Seminars and Colloquia by Series

Introduction to symplectic flexibility

Series
Geometry Topology Seminar Pre-talk
Time
Monday, December 3, 2018 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Oleg Lazarev – Columbia
I will describe the h-principle philosophy and explain some recent developments on the flexible side of symplectic topology, including Murphy's h-principle for loose Legendrians and Cieliebak and Eliashberg's construction of flexible symplectic manifolds in high-dimensions.

Spectra of limit-periodic Schrödinger operators

Series
Math Physics Seminar
Time
Friday, November 30, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jake Fillman – Virginia Polytechnic Institute
A limit-periodic function on R^d is one which lies in the L^\infty closure of the space of periodic functions. Schr\"odinger operators with limit-periodic potentials may have very exotic spectral properties, despite being very close to periodic operators. Our discussion will revolve around the transition between ``thick'' spectra and ``thin'' spectra.

An Oral Exam: Curvature, Contact Topology and Reeb Dynamics

Series
Geometry Topology Working Seminar
Time
Friday, November 30, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena Hozoori – Georgia Institute of Technology –
In post-geometrization low dimensional topology, we expect to be able to relate any topological theory of 3-manifolds to the Riemannian geometry of those manifolds. On the other hand, originated from reformalization of classical mechanics, the study of contact structures has become a central topic in low dimensional topology, thanks to the works of Eliashberg, Giroux, Etnyre and Taubes, to name a few. Yet we know very little about how Riemannian geometry fits into the theory.In my oral exam, I will talk about "Ricci-Reeb realization problem" which asks which functions can be prescribed as the Ricci curvature of a "Reeb vector field" associated to a contact manifold. Finally motivated by Ricci-Reeb realization problem and using the previous study of contact dynamics by Hofer-Wysocki-Zehnder, I will prove new topological results using compatible geometry of contact manifolds. The generalization of these results in higher dimensions is the first known results achieving tightness based on curvature conditions.

Low degree points on curves

Series
Algebra Seminar
Time
Friday, November 30, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Isabel Vogt – Massachusetts Institute of Technology –
In this talk we will discuss an arithmetic analogue of the gonality of a nice curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris--Silverman and Abramovich--Harris, it is understood when this invariant is 1, 2, or 3; by work of Debarre-Fahlaoui these criteria do not generalize. We will focus on scenarios under which we can guarantee that this invariant is actually equal to the gonality using the auxiliary geometry of a surface containing the curve. This is joint work with Geoffrey Smith.

Sparse random graphs with overlapping community structure

Series
ACO Student Seminar
Time
Friday, November 30, 2018 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Samantha Petti – Math, Georgia Tech –
In this talk we introduce two different random graph models that produce sparse graphs with overlapping community structure and discuss community detection in each context. The Random Overlapping Community (ROC) model produces a sparse graph by constructing many Erdos Renyi random graphs (communities) on small randomly selected subsets of vertices. By varying the size and density of these communities, ROC graphs can be tuned to exhibit a wide range normalized of closed walk count vectors, including those of hypercubes. This is joint work with Santosh Vempala. In the second half of the talk, we introduce the Community Configuration Model (CCM), a variant of the configuration model in which half-edges are assigned colors and pair according to a matching rule on the colors. The model is a generalization of models in the statistical physics literature and is a natural finite analog for classes of graphexes. We describe a hypothesis testing algorithm that determines whether a graph came from a community configuration model or a traditional configuration model. This is joint work with Christian Borgs, Jennifer Chayes, Souvik Dhara, and Subhabrata Sen.

