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Series: Research Horizons Seminar

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

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: Other Talks

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

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).

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: Combinatorics Seminar

Series: ACO Student Seminar

Series: Geometry Topology Seminar

Mapping classes are the natural topological symmetries of surfaces. Their study is often restricted to the orientation-preserving ones, which form a normal subgroup of index two in the group of all mapping classes. In this talk, we discuss orientation-reversing mapping classes. In particular, we show that Lehmer's question from 1933 on Mahler measures of integer polynomials can be reformulated purely in terms of a comparison between orientation-preserving and orientation-reversing mapping classes.

Friday, November 16, 2018 - 15:05 ,
Location: Skiles 156 ,
Sergio Mayorga ,
Georgia Tech ,
Organizer: Jiaqi Yang

In this talk I will begin by discussing the main ideas of mean-field games and then I will introduce one specific model, driven by a smooth hamiltonian with a regularizing potential and no stochastic noise. I will explain what type of solutions can be obtained, and the connection with a notion of Nash equilibrium for a game played by a continuum of players.