Biography: Professor Lan-Hsuan Huang received her PhD from Stanford University in 2009. She is currently Professor at the University of Connecticut and has held positions at Columbia University and Institute for Advanced Study, Princeton. She received the CAREER Award from the National Science Foundation in 2015 and Simons Fellowship in Mathematics in 2018. She is an invited speaker of the upcoming International Congress on Mathematical Physics in 2021. She works in geometric analysis and mathematical relativity.
Title: The shape of black holes
Abstract: Einstein’s theory of gravity has been a strong driving force for the current development in several branches of mathematics. Among its profound and wide applications, the theory successfully describes and even predicts celestial objects that were not known to exist, such as black holes. Over the past few decades, remarkable progress using advanced techniques in geometry and analysis has been made to resolve several fundamental questions in general relativity; it also leads to an astonishing realization that black holes are governed by the same mathematical principles as daily life objects, such as soap films. In this lecture, we will discuss the mathematical models of black holes and their intriguing interconnections to topology, geometry, and analysis.
Biography: Misha Elena Kilmer is the William Walker Professor of Mathematics and Adjunct Professor of Computer Science at Tufts University. She was named Fellow of the Society for Industrial and Applied Mathematics in 2019. Prof. Kilmer obtained her Ph.D. in Applied Mathematics from the University of Maryland, College Park. She specializes in the development of fast algorithms for solving large-scale, forward and inverse problems, as well as on theoretical and applied aspects of tensor computation.
Prof. Kilmer is a 2001 recipient of the Tufts Undergraduate Initiative in Teaching Award and was promoted directly to Full Professor in 2005. She is a member of AWM and SIAM. She currently serves as Section Editor for SIAM Review Research Spotlights and as an associate editor for SIAM Journal on Scientific Computing. She is a former Associate Editor for SIAM Journal on Matrix Analysis and Applications and for SIAM Undergraduate Research Online. She is the author of numerous refereed articles and conference proceedings papers appearing in a wide range of computational math and engineering publications. Her work has been or is being funded by the NSF, NIH, IARPA, DARPA and IBM.
Title: The Case for Tensor Factorization: Compression, Analysis, and Reconstruction of Image Data
Abstract: A grayscale digital image is a matrix (m x n array) whose entries represent intensity values. One way to compress an image, therefore, is to treat the image as a matrix for which a rank-revealing factorization, such as the singular value decomposition (SVD), can be computed. Vectors in the SVD corresponding to the largest singular values represent the directions with the most information content about the matrix. This information is retained and the rest of the vectors are discarded, providing an implicitly compressed representation of the image that retains the important features of the image for later analysis or reconstruction. However, a sequence or collection of k grayscale images (e.g. slices of a 3D medical image or frames in a video) can be arranged as an m x k x n data object. This multiway array is called a tensor and general concepts and algorithms from linear algebra are not easily generalizable to tensors. We introduce new methods for factoring such tensors which resemble matrix factorizations and illustrate how these can be used to successfully compress, analyze and reconstruct multiway image data. This talk is intended to accessible to students who have had a course in Linear Algebra.
Saturday, October 24th
University of Connecticut, Storrs, CT
|WebEx Room 1||WebEx Room 2|
|10:00-11:00||Plenary talk (Lan-Hsuan Huang)||The shape of black holes|
|11:05-11:30||Parallel talks||Ryan Alvarado
Title: The Game of Cycles: How to win before you even begin!
Title: Arithmetic dynamics of post-critically finite functions
|11:35-12:00||Parallel talks||Anthony Della Pella
Title: Counting Cliques Using Polynomials
Title: Hot Tip: Use Math to Study our Changing Climate
|12:10-1:00||Graduate school panel|
|2:15-2:40||Parallel talks||Sherli Koshy Chenthittayil
Title: Using agent based models to understand biofilm interactions
Title: The Heisenberg Group
|2:45-3:10||Parallel talks||Briana Oshiro
Title: The Study of Mathematical Problem Solving
Title: Sets of Finite Perimeter
|3:20-4:20||Plenary talk (Misha Kilmer)||The Case for Tensor Factorization: Compression, Analysis, and Reconstruction of Image Data|