker
Andrei Caragea – Katholische Universität Eichstätt-Ingolstadt
The Balian-Low theorem is a classical result in time-frequency analysis that describes a trade off between the basis properties of a Gabor system and the smoothness and decay of the Gabor window. 
In particular a Gabor system with well localized window cannot be a Riesz basis for the space of finite energy signals.
We explore a few generalizations of this fact in the setting of Riesz bases for subspaces of L^2 and we show that the Gabor space being invariant under additional time-frequency shifts is incompatible with two different notions of smoothness and decay for the Gabor window.

Off the rails: Train tracks on surfaces

Series
Undergraduate Seminar
Time
Monday, September 28, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
Bluejeans meeting https://bluejeans.com/759112674
Speaker
Dr. Marissa Loving – Georgia Tech

Our mantra throughout the talk will be simple, "Train tracks approximate simple closed curves." Our goal will be to explore some examples of train tracks, draw some meaningful pictures, and develop an analogy between train tracks and another well known method of approximation. No great knowledge of anything is required for this talk as long as one is willing to squint their eyes at their computer's screen a bit at times.

SL3 Skein Algebras of Surfaces by Vijay Higgins

Series
Geometry Topology Seminar
Time
Monday, September 28, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Virtual
Speaker
Vijay Higgins – UC Santa Barbara –

The SL2 skein algebra of a surface is built from diagrams of curves on the surface. To multiply two diagrams, we draw one diagram on top of the other and then resolve the crossings with the Kauffman bracket. If we replace SL2 with another quantum group, we replace curves by embedded graphs on the surface. Recently, Thang Le showed that the SL2 skein algebra has a nice decomposition into simpler algebras whenever the surface has an ideal triangulation. This triangular decomposition is a powerful tool and should help us to study other skein algebras if we are able to show that the necessary ingredients exist. In this talk, I will explain what these ingredients are and how to find them for the SL3 skein algebra of trivalent webs on a surface.

8.3.3

Minimal problems in 3D reconstruction

Series
ACO Student Seminar
Time
Friday, September 25, 2020 - 13:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/264244877/0166
Speaker
Timothy Duff – Math, Georgia Tech –

I describe my ongoing work using tools from computational and combinatorial algebraic geometry to classify minimal problems and identify which can be solved efficiently. I will not assume any background in algebraic geometry or computer vision.

Structure-from-motion algorithms reconstruct a 3D scene from many images, often by matching features (such as point and lines) between the images. Matchings lead to constraints, resulting in a nonlinear system of polynomial equations that recovers the 3D geometry. Since many matches are outliers, these methods are used in an iterative framework for robust estimation called RANSAC (RAndom SAmpling And Consensus), whose efficiency hinges on using a small number of correspondences in each iteration. As a result, there is a big focus on constructing polynomial solvers for these "minimal problems" that run as fast as possible. Our work classifies these problems in cases of practical interest (calibrated cameras, complete and partial visibility.) Moreover, we identify candidates for practical use, as quantified by "algebraic complexity measures" (degree, Galois group.)

joint w/ Anton Leykin, Kathlen Kohn, Tomas Pajdla arxiv1903.10008 arxiv2003.05015+ Viktor Korotynskiy, TP, and Margaret Regan (ongoing.)

Taming the randomness of chaotic systems

Series
Research Horizons Seminar
Time
Friday, September 25, 2020 - 12:30 for 1 hour (actually 50 minutes)
Location
Microsoft Teams
Speaker
Alex Blumenthal – Georgia Tech –
All around us in the physical world are systems which evolve in chaotic, seemingly random ways: fire, smoke, turbulent fluids, the flow of gas around us. Over the last ~60 years, mathematicians have made tremendous progress in understanding these processes and how chaotic behavior can emerge and, remarkably, the extent to which chaotic systems emulate probabilistic randomness. This talk is a brief introduction to these ideas, with an emphasis on examples and pretty pictures. 

