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Today

Tamara G. Kolda , Sandia National Laboratories, Tensor Decomposition: A Mathematical Tool for Data Analysis

SAS 2203

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.…

Ben Randall, NC State, Cardiovascular and neurological modeling in response to the Valsalva maneuver

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.…

Mid-Semester Evaluations

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…

Naihuan Jing, NC State, Yangian algebras of classical types

SAS 4201

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…

Alex Zupan, University of Nebraska, A special case of the Smooth 4-dimensional Poincare Conjecture

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. …

Yaiza Canzani, UNC Chapel Hill, Understanding the growth of Laplace eigenfunctions

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…

Jonathan Mattingly, Duke University, Quantifying Gerrymandering: A mathematician goes to court

SAS 1102

In October 2017, I found myself testify for hours in a Federal court. I had not been arrested. Rather I was attempting to quantifying gerrymandering using analysis which grew from asking if a surprising 2012 election was in fact surprising. It hinged on probing the geopolitical structure of North Carolina using a Markov Chain Monte…

Triangle Lectures in Combinatorics

Hanes Hall, Room 120 University of North Carolina, Chapel Hill

Hanes Hall, Room 120 University of North Carolina, Chapel Hill Chapel Hill, North Carolina   The Triangle Lectures in Combinatorics is a series of combinatorial workshops held each semester on a Saturday in the Research Triangle region of North Carolina, funded by the National Science Foundation.  The workshop this coming fall, the 16th installment of the Triangle Lectures in Combinatorics,…

Malgorzata Peszynska, Modeling hysteresis using ODEs with constraints: Numerical stability and other properties

SAS 4201

In nonlinear conservation laws the flux function f(u) is usually single valued, but in many important applications it is hysteretic, i.e., it assigns different values depending on whether the input u(t) is increasing or decreasing in t. We present our recent results on a hysteresis model built with a collection of auxiliary ODEs under constraints. The model shares some similarities…

John Baldwin, Boston College, Contact structures, instantons, and SU(2) representations

A strengthening of the Poincare Conjecture asks whether the fundamental group of every closed 3-manifold which is not the 3-sphere admits a nontrivial homomorphism to SU(2). With that as motivation, I'll describe a connection between Stein fillings of a 3-manifold and SU(2) representations of its fundamental group, coming from instanton Floer homology. This connection can…