## Seminars and Colloquia by Series

Friday, April 20, 2018 - 15:05 , Location: Skiles 271 , Prof. Rafael de la Llave , GT Math , Organizer: Jiaqi Yang
A well known paper of H. Federer on Flat chains contains a remarkable example attributed  to F. Almgren. We intend to give a geometric exposition of the example and explain its relevance in the global theory of geodesic flows and some global problems such as homogenization in quasi-periodic media. This is part of an expository paper with X. Su.
Friday, April 20, 2018 - 13:05 , Location: Skiles 005 , , CSE, University of Washington , , Organizer: He Guo
Friday, April 20, 2018 - 10:00 , Location: Skiles 006 , Jose Acevedo , Georgia Tech , Organizer: Kisun Lee
In this talk we show how to obtain some (sometimes sharp) inequalities between subgraph densities which are valid asymptotically on any sequence of finite simple graphs with an increasing number of vertices. In order to do this we codify a simple graph with its edge monomial and establish a nice graphical notation that will allow us to play around with these densities.
Thursday, April 19, 2018 - 15:05 , Location: Skiles 006 , , Carnegie Mellon University , , Organizer: Michael Damron
We shall prove that a certain stochastic ordering defined in terms of convex symmetric sets is inherited by sums of independent symmetric random vectors. Joint work with W. Bednorz.
Thursday, April 19, 2018 - 13:30 , Location: Skiles 005 , Alexander Hoyer , Math, GT , Organizer: Robin Thomas
Györi and Lovasz independently proved that a k-connected graph can be partitioned into k subgraphs, with each subgraph connected, containing a prescribed vertex, and with a prescribed vertex count. Lovasz used topological methods, while Györi found a purely graph theoretical approach. Chen et al. later generalized the topological proof to graphs with weighted vertices, where the subgraphs have prescribed weight sum rather than vertex count. The weighted result was recently proven using Györi's approach by Chandran et al. We will use the Györi approach to generalize the weighted result slightly further. Joint work with Robin Thomas.
Thursday, April 19, 2018 - 11:00 , Location: Skiles 006 , , UCLA Mathematics Department , Organizer: Mayya Zhilova
This talk is about the structure theory of measure-preserving systems: transformations of a finite measure space that preserve the measure. Many important examples arise from stationary processes in probability, and simplest among these are the i.i.d. processes. In ergodic theory, i.i.d. processes are called Bernoulli shifts. Some of the main results of ergodic theory concern an invariant of systems called their entropy, which turns out to be intimately related to the existence of `structure preserving' maps from a general system to Bernoulli shifts. I will give an overview of this area and its history, ending with a recent advance in this direction. A measure-preserving system has the weak Pinsker property if it can be split, in a natural sense, into a direct product of a Bernoulli shift and a system of arbitrarily low entropy. The recent result is that all ergodic measure-preserving systems have this property. This talk will assume graduate-level real analysis and measure theory, and familiarity with the basic language of random variables. Past exposure to entropy, measure-theoretic probability or ergodic theory will be helpful, but not essential.
Wednesday, April 18, 2018 - 14:10 , Location: Skiles 006 , Sarah Davis , GaTech , Organizer: Anubhav Mukherjee
The theorem of Dehn-Nielsen-Baer says the extended mapping class group is isomorphic to the outer automorphism group of the fundamental group of a surface. This theorem is a beautiful example of the interconnection between purely topological and purely algebraic concepts. This talk will discuss the background of the theorem and give a sketch of the proof.
Wednesday, April 18, 2018 - 13:55 , Location: Skiles 005 , , Clemson University , , Organizer: Galyna Livshyts
We discuss the probability that a continuous stationary Gaussian process on whose spectral measure vanishes in a neighborhood of the origin stays non-negative on an interval of long interval.  Joint work with  Naomi Feldheim, Ohad Feldheim, Fedor Nazarov,  and Shahaf Nitzan
Series: PDE Seminar
Tuesday, April 17, 2018 - 15:00 , Location: Skiles 006 , , Duke University , , Organizer: Yao Yao
Epitaxial growth is an important physical process for forming solid films or other nano-structures.  It occurs as atoms, deposited from above, adsorb and diffuse on a crystal surface.  Modeling the rates that atoms hop and break bonds leads in the continuum limit to degenerate 4th-order PDE that involve exponential nonlinearity and the p-Laplacian with p=1, for example.  We discuss a number of analytical results for such models, some of which involve subgradient dynamics for Radon measure solutions.
Monday, April 16, 2018 - 15:30 , Location: Skiles 005 , Yu Pan , MIT , Organizer: Caitlin Leverson
Augmentations and exact Lagrangian fillings are closely related. However, not all the augmentations of a Legendrian knot come from embedded exact Lagrangian fillings. In this talk, we show that all the augmentations come from possibly immersed exact Lagrangian fillings. In particular, let ∑ be an immersed exact Lagrangian filling of a Legendrian knot in $J^1(M)$ and suppose it can be lifted to an embedded Legendrian L in J^1(R \times M). For any augmentation of L, we associate an induced augmentation of the Legendrian knot, whose homotopy class only depends on the compactly supported Legendrian isotopy type of L and the homotopy class of its augmentation of L. This is a joint work with Dan Rutherford.