Noetherian operators and primary decomposition

Series
Student Algebraic Geometry Seminar
Time
Friday, September 25, 2020 - 09:00 for 1 hour (actually 50 minutes)
Location
Microsoft Teams Meeting
Speaker
Marc Härkönen – Georgia Tech –

Please Note: Teams link: https://teams.microsoft.com/l/meetup-join/19%3a3a9d7f9d1fca4f5b991b4029b09c69a1%40thread.tacv2/1600608874868?context=%7b%22Tid%22%3a%22482198bb-ae7b-4b25-8b7a-6d7f32faa083%22%2c%22Oid%22%3a%223eebc7e2-37e7-4146-9038-a57e56c92d31%22%7d

Noetherian operators are differential operators that encode primary components of a polynomial ideal. We develop a framework, as well as algorithms, for computing Noetherian operators with local dual spaces, both symbolically and numerically. For a primary ideal, such operators provide an alternative representation to one given by a set of generators. This description fits well with numerical algebraic geometry, taking a step toward the goal of numerical primary decomposition. This is joint work with Justin Chen, Robert Krone and Anton Leykin.

Statistical Inference in Popularity Adjusted Stochastic Block Model

Series
Stochastics Seminar
Time
Thursday, September 24, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
https://ucf.zoom.us/j/92646603521?pwd=TnRGSVo1WXo2bjE4Y3JEVGRPSmNWQT09
Speaker
Marianna Pensky – University of Central Florida

The talk considers the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen (2018). We argue that the main appeal of the PABM is the flexibility of the spectral properties of the graph which makes the PABM an attractive choice for modeling networks that appear in, for example, biological sciences. In addition, to the best of our knowledge, the PABM is the only stochastic block model that allows to treat the network sparsity as the structural sparsity that describes community patterns, rather than being an attribute of the network as a whole.

Link to Zoom meeting: https://ucf.zoom.us/j/92646603521?pwd=TnRGSVo1WXo2bjE4Y3JEVGRPSmNWQT09

Symmetrization for functions of bounded mean oscillation

Series
School of Mathematics Colloquium
Time
Thursday, September 24, 2020 - 11:00 for
Location
https://us02web.zoom.us/j/89107379948
Speaker
Almut Burchard – University of Toronto –

Spaces of bounded mean oscillation (BMO) are relatively
large function spaces that are often used in place
of L^\infinity to do basic Fourier analysis.
It is not well-understood how geometric properties
of the underlying point space enters into the functional
analysis of BMO.  I will describe recent work with
Galia Dafni and Ryan Gibara, where we take some
steps towards geometric inequalities.
Specifically, we show that the symmetric decreasing
rearrangement in n-dimensions is bounded, but not
continuous in BMO. The question of sharp bounds
remains open. 

Recording: https://us02web.zoom.us/rec/share/pjIM7jMdtcDAl70hT8e7V_MBqUzPwnl1scdcQUsE6WDuKGLev6hz468_v1F_mwc1.t31L3k8qvvmXiexP

The skein algebra as a quantized character variety

Series
Geometry Topology Student Seminar
Time
Wednesday, September 23, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Tao Yu – Georgia Tech

In 1925, Heisenberg introduced non-commutativity of coordinates, now known as quantization, to explain the spectral lines of atoms. In topology, finding quantizations of (symplectic or more generally Poisson) spaces can reveal more intricate structures on them. In this talk, we will introduce the main ingredients of quantization. As a concrete example, we will discuss the SL2-character variety, which is closely related to the Teichmüller space, and the skein algebra as its quantization.

Packing A-paths and cycles in undirected group-labelled graphs

Series
Graph Theory Working Seminar
Time
Tuesday, September 22, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Youngho Yoo – Georgia Institute of Technology –

An $A$-path is a path whose intersection with a vertex set $A$ is exactly its endpoints. We show that, for all primes $p$, the family of $A$-paths of length $0 \,\mathrm{mod}\, p$ satisfies an approximate packing-covering duality known as the Erdős-Pósa property. This answers a recent question of Bruhn and Ulmer. We also show that, if $m$ is an odd prime power, then for all integers $L$, the family of cycles of length $L \,\mathrm{mod}\, m$ satisfies the Erdős-Pósa property. This partially answers a question of Dejter and Neumann-Lara from 1987 on characterizing all such integer pairs $L$ and $m$. Both results are consequences of a structure theorem which refines the Flat Wall Theorem of Robertson and Seymour to undirected group-labelled graphs analogously to a result of Huynh, Joos, and Wollan in the directed setting. Joint work with Robin Thomas.

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