Seminars and Colloquia by Series

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.

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.

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