Seminars and Colloquia by Series

The fractal uncertainty principle

Series
Analysis Seminar
Time
Wednesday, November 28, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rui Han – Georgia Tech
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.

Lattice points and cube slicing

Series
High Dimensional Seminar
Time
Wednesday, November 28, 2018 - 12:55 for 1 hour (actually 50 minutes)
Location
skiles 006
Speaker
Marcel Celaya – Georgia Institute of technology –

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 $2^{k/2}$.

Efficient Prediction of User Activity using Mass Transport Equation

Series
GT-MAP Seminar
Time
Tuesday, November 27, 2018 - 15:00 for 2 hours
Location
Skiles 005
Speaker
Prof. Le Song – GT CSE

Please Note: 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.

Steady Rapidly Rotating Stars

Series
PDE Seminar
Time
Tuesday, November 27, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
skiles 006
Speaker
Yilun(Allen) Wu – The University of Oklahoma –
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.

The power of parallelization in large-scale convex optimization

Series
ACO Alumni Lecture
Time
Tuesday, November 27, 2018 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Cristobal Guzman – Universidad Católica de Chile, Chile

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).

Granular sessile drops

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 26, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ray Treinen – Texas State University –

Please Note: This should be unpublished. Againx3

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.

Granular sessile drops

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 26, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
005 Skiles
Speaker
Ray Treinen – Texas State University –

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.

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