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Monday, November 26, 2018 - 13:55 ,
Location: 005 Skiles ,
Ray Treinen ,
Texas State University ,
rt30@txstate.edu ,
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>

Series: ACO Alumni Lecture

Recently there has been an outburst of parallelization techniques to speed up optimization algorithms, particularly in applications in statistical learning and structured linear programs. Motivated by these developments, we seek for theoretical explanations of provable improvements (or the lack thereof) in performance obtained by parallelizing optimization algorithms. In 1994, Nemirovski proved that for low-dimensional optimization problems there is a very limited improvement that could be obtained by parallelization, and furthermore conjectured that no acceleration should be achievable by these means. In this talk, I will present new results showing that in high-dimensional settings no acceleration can be obtained by parallelization, providing strong evidence towards Nemirovski's conjecture. This is joint work with Jelena Diakonikolas (UC Berkeley).

Series: Other Talks

Cristobal Guzman will discuss his employment experience as an ACO alummus. The conversations will take place over coffee.

Series: PDE Seminar

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.

Series: GT-MAP Seminars

This is a part of GT MAP seminar. See gtmap.gatech.edu 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.

Series: Research Horizons Seminar

This is a survey talk on the knot concordance group and the homology cobordism group.

Series: High Dimensional Seminar

In this talk I will describe those linear subspaces of $\mathbf{R}^d$ which can be formed by taking the linear span of lattice points in a half-open parallelepiped. I will draw some connections between this problem and 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 $2^{k/2}$.

Series: Analysis Seminar

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 can not be simultaneously localized in
$\delta$-dimensional fractal
sets, $0<\delta<1$. In this talk, I will discuss a joint work
with Schlag, where we obtained 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.

Series: Graph Theory Working Seminar

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.

Series: Other Talks

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>

Series: Job Candidate Talk

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.

Series: Stochastics Seminar

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).

Series: ACO Student Seminar

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.

Series: Algebra Seminar

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.

Friday, November 30, 2018 - 14:00 ,
Location: Skiles 006 ,
Surena Hozoori ,
Georgia Institute of Technology ,
shozoori3@gatech.edu ,
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. 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.

Series: Math Physics Seminar

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.