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…
Wednesday to Saturday Nov. 7-10 in SAS Hall 4201. Lectures are open to all. Conference Information is located here.
Target Audience: All students
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,…
Wednesday to Saturday Nov. 7-10 in SAS Hall 4201. Lectures are open to all. Conference Information is located here.
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…
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…
We consider a controllability problem for the evolution of a set in V(t). This problem was originally motivated by a model where a dog controls a flock of sheep. Here, V(t) is the region occupied by the sheep and the position of the dog is regarded as a control function. We will discuss necessary conditions…
A brief overview of SNL’s mission, R&D areas, and opportunities in mathematics, statistics, and computational science will be given.
Affine Lie algebras are infinite dimensional analogs of finite dimensional simple Lie algebras. It is known there are finitely many maximal dominant weights for any integrable highest weight representation of an affine Lie algebra. However, determining these maximal dominant weights is a nontrivial task. So far only the descriptions of these weights are known for…
Kitware develops and supports modeling and simulation platforms that power medical training, planning, and predictive applications for improved patient treatment and outcomes. Our capabilities include whole-body computational physiology models for faster than real-time simulation, surgical planning, and guidance applications, high-fidelity computational fluid dynamics for patient-specific treatment planning, and virtual/augmented reality solutions for immersive training, and…
In this talk, I will present basic Bayesian statistics and multi-source Bayesian data fusion methods. It will start with basic statistical definitions, working through a coin flip problem. From there, I will outline multi-source fusion using several simple methods that require the previous Bayesian background. I will also provide several motivating examples, including one drawn…
The main goal of geometric topology is the classification of manifolds within a certain framework (topological, piecewise linear, smooth, simply-connected, symplectic, etc.). Dimension four is special, as it is the only dimension in which a manifold can admit infinitely many non-equivalent smooth structures, and the only dimension in which there exist manifolds homeomorphic but not…
Who: Any math graduate or undergraduate students What: Taking time to relax before dead week begins! We will have coloring sheets and origami paper/patterns. Come make something to brighten your office or apartment for the holidays, or just come hang out and enjoy lots of free treats! We will also have AWM bags available for purchase to raise money…
Target Audience: All students
The pancake graph has the elements of the symmetric group as vertices and there is an edge between two permutations if there is a prefix reversal that transforms one permutation into the other. One can similarly define the burnt pancake graph using signed permutations instead of permutations. Since these graphs are Cayley graphs, they have several interesting properties such as being regular and…
In this talk I’ll describe an overview of results on the Navier-Stokes equations for viscous compressible flows both in the deterministic and stochastic frame- work. A contrast will be drawn between the one-dimensional flows and the multidimensional case. In the case of 1d isentropic compressible flow, the existence of invariant mea- sures will be established…
Grant Barkley Title: Domino Tilings and Divisibility Abstract: A domino tiling of a region in the plane is an arrangement of 2x1 domino tiles that completely covers that region. These tilings are an example of a more general construction in graph theory called perfect matchings. We are interested in counting the number of ways to cover certain…