A Kirillov-Reshetikhin(KR) module is a certain finite dimensional U_q'(\mathfrak{g}) module that is determined by its Drinfeld polynomials. KR modules are an important class of modules for quantum groups with many applications to Mathematical physics. KR modules are conjectured to have many nice properties, one of which is the existence of a crystal basis. In this talk, we will give a…
We propose a Mixed Integer Partial Differential Equation Constrained Optimization (MIPDECO) formulation of the topological optimization for electromagnetic cloaking. Our formulation introduces binary variables to indicate the presence/absence of metamaterial at a given location within the cloaking device. The cloaking device is discretized on a 20x20 and 40x40 domain of squared material locations, and has two to…
The leading eigenvalue problems arise in many applications. When the dimension of the matrix is super huge, such as for applications in quantum many-body problems, conventional algorithms become impractical due to computational and memory complexity. In this talk, we will describe some recent works on new algorithms for the leading eigenvalue problems based on randomized and coordinate-wise methods (joint work with…
Machine learning has become widely popular in fields like computer vision, natural language processing, and speech recognition, often performing tasks better than humans. A fundamental building block of many of these algorithms is a neural network known as a multilayer perceptron. In this tutorial we will discuss how to construct these networks and how to…
Target Audience: Third, Fourth, and Fifth Years
Tensors are multiway arrays, and these occur naturally in many data analysis. Consider a series of experiments tracking multiple sensors over time, resulting in a three-way tensor of the form experiment-by-sensor-by-time. Tensor decompositions are powerful tools for data analysis that can be used for data interpretation, dimensionality reduction, outlier detection, and estimation of missing data.…
In this overview talk, I will first explain several mathematical approaches of mirror symmetry. Then I will focus on the mathematical theory of Witten's gauged linear sigma model based on the recent joint work with Gang Tian, which settles the mathematical foundation of the approach of Hori and Vafa.
The Valsalva maneuver (VM) is a quick, noninvasive, clinical procedure with a variety of uses. In particular, the VM can aid in the diagnosis of autonomic nervous system dysfunction. The VM induces changes in blood pressure, which reflexively induces a neural signaling cascade to adjust heart rate, heart contractility, peripheral vascular resistance, and venous compliance.…
Suzanne Crifo will begin with a general discussion of class evaluations- why they may be important, how you can use them, how to interpret them, how to get higher response rates, etc., and then move into the specifics of mid-semester evaluations. In the second half of the workshop, participants will be given time and assistance…
Yangians are one of the main examples of quantum groups introduced by Drinfeld and have found applications in combinatorics, representation theory and algebraic geometry. It is well-known that the R-matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation. It has been an open problem to extend this result to the remaining types since…
xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This presentation is intended to clarify the notion of xVA as well as the usage of the xVA items in…
The smooth version of the 4-dimensional Poincare Conjecture (S4PC) states that every homotopy 4-sphere is diffeomorphic to the standard 4-sphere. One way to attack the S4PC is to examine a restricted class of 4-manifolds. For example, Gabai's proof of Property R implies that every homotopy 4-sphere built with one 2-handle and one 3-handle is standard. …
Wednesday to Saturday Nov. 7-10 in SAS Hall 4201. Lectures are open to all. Conference Information is located here.
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical…
Wednesday to Saturday Nov. 7-10 in SAS Hall 4201. Lectures are open to all. Conference Information is located here.