## Seminars and Colloquia Schedule

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.
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.
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).
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