Prevalence of heavy-tailed distributions in systems with multiple scales: insights through stochastic averaging

Series
Stochastics Seminar
Time
Thursday, November 29, 2018 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rachel Kuske – School of Mathematics, GaTech
Heavy tailed distributions have been shown to be consistent with data in a variety of systems with multiple time scales. Recently, increasing attention has appeared in different phenomena related to climate. For example, correlated additive and multiplicative (CAM) Gaussian noise, with infinite variance or heavy tails in certain parameter regimes, has received increased attention in the context of atmosphere and ocean dynamics. We discuss how CAM noise can appear generically in many reduced models. Then we show how reduced models for systems driven by fast linear CAM noise processes can be connected with the stochastic averaging for multiple scales systems driven by alpha-stable processes. We identify the conditions under which the approximation of a CAM noise process is valid in the averaged system, and illustrate methods using effectively equivalent fast, infinite-variance processes. These applications motivate new stochastic averaging results for systems with fast processes driven by heavy-tailed noise. We develop these results for the case of alpha-stable noise, and discuss open problems for identifying appropriate heavy tailed distributions for these multiple scale systems. This is joint work with Prof. Adam Monahan (U Victoria) and Dr. Will Thompson (UBC/NMi Metrology and Gaming).

Large-time dynamics in intracellular transport

Series
Job Candidate Talk
Time
Thursday, November 29, 2018 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dr. Veronica Ciocanel – Mathematical Biosciences Institute at The Ohio State University –
The cellular cytoskeleton ensures the dynamic transport, localization, and anchoring of various proteins and vesicles. In the development of egg cells into embryos, messenger RNA (mRNA) molecules bind and unbind to and from cellular roads called microtubules, switching between bidirectional transport, diffusion, and stationary states. Since models of intracellular transport can be analytically intractable, asymptotic methods are useful in understanding effective cargo transport properties as well as their dependence on model parameters.We consider these models in the framework of partial differential equations as well as stochastic processes and derive the effective velocity and diffusivity of cargo at large time for a general class of problems. Including the geometry of the microtubule filaments allows for better prediction of particle localization and for investigation of potential anchoring mechanisms. Our numerical studies incorporating model microtubule structures suggest that anchoring of mRNA-molecular motor complexes may be necessary in localization, to promote healthy development of oocytes into embryos. I will also briefly go over other ongoing projects and applications related to intracellular transport.

Approximation of Generic Hamiltonian Systems by Those with a Finite Number of Islands

Series
Other Talks
Time
Thursday, November 29, 2018 - 09:00 for 1 hour (actually 50 minutes)
Location
Skiles, Room 114
Speaker
Hassan Attarchi – Georgia Institute of Technology –

Please Note: Oral Comprehensive Exam

The purpose of this work is approximation of generic Hamiltonian dynamical systems by those with a finite number of islands. In this work, we will consider a Lemon billiard as our Hamiltonian dynamical system apparently with an infinitely many islands. Then, we try to construct a Hamiltonian dynamical system by deforming the boundary of our lemon billiard to have a finite number of islands which are the same or sub-islands of our original system. Moreover, we want to show elsewhere in the phase space of the constructed billiard is a chaotic sea. In this way, we will have a dynamical system which preserves some properties of our lemon billiards while it has much simpler structure.

Exposition on the entropy method and the occupancy method

Series
Graph Theory Working Seminar
Time
Wednesday, November 28, 2018 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prasad Tetali – Georgia Tech
Continuing on the theme mentioned in my recent research horizons lecture, I will illustrate two techniques by deriving upper and lower bounds on the number of independent sets in bipartite and triangle-free graphs.

The Converse Of The Archimedean Property of the Sphere and Related Results in Convex Geometry and Measure Theory

Series
Geometry Topology Student Seminar
Time
Wednesday, November 28, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sidhanth Raman – Georgia Tech
The Archimedes Hatbox Theorem is a wonderful little theorem about the sphere and a circumscribed cylinder having the same surface area, but the sphere can potentially still be characterized by inverting the statement. There shall be a discussion of approaches to prove the claim so far, and a review of a weaker inversion of the Hatbox Theorem by Herbert Knothe and discussion of a related problem in measure theory that would imply the spheres uniqueness in this property.

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