Seminars and Colloquia by Series

Results on the construction of whiskered invariant tori for fibered holomorphic dynamics and on compensated domains.

Series
Dissertation Defense
Time
Monday, May 15, 2017 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mikel Viana – Georgia Tech
We first discuss the construction of whiskered invariant tori for fibered holomorphic dynamics using a Nash-Moser iteration. The results are in a-posteriori form. The iterative procedure we present has numerical applications (it lends itself to efficient numerical implementations) since it is not based on transformation theory but rather in applying corrections which ameliorate notably the curse of dimensionality. Then we will discuss results on compensated domains in a Banach space.

A fractalization process for affine skew-products on the complex plane

Series
CDSNS Colloquium
Time
Wednesday, May 10, 2017 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Marc Jorba-Cusco – Universitat de Barcelona
Consider an affine skew product of the complex plane. \begin{equation}\begin{cases} \omega \mapsto \theta+\omega,\\ z \mapsto =a(\theta \mu)z+c, \end{cases}\end{equation}where $\theta \in \mathbb{T}$, $z\in \mathbb{C}$, $\omega$ is Diophantine, and $\mu$ and $c$ are real parameters. In this talk we show that, under suitable conditions, the affine skew product has an invariant curve that undergoes a fractalization process when $\mu$ goes to a critical value. The main hypothesis needed is the lack of reducibility of the system. A characterization of reducibility of linear skew-products on the complex plane is provided. We also include a linear and topological classification of these systems. Join work with: N\'uria Fagella, \`Angel Jorba and Joan Carles Tatjer

Working Group for Problems in Transport and Related Topics in Graphs

Series
GT-MAP Seminar
Time
Tuesday, May 9, 2017 - 10:00 for 8 hours (full day)
Location
Skiles 006
Speaker
Speaker list and schedule can be found at http://www.math.gatech.edu/hg/item/589661 – Organizers: Shui-Nee Chow, Wilfrid Gangbo, Prasad Tetali, and Haomin Zhou

Please Note: This workshop is sponsored by College of Science, School of Mathematics, GT-MAP and NSF.

The goal of this workshop is to bring together experts in various aspects of optimal transport and related topics on graphs (e.g., PDE/Numerics, Computational and Analytic/Probabilistic aspects).

Concordance and Dehn surgery

Series
Geometry Topology Seminar
Time
Monday, May 8, 2017 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tye Lidman – NCSU
We will discuss a relation between some notions in three-dimensional topology and four-dimensional aspects of knot theory.

Weak KAM theorem for Frenkel-Kontorova models and related topics

Series
CDSNS Colloquium
Time
Monday, May 8, 2017 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xifeng Su – Beijing Normal University
We will consider the Frenkel-Kontorova models and their higher dimensional generalizations and talk about the corresponding discrete weak KAM theory. The existence of the discrete weak KAM solutions is related to the additive eigenvalue problem in ergodic optimization. In particular, I will show that the discrete weak KAM solutions converge to the weak KAM solutions of the autonomous Tonelli Hamilton-Jacobi equations as the time step goes to zero.

Opening meeting for the Stability and Transitions in Physical Processes (TraX)

Series
Other Talks
Time
Thursday, May 4, 2017 - 08:03 for 8 hours (full day)
Location
Skiles 005
Speaker
Several speakers – 8 Institutions.
The TraX project is an inter-university effort, involving researchers from 8 universities, aimed at elucidating the geometric structures in phase space which determine the speed and nature of chemical reactions and how they are affected by external influences such as light pulses or noise. The effort is highly interdisciplinary and it involves Mathematics (Dynamical Systems), Numerical Computations, Physics, and Chemistry all working together to understand experimental phenomena and make predictions. The project has been funded by the European Research Council, Mathematics Division for 4 years and it will sponsor visits of European scientists to GT and provide opportunities for graduate students to collaborate in this area. http://traxkickoff.gatech.edu/

Cutoff for the random to random shuffle

Series
ACO Student Seminar
Time
Friday, April 28, 2017 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Megan Bernstein – School of Mathematics, Georgia Tech
The random to random shuffle on a deck of cards is given by at each step choosing a random card from the deck, removing it, and replacing it in a random location. We show an upper bound for the total variation mixing time of the walk of 3/4n log(n) +cn steps. Together with matching lower bound of Subag (2013), this shows the walk mixes with cutoff at 3/4n log(n) steps, answering a conjecture of Diaconis. We use the diagonalization of the walk by Dieker and Saliola (2015), which relates the eigenvalues to Young tableaux. Joint work with Evita Nestorid.

Abelian varieties isogenous to Jacobians

Series
Algebra Seminar
Time
Friday, April 28, 2017 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ananth Shankar – Harvard University
Chai and Oort have asked the following question: For any algebraically closed field $k$, and for $g \geq 4$, does there exist an abelian variety over $k$ of dimension $g$ not isogenous to a Jacobian? The answer in characteristic 0 is now known to be yes. We present a heuristic which suggests that for certain $g \geq 4$, the answer in characteristic $p$ is no. We will also construct a proper subvariety of $X(1)^n$ which intersects every isogeny class, thereby answering a related question, also asked by Chai and Oort. This is joint work with Jacob Tsimerman.

Analysis and Numerical Methods in Solid State Physics and Chemistry

Series
Dissertation Defense
Time
Thursday, April 27, 2017 - 10:00 for 2 hours
Location
Skiles 005
Speaker
Lei Zhang – Georgia Institute of Technology
We present two distinct problems in the field of dynamical systems.I the first part, we cosider an atomic model of deposition of materials over a quasi-periodic medium, that is, a quasi-periodic version of the well-known Frenkel-Kontorova model. We consider the problem of whether there are quasi-periodic equilibria with a frequency that resonates with the frequencies of the medium. We show that there are always perturbative expansions. We also prove a KAM theorem in a-posteriori form.In the second part, we consider a simple model of chemical reaction and present a numerical method calculating the invariant manifolds and their stable/unstable bundles based on parameterization method.

Approach to equilibrium in Mark Kac's model

Series
Dissertation Defense
Time
Wednesday, April 26, 2017 - 09:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hagop Tossounian – Georgia Tech –
Kinetic theory is the branch of mathematical physics that studies the motion of gas particles that undergo collisions. A central theme is the study of systems out of equilibrium and approach of equilibrium, especially in the context of Boltzmann's equation. In this talk I will present Mark Kac's stochastic N-particle model, briefly show its connection to Boltzmann's equation, and present known and new results about the rate of approach to equilibrium, and about a finite-reservoir realization of an ideal thermostat.

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