|
3:00pm to 3:50pm - RH 340P - Inverse Problems Joonas Ilmavirta - (University of Jyvaskyla, Finland) Metric inverse problems I will discuss inverse problems for metric spaces and their relation to more familiar types of inverse problems. Some non-metric problems have been recently solved with metric tools, and I will explain the benefits of this approach. |
|
4:00pm to 5:00pm - RH 340N - Geometry and Topology Brian Shin - (UCLA) Norms and Hermitian K-theory Over the past century, cohomology operations have played a crucial role in homotopy theory and its applications. A powerful framework for constructing such operations is the theory of commutative (i.e. $\mathbb{E}_\infty$) ring spectra. In this talk, I will discuss an algebro-geometric analogue of this framework, called the theory of normed motivic ring spectra. As a particular example of interest, I'll show that (very effective) Hermitian K-theory can be equipped with a normed ring structure. |
|
4:00pm to 5:00pm - RH 306 - Applied and Computational Mathematics Yunho Kim - (Ulsan National Institute of Science and Technology) Introduction to reservoir computing Reservoir computing is a branch of neuromorphic computing, which is usually realized in the form of ESNs (Echo State Networks). In this talk, I will present some fundamentals of reservoir computing from both the mathematical and the computational points of view. While reservoir computing was designed for sequential/time-series data, we recently observed its great performances in dealing with static image data once the reservoir is set to process certain image features, not the images themselves. Hence, I will discuss possible applications and open questions in reservoir computing. |
|
4:00pm to 4:50pm - RH 340P - Inverse Problems Teemu Saksala - (NC State) Geometric Inverse Problems Arising from Hyperbolic PDEs In this talk I will survey the classical Boundary Control method, originally developed by Belishev and Kurylev, which can be used to reduce an inverse problem for a hyperbolic equation, on a complete Riemannian manifold, to a purely geometric problem involving the so-called travel time data. For each point in the manifold the travel time data contains the distance function from this point to any point in a fixed a priori known closed observation set. If the Riemannian manifold is closed then the observation set is a closure of an open and bounded set, and in the case of a manifold with boundary the observation set is an open subset of the boundary. We will survey many known uniqueness and stability results related to the travel time data. |
|
3:00pm to 4:00pm - RH 306 - Analysis Junbang Liu - (Stony Brook) An improved ABP estimate in the complex setting In this talk, we will present an improved ABP estimate in the complex setting and discuss its applications to complex Hessian equations. These include a sharp gradient estimate for complex Monge-Ampere equations and a bound on the sup-slope for a class of Hessian equations. The approach is based on a comparison version of the iteration method developed by Guo, Phong, and Tong. |
|
3:00pm to 4:00pm - Rowland Hall 510R - Combinatorics and Probability Thomas Mountford - (EPFL) Mean field results for queueing models with infection This is joint work in progress with Zhe Wang. We consider the model introduced by Baccelli, Foss and Schneer where we consider a closed system of n queues where clients can infect other clients in a contact process like manner. We show in the super critical phase convergence to the "invariant measure". |
|
10:00am to 11:00am - RH 306 - Analysis Siyuan Lu - (McMaster University) Interior C^2 estimate for Hessian quotient equation In this talk, I will first review the history of interior C^2 estimate for fully nonlinear equations. Notably, very few equations were shown to admit such property. In the second part, I will discuss my recent work on interior C^2 estimate for Hessian quotient equations. Such equations have deep connections with the Monge-Ampere equation, Hessian equations and special Lagrangian equations. I will then discuss the main idea behind the proof and some future directions in this area. |
|
4:00pm to 5:00pm - NSII 1201 - Special Colloquium Alexander Volberg - (Michigan State U) Removability, rectifiability, and harmonic measure What are the removable singularities of harmonic functions with bounded gradient? This problem, that takes its origins in certain problems of complex analysis, which are 140 years old, was solved relatively recently. Its solution is based on extension to a new territory of classical theory of singular integrals. Singular integrals are ubiquitous objects and play an important part in Geometric Measure Theory. The simplest ones are called Calderon–Zygmund operators. Their theory was completed in the 50′s by Zygmund and Calderon. Or it seemed like that. The last 25 years saw the need to consider CZ operators in very bad environment, so kernels are still very good, but the ambient set/measure has no regularity whatsoever. Initially such situations appeared from the wish to solve some outstanding problems in complex analysis: such as problems of Painleve, Ahlfors, Denjoy and Vitushkin. The analysis of CZ operators on very bad sets is very fruitful in the part of Geometric Measure Theory that deals with removability mentioned above and rectifiability. It can be viewed as the study of very low regularity free boundary problems. We will explain the genesis of ideas that led to several long and difficult proves that culminated in the solutions of problems of Denjoy, Vitushkin, David-Semmes, and Bishop, and brought also the solution by Tolsa of Painleve’s problem. |