Seminars and Colloquia Schedule

Monday, November 26, 2018 - 13:55 , Location: 005 Skiles , Ray Treinen , Texas State University , , Organizer: John McCuan
<p>We consider one or more volumes of a liquid or semi-molten material sitting on a substrate, while the vapor above is assumed to have the same medium in suspension. There may be both evaporation and condensation to move mass from one cell to another. We explore possible equilibrium states of such configurations. Our examples include a single sessile drop (or cell) on the plate, connected clusters of cells of the material on the plate, as well as a periodic configuration of connected cells on the plate. The shape of the configurations will depend on the type of energy that we take into consideration, and in settings with a vertical gravitational potential energy the clusters are shown to exhibit a preferred granular scale. The majority of our results are in a lower dimensional setting, however, some results will be presented in 3-D.</p>
Tuesday, November 27, 2018 - 12:00 , Location: Skiles 006 , Cristobal Guzman , Universidad Católica de Chile, Chile , Organizer: Prasad Tetali
Recently there has been an outburst of parallelization&nbsp;&nbsp;techniques to speed up optimization algorithms, particularly in&nbsp;&nbsp;applications in statistical learning and structured linear programs.&nbsp;&nbsp;Motivated by these developments, we seek for theoretical explanations of&nbsp;&nbsp;provable improvements (or the lack thereof) in performance obtained by&nbsp;&nbsp;parallelizing optimization algorithms. In 1994, Nemirovski proved that&nbsp;&nbsp;for low-dimensional optimization problems there is a very limited&nbsp;&nbsp;improvement that could be obtained by parallelization, and furthermore&nbsp;&nbsp;conjectured that no acceleration should be achievable by these means. In&nbsp;&nbsp;this talk, I will present new results showing that in high-dimensional&nbsp;&nbsp;settings no acceleration can be obtained by parallelization, providing&nbsp;&nbsp;strong evidence towards Nemirovski's conjecture.&nbsp;&nbsp;This is joint work with Jelena Diakonikolas (UC Berkeley).&nbsp;
Series: Other Talks
Tuesday, November 27, 2018 - 13:05 , Location: Skiles Atrium , Cristobal Guzmanal Guzman , Universidad Católica de Chile, Chile , Organizer: Prasad Tetali
Cristobal Guzman will discuss his employment experience as an ACO alummus. The&nbsp;conversations will take place over coffee.
Series: PDE Seminar
Tuesday, November 27, 2018 - 15:00 , Location: skiles 006 , Yilun(Allen) Wu , The University of Oklahoma , , Organizer: Xukai Yan
A rotating star may be modeled as gas under self gravity with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler-Poisson system. In this talk, we present an existence theorem for such stars that are rapidly rotating, depending continuously on the speed of rotation. No previous results using continuation methods allowed rapid rotation. The key tool for the result is global continuation theory via topological degree, combined with a delicate limiting process. The solutions form a connected set $\mathcal K$ in an appropriate function space. Take an equation of state of the form $p = \rho^\gamma$; $6/5 < \gamma < 2$, $\gamma\ne 4/3$. As the speed of rotation increases, we prove that either the density somewhere within the stars becomes unbounded, or the supports of the stars in $\mathcal K$ become unbounded. Moreover, the latter alternative must occur if $\frac43<\gamma<2$. This result is joint work with Walter Strauss.
Tuesday, November 27, 2018 - 15:00 , Location: Skiles 005 , Prof. Le Song , GT CSE , Organizer: Sung Ha Kang

This is a part of GT MAP seminar.  See for more information.

