Colloquium Series
Spring 2015
All talks are from 3:454:45 p.m. in the Colloquium Room, unless otherwise specified.

Apr23

A Game of CrownsProf. Pam HarrisUSMA (West Point)Time: 03:45 PM
View Abstract
The generalized crown, $\mathbb{S}^k_n$, is a wellknown family of bipartite graphs whose order dimension is given in terms of the parameters $n$ and $k$. To each generalized crown one can associate a graph of critical pairs whose chromatic number is bounded above by the order dimension of the poset. In this talk we characterize the adjacency matrix of these graphs and through Mathematica can quickly produce an image of these graphs.

Apr08

Interplay between Mathematics and PhysicsShouhong WangIndiana UniversityTime: 03:45 PM
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In this talk, we shall present two examples, demonstrating the symbiotic interplay between modern physics and advanced mathematics. The first example is on the mystery of dark matter and dark energy phenomena. We show that the presence of dark energy and dark matter gives rise to a new basic principle, the principle of interaction dynamics (PID). Intuitively, PID takes the variation under the energymomentum constraints. With PID, we derive a new set of gravitational field equations, which demonstrate that gravity can display both attractive and repulsive effect. Dark energy and dark matter are then simply a property of gravity. This part of the talk is based on the joint work with Tian Ma. The second example introduces a novel approach to deal with the parameterization problem of the "small" spatial scales by the "large" ones for stochastic partial differential equations. This approach relies on stochastic parameterizing manifolds (PMs) which are random manifolds aiming to providein a mean square senseapproximate parameterizations of the small scales by the large ones. Backwardforward systems will be introduced to give access to such PMs as pullback limits dependingthrough the nonlinear termson the timehistory of the dynamics of the low modes. It will be shown that the corresponding pullback limits can be efficiently determined in practice, leading in turn to an operational procedure for the derivation of nonMarkovian reduced equations able to achieve good modeling performances. A stochastic Burgerstype equation will serve to illustrate how the memory effects conveyed by such reduced systems play a key role to reach such performances, in particular concerning the ability of these reduced systems to capture transitions or large excursions caused by the interactions between the noise and the nonlinear term. This part of the talk is based on a joint work with Mickael Chekroun and Honghu Liu.

Apr07

Fast Times in Linear Programming: Early Success, Two Revolutions, and Continuing MysteriesProf. Margaret WrightNew York UniversityTime: 07:30 PM
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Linear programming (LP), which isn't really about programming, is a simpletostate mathematical problem of enormous practical importance. The dramatic saga of LP solution methods began immediately after World War II with unexpected practical success that continued for more than 30 years despite theoretical reservations; next came two sweeping revolutions whose effects are often misunderstood. This talk will describe mathematical and computational issues from the history of LP, enlivened by controversy and international politics, as well as some remaining mysteries.

Apr01

Tools from Computational Topology, with applications in the life sciencesProf. Sarah DayCollege of William and MaryTime: 03:45 PM
View Abstract
The field of topology, and in particular computational topology, has produced a powerful set of tools for studying both model systems and data measured directly from physical systems. I will focus on three classes of topological tools: computational homology, topological persistence, and, very briefly, Conley index theory. To illustrate their use, I will discuss recent projects studying coupledpatch population dynamics, flickering red blood cells, and pulsecoupled neurons.

Mar04

Strong shift equivalence and algebraic KtheoryProf. Mike BoyleUniversity of MarylandTime: 03:45 PM
View Abstract
This will be a colloquium talk, assuming no background in Ktheory. Let R (always assumed to contain 0 and 1) be a subset of a ring. Let A,B be square matrices over R (not necessarily of equal size). A and B over R are elementary strong shift equivalent over R (ESSER) if there exist matrices U,V over R such that A=UV and B=VU. A and B are strong shift equivalent over R (SSER) if they are connected by a chain of elementary strong shift equivalences. If R is a ring, what does it mean for A and B to be strong shift equivalent? This question is motivated by classification problems in symbolic dynamics, as I'll describe, but is natural enough on its own. In his 1973 Annals paper, Williams took the first step, introducing shift equivalence (SE) as an invariant of strong shift equivalence. Whether SE implies SSE for a ring R remained open. It turns out that for a ring R, the refinement of SE by SSE can be nontrivial, and is captured exactly by the algebraic Ktheory group NK_1(R). This is joint work with Scott Schmieding.

Jan21

Special loci for the moduli space of rational mapsLT Brian StoutUSNATime: 03:45 PM