|
11:00am - 340P - Combinatorics and Probability Michael Krivelevich - (Tel Aviv University) Embedding large minors in weak expanders and in sparse random graphs A graph G on n vertices is called an alpha-expander if the external neighborhood of every vertex subset U of size |U|<=n/2 in G has size at least alpha*|U|. Extending and improving the results of Plotkin, Rao and Smith, and of Kleinberg and Rubinfeld from the 90s, we prove that for every alpha>0, an alpha-expander G on n vertices contains every graph H with at most cn/log n vertices and edges as a minor, for c=c(alpha)>0. Alternatively, every n-vertex graph G without sublinear separators contains all graphs with cn/logn vertices and edges as minors. Consequently, a supercritical random graph G(n,(1+epsilon)/n) is typically minor-universal for the class of graphs with cn/log n vertices and edges. The order of magnitude n/log n in the above results is optimal.
A joint work with Rajko Nenadov. |
|
2:00pm to 2:50pm - RH 510R - Working Group in Information Theory Amirhossein Taghvaei - (UC Irvine) Local behavior of divergence This week, we will discuss Section 4.2-4.3 of the lecture notes of Wu and Polyanski: Working Group in Information Theory is a self-educational project in the department. Techniques based on information theory have become essential in high-dimensional probability, theoretical computer science and statistical learning theory. On the other hand, information theory is not taught systematically. The goal of this group is to close this gap. |
|
3:00pm to 3:50pm - RH 306 - Analysis Min Ru - (Houston University) The geometric and arithmetic aspect of algebraic varieties In this talk, I will first discuss some geometric properties of the algebraic varieties which are related to (and determine) their arithmetic properties (in particular the finiteness of the number of the rational points). I will then state and discussion my recent result with Paul Vojta, as well as its application. |
|
4:00pm - RH 306 - Differential Geometry Daniel Stern - (University of Toronto) Scalar curvature and harmonic functions We'll discuss a new technique for relating scalar curvature bounds to the global structure of 3-dimensional manifolds, exploiting a relationship between the scalar curvature and the topology of level sets of harmonic functions. We will describe several geometric applications in both the compact and asymptotically flat settings, including a simple and effective new proof (joint with Bray, Kazaras, and Khuri) of the three-dimensional Riemannian positive mass theorem.
|
|
3:00pm to 3:50pm - 340P - Harmonic Analysis Ioan Bejenaru - (UCSD) The multilinear restriction estimates for hypersurfaces with curvature Abstract: I will present an overview of the multilinear restriction theory, with an emphasis on the case when the hypersurfaces have some curvature. I will discuss a new result: the case of n-1 hypersurfaces in n dimensions where a fairly general theory is developed. |
|
2:00pm to 3:00pm - RH 340P - Differential Geometry Zuoqin Wang - (USTC and MIT) Semi-classical isotropic functions and applications Rapidly oscillating functions associated with Lagrangian submanifolds play a fundamental role in semi-classical analysis. In this talk I will describe how to associate spaces of semi-classical oscillatory functions to isotropic submanifolds of phase space, and sketch their symbol calculus. As a special case we obtain the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin. I will also discuss a couple applications of the theory. This is based on joint works with Victor Guillemin and Alejandro Uribe. |
|
2:00pm to 3:00pm - 340P Rowland Hall - Differential Geometry Zuoqin Wang - (USTC and MIT) Semi-classical isotropic functions and applications Rapidly oscillating functions associated with Lagrangian submanifolds play a fundamental role in semi-classical analysis. In this talk I will describe how to associate spaces of semi-classical oscillatory functions to isotropic submanifolds of phase space, and sketch their symbol calculus. As a special case we obtain the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin. I will also discuss a couple applications of the theory. This is based on joint works with Victor Guillemin and Alejandro Uribe. |
|
3:00pm - RH 306 - Algebra Tomasz Prytuła - (Technical University of Denmark) Commensurators of abelian subgroups in CAT(0) groups This talk will introduce work in the area of Geometric Group Theory; no prior background in this area will be assumed. The commensurator of a subgroup H of a group G may be seen as a coarse approximation of the normalizer of H. We consider the situation where H is free abelian and G acts properly on a CAT(0) space, that is, a simply connected space of metric non-positive curvature. The structure of the normalizer of H and its action on the space are well understood in this context. However, the commensurator is more mysterious and it contains subtle information about the action which is not seen by the normalizer. For various classes of CAT(0) spaces we obtain structural results about the commensurator and its relation to the normalizer. In this talk, first I will give background on the commensurator and on CAT(0) spaces and groups, and then I will discuss various geometric tools and constructions used in our approach. This is joint work with Jingyin Huang. |
|
3:00pm - RH 306 - Number Theory Tomasz Prytuła - (Technical University of Denmark) Commensurators of abelian subgroups in CAT(0) groups This talk will introduce work in the area of Geometric Group Theory; no prior background in this area will be assumed. The commensurator of a subgroup H of a group G may be seen as a coarse approximation of the normalizer of H. We consider the situation where H is free abelian and G acts properly on a CAT(0) space, that is, a simply connected space of metric non-positive curvature. The structure of the normalizer of H and its action on the space are well understood in this context. However, the commensurator is more mysterious and it contains subtle information about the action which is not seen by the normalizer. For various classes of CAT(0) spaces we obtain structural results about the commensurator and its relation to the normalizer. In this talk, first I will give background on the commensurator and on CAT(0) spaces and groups, and then I will discuss various geometric tools and constructions used in our approach. This is joint work with Jingyin Huang. |
|
4:00pm to 5:00pm - RH306 - Colloquium Susan Friedlander - (USC) Kolmogorov, Onsager and a stochastic model for turbulence We will briefly review Kolmogorov’s (41) theory of homogeneous turbulence and Onsager’s ( 49) This is joint work with Vlad Vicol and Nathan Glatt-Holtz. |