Point processes such as Hawkes processes are powerful tools to model user activities and have a plethora of applications in social sciences. Predicting user activities based on point processes is a central problem which is typically solved via sampling. In this talk, I will describe an efficient method based on a differential-difference equation to compute the conditional probability mass function of point processes. This framework is applicable to general point processes prediction tasks, and achieves marked efficiency improvement in diverse real-world applications compared to existing methods.
Wednesday, November 28, 2018 - 12:20 , Location: Skiles 005 , JungHwan Park , Georgia Tech , Organizer: Trevor Gunn
This is a survey talk on the knot concordance group and the homology cobordism group.
Wednesday, November 28, 2018 - 12:55 , Location: skiles 006 , Marcel Celaya , Georgia Institute of technology , , Organizer: Galyna Livshyts
&nbsp;In this talk I will describe those&nbsp;linear subspaces of $\mathbf{R}^d$ which&nbsp;can be formed by taking the linear span of lattice points in a&nbsp;half-open parallelepiped. I&nbsp;will&nbsp;draw some&nbsp;connections between this problem and&nbsp;Keith Ball's cube slicing theorem, which states that the volume of any slice of the unit cube $[0,1]^d$ by a codimension-$k$ subspace is at most $2^{k/2}$.
Wednesday, November 28, 2018 - 13:55 , Location: Skiles 005 , Rui Han , Georgia Tech , Organizer: Shahaf Nitzan
Recently Bourgain and Dyatlov proved a fractal uncertainty principle (FUP), which roughly speaking says a function in $L^2(\mathbb{R})$ and its Fourier transform&nbsp;can not be simultaneously localized in $\delta$-dimensional&nbsp;fractal sets, $0<\delta<1$. In this talk, I will discuss a joint work with Schlag, where we obtained&nbsp;a higher dimensional version of the FUP. Our method combines the original approach by Bourgain and Dyatlov, in the more quantitative rendition by Jin and Zhang, with Cantan set techniques.
Wednesday, November 28, 2018 - 14:00 , Location: Skiles 006 , Sidhanth Raman , Georgia Tech , Organizer: Sudipta Kolay
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.
Wednesday, November 28, 2018 - 16:30 , Location: Skiles 006 , Prasad Tetali , Georgia Tech , Organizer: Xingxing Yu
Continuing on the theme mentioned in my recent&nbsp;research horizons lecture, I will illustrate two techniques by deriving upper and lower&nbsp;bounds on the number of independent sets in bipartite and triangle-free graphs.
Series: Other Talks
Thursday, November 29, 2018 - 09:00 , Location: Skiles, Room 114 , Hassan Attarchi , Georgia Institute of Technology , , Organizer: Hassan Attarchi

Oral Comprehensive Exam

<p>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.</p>
Thursday, November 29, 2018 - 11:00 , Location: Skiles 006 , Dr. Veronica Ciocanel , Mathematical Biosciences Institute at The Ohio State University , , Organizer: Howie Weiss
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.
Thursday, November 29, 2018 - 15:05 , Location: Skiles 006 , Rachel Kuske , School of Mathematics, GaTech , Organizer: Christian Houdre
Heavy tailed distributions have been shown to be consistent with data in a variety of systems with multiple time scales.&nbsp; Recently, increasing attention has appeared in different phenomena related to climate.&nbsp; For example,&nbsp; correlated additive and multiplicative (CAM) Gaussian noise, with infinite variance or heavy tails in certain parameter regimes,&nbsp; has received increased attention in the context of atmosphere and ocean dynamics.&nbsp; 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. &nbsp; 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. &nbsp; These applications motivate new stochastic averaging results for systems with fast processes driven by heavy-tailed noise.&nbsp; 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).
Friday, November 30, 2018 - 13:05 , Location: Skiles 005 , Samantha Petti , Math, Georgia Tech , , Organizer: He Guo
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.
Friday, November 30, 2018 - 14:00 , Location: Skiles 005 , Isabel Vogt , Massachusetts Institute of Technology , , Organizer: Padmavathi Srinivasan
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.&nbsp; 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.&nbsp; 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.
Friday, November 30, 2018 - 14:00 , Location: Skiles 006 , Surena Hozoori , Georgia Institute of Technology , , Organizer: Surena Hozoori
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. &nbsp;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.
Friday, November 30, 2018 - 16:00 , Location: Skiles 006 , Jake Fillman , Virginia Polytechnic Institute , Organizer: Michael Loss
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.&nbsp;