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…
Many contemporary problems in the calculus of variations involve describing the limit of singular perturbations of variational problems. These problems arise naturally in a number of fields, for example in materials science (phase transition problems) and mathematical statistics (regularized empirical risk minimization). This talk will give an introduction to these problems, their applications, and recent work…
A wide range of natural and engineering systems exhibit extreme events; i.e., spontaneous intermittent behavior manifested through sporadic bursts in the time series of their observables. Examples include ocean rogue waves, intermittency in turbulence, extreme weather patterns and epileptic seizure. Because of their undesirable impact on the system or the surrounding environment, the real-time prediction and mitigation of extreme events is of great interest.…
Variational methods can be used to create numerical methods that respect conservation laws. I will discuss applications to electromagnetism, the Yang-Mills equations, and mean curvature flow. I will also discuss some new ideas about finite element spaces of differential forms.
Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. This talk focuses on certain biological signaling networks, namely, phosphorylation networks, and their resulting dynamical systems. For many of these systems, the set of steady states admits a rational parametrization (that is, the set is the image of a map…