## Seminars and Colloquia by Series

Thursday, May 18, 2017 - 15:05 , Location: Skiles 005 , Daniel Kral , University of Warwick , Organizer: Robin Thomas
We study the uniqueness of optimal configurations in extremal combinatorics. An empirical experience suggests that optimal solutions to extremal graph theory problems can be made asymptotically unique by introducing additional constraints. Lovasz conjectured that this phenomenon is true in general: every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints such that the resulting set is satisfied by an asymptotically unique graph. We will present a counterexample to this conjecture and discuss related results. The talk is based on joint work with Andrzej Grzesik and Laszlo Miklos Lovasz.
Monday, May 15, 2017 - 10:05 , Location: Skiles 006 , Mikel Viana , Georgia Tech , Organizer:
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.
Wednesday, May 10, 2017 - 13:00 , Location: Skiles 005 , Marc Jorba-Cusco , Universitat de Barcelona , Organizer: Rafael de la Llave
Consider an affine skew product of the complex plane. $$\begin{cases} \omega \mapsto \theta+\omega,\\ z \mapsto =a(\theta \mu)z+c, \end{cases}$$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
Tuesday, May 9, 2017 - 10:00 , Location: Skiles 006 , , Organizers: Shui-Nee Chow, Wilfrid Gangbo, Prasad Tetali, and Haomin Zhou , Organizer: Haomin Zhou

This workshop is sponsored by College of Science, School of Mathematics, GT-MAP and NSF.&nbsp;

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).
Monday, May 8, 2017 - 14:00 , Location: Skiles 006 , Tye Lidman , NCSU , Organizer: Jennifer Hom
We will discuss a relation between some notions in three-dimensional topology and four-dimensional aspects of knot theory.
Monday, May 8, 2017 - 11:00 , Location: Skiles 005 , Xifeng Su , Beijing Normal University , Organizer: Rafael de la Llave
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.
Series: Other Talks
Thursday, May 4, 2017 - 08:03 , Location: Skiles 005 , Several speakers , 8 Institutions. , Organizer: Rafael de la Llave
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/
Friday, April 28, 2017 - 13:05 , Location: Skiles 005 , Megan Bernstein , School of Mathematics, Georgia Tech , Organizer: Marcel Celaya
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.
Friday, April 28, 2017 - 11:05 , Location: Skiles 006 , , Harvard University , Organizer: Padmavathi Srinivasan
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.
Thursday, April 27, 2017 - 10:00 , Location: Skiles 005 , Lei Zhang , Georgia Institute of Technology , Organizer: Lei Zhang
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.