Seminars and Colloquia by Series

The three-body problem and low energy space missions

Series
Time
Friday, October 7, 2022 - 11:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Marian GideaYU

https://gatech.zoom.us/j/95197085752?pwd=WmtJUVdvM1l6aUJBbHNJWTVKcVdmdz09

The three-body problem, on the dynamics of three masses under mutual gravity, serves as a model for the motion of a spacecraft relative to the Earth-Moon or Sun-Earth system. We describe the equations of motion for the three-body problem and the geometric objects that organize the dynamics: equilibriums points, periodic and quasi-periodic orbits, and their stable and unstable manifolds. As it turns out, trajectories that follow these manifolds require zero energy cost. We describe several methods to design low energy spacecraft trajectories from Earth to Moon, as well as maneuvers to change the inclination of the orbit of a satellite relative to the ecliptic. This is based on joint works with E. Belbruno, F. Topputo, A. Delshams, and P. Roldan.   
 

Recovery of quantum information: quantum Markov chains and matrix product states

Series
Math Physics Seminar
Time
Thursday, October 6, 2022 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles Room 005
Speaker
Brian KennedySchool of Physics, Georgia Tech

The mathematical theory of the recovery of quantum states stored in a quantum memory, is intimately related to the subadditivity property of the entropy function, and the class of states known as quantum Markov chains. In this talk we will introduce some of the basic ideas of this area of quantum information theory. We discuss a theorem regarding recovery of a widely studied class of quantum states, the matrix product states, and its implication for the mutual information stored over separated regions of a one dimensional quantum memory. This is joint work with Pavel Svetlichnyy and Shivan Mittal.

A stochastic approach for noise stability on the hypercube

Series
Stochastics Seminar
Time
Thursday, October 6, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/86578123009
Speaker
Dan MikulincerMIT

Please Note: Recording: https://us02web.zoom.us/rec/share/cIdTfvS0tjar04MWv9ltWrVxAcmsUSFvDznprSBT285wc0VzURfB3X8jR0CpWIWQ.Sz557oNX3k5L1cpN

We revisit the notion of noise stability in the hypercube and show how one can replace the usual heat semigroup with more general stochastic processes. We will then introduce a re-normalized Brownian motion, embedding the discrete hypercube into the Wiener space, and analyze the noise stability along its paths. Our approach leads to a new quantitative form of the 'Majority is Stablest' theorem from Boolean analysis and to progress on the 'most informative bit' conjecture of Kumar and Courtade.

3-Manifolds up to 1957

Series
Geometry Topology Student Seminar
Time
Wednesday, October 5, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Weizhe ShenGeorgia Institute of Technology

Please Note: A three-manifold is a space that locally looks like the Euclidean three-dimensional space. The study of three-manifolds has been at the heart of many beautiful constructions in low dimensional topology. This talk will provide a quick tour through some fundamental results about three-manifolds that were discovered between the late nineteenth century and the Fifties.

Latin squares in extremal and probabilistic combinatorics

Series
Research Horizons Seminar
Time
Wednesday, October 5, 2022 - 12:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tom KellyGeorgia Tech

An order-n Latin square is an n by n array of n symbols such that each row and column contains each symbol exactly once.  Latin squares were famously studied by Euler in the 1700s, and at present they are still a central object of study in modern extremal and probabilistic combinatorics.  In this talk, I will give some history about Latin squares, share some simple-to-state yet notoriously difficult open problems, and present some of my own research on Latin squares.

The complexity of list-5-coloring with forbidden induced substructures

Series
Graph Theory Seminar
Time
Tuesday, October 4, 2022 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
Yanjia LiGeorgia Tech

The list-$k$-coloring problem is to decide, given a graph $G$ and a list assignment $L$ of $G$ from $V(G)$ to subsets of $\{1,...,k\}$, whether $G$ has a coloring $f$ such that $f(v)$ in $L(v)$ for all $v$ in $V(G)$. The list-$k$-coloring problem is a generalization of the $k$-coloring problem. Thus for $k\geq 3$, both the $k$-coloring problem and the list-$k$-coloring problem are NP-Hard. This motivates studying the complexity of these problems restricted to graphs with a fixed forbidden induced subgraph $H$, which are called $H$-free graphs.

In this talk, I will present a polynomial-time algorithm to solve the list-5-coloring $H$-free graphs with $H$ being the union of $r$ copies of mutually disjoint 3-vertex paths. Together with known results, it gives a complete complexity dichotomy of the list-5-coloring problem restricted to $H$-free graphs. This is joint work with Sepehr Hajebi and Sophie Spirkl.

The existence of Prandtl-Batchelor flows on disk and annulus

Series
PDE Seminar
Time
Tuesday, October 4, 2022 - 15:00 for 1 hour (actually 50 minutes)
Location
Speaker
Zhiwu LinGeorgia Tech

For steady two-dimensional incompressible flows with a single eddy (i.e. nested closed streamlines), Prandtl (1905) and Batchelor (1956) proposed that in the limit of vanishing viscosity the vorticity is constant in an inner region separated from the boundary layer. By constructing higher order approximate solutions of the Navier-Stokes equations and establishing the validity of Prandtl boundary layer expansion, we give a rigorous proof of the existence of Prandtl-Batchelor flows on a disk with the wall velocity slightly different from the rigid-rotation. The leading order term of the flow is the constant vorticity solution (i.e. rigid rotation) satisfying the Batchelor-Wood formula. For an annulus with wall velocities slightly different from the rigid-rotation, we also constructed Prandtl-Batchelor flows, whose leading order terms are rotating shear flows. This is a joint work with Chen Gao, Mingwen Fei and Tao Tao. 

Geography of surface bundles over surfaces

Series
Geometry Topology Seminar
Time
Monday, October 3, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
İnanç BaykurUMass Amherst / Harvard

An outstanding problem for surface bundles over surfaces, closely related to the symplectic geography problem in dimension four, is to determine for which fiber and base genera there are examples with non-zero signatures. I will report on our recent progress (joint with M. Korkmaz), which resolves the problem for all fiber and base genera except for 18 pairs at the time of writing.

Generic and non-generic synchronization configurations in networks of coupled oscillators

Series
Algebra Seminar
Time
Monday, October 3, 2022 - 13:30 for 1 hour (actually 50 minutes)
Location
Clough 125 Classroom
Speaker
Tianran ChenAuburn University at Montgomery

Networks of coupled oscillators are studied in biology, chemistry, physics, and engineering. The Kuramoto model is a simple dynamical system that models the nonlinear interaction among coupled oscillators. It has received widespread attention since it is simple enough to be analyzed rigorously yet complex enough to exhibit interesting emergent behaviors.

One such emergent behavior is the spontaneous synchronization of oscillators into special configurations. In the past decades, rigorous analysis of such synchronization configurations has been the focus of intensive studies.

In this talk, we explore the new insight to this problem provided by an algebraic and tropical approach.

Functional Poisson approximations for some dissipative systems

Series
CDSNS Colloquium
Time
Friday, September 30, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
In-person in Skiles 006
Speaker
Yaofeng SuGeorgia Tech

The study of Poisson approximations of the process of recurrences to small subsets in the phase spaces of chaotic dynamical systems, started in 1991, have developed by now into a large active area of the dynamical systems theory. In this talk, I will present some new results. This is a joint work with Prof. Leonid Bunimovich.

  1. I will start with some examples of dissipative hyperbolic systems,
  2. then formulate the question of functional Poisson approximations for these systems.
  3. To study Poisson approximations, I will present two difficulties, called short returns and ring conditions.
  4. These two difficulties can be partially solved under some conditions of, e.g. the dimension of the dynamics, the Hausdorff dimension of the SRB measure, etc. I will present a new method which does not depend on dimensions but can completely solve these two difficulties for dissipative systems.

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