# Colloquia

## Professor Bing Wei 9/25/2015

Hamiltonian properties, branch number and k-tree related graphs

**Date:** 9/25/2015**Time:** 3:30PM-4:30PM**Place:** 315 Armstrong Hall

Bing Wei

Abstract: Download Here

## Professor Suohai Fan 8/13/2015

On $r$-hued colorings

of graphs

**Date:** 8/13/2015**Time:** 2:30PM-3:20PM**Place:** 315 Armstrong Hall

Suohai Fan

Abstract:For integers $k, r > 0$, a $(k, r )$-coloring of a graph $G$

is a proper $k$-coloring $c$ such that for any vertex $v$ with degree

$d(v)$, $v$ is adjacent to at least

min$\{d(v),r\}$ different colors. Such coloring is also called as an $r$-hued

coloring. The {\it $r$-hued chromatic number} of $G$, $\chi_{r}(G)$, is the least integer

$k$ such that a $(k, r )$-coloring of $G$ exists. In this talk, we will present some

of the progresses in this area.

## Michael Wester 4/29/2015

Determining the Parameters in Spatially Resolved Models of the

Motion of Proteins in the Membranes of Stimulated Cells

**Date:** 4/29/2015**Time:** 3:30PM-4:30PM**Place:** 315 Armstrong Hall

Michael Wester

Abstract: We show how to compute a dimerization rate from stimulated cell diffusion

data which can be used in a spatially resolved stochastic simulator to

accurately reproduce the data. For our data and for strong stimuli,

the time dependent diffusion coefficient rapidly transitions from the

diffusion constant for unstimulated cells to a significantly smaller

value. The diffusion data is generated using sparse labeling with

quantum dots which allows us to analyze using a non-spatial system

of two linear differential equations. We then use a closely related

system of two non-spatial nonlinear differential equations to compute a

spatially resolved reaction rate to use in our simulation code. Using

these reaction rates we successfully reproduce the biological data.

The framework developed here can be extended to analyze other time

dependent diffusion data.

## John Thompson 4/15/2015

Investigating student understanding and application of mathematics needed in physics: Definite integrals and the Fundamental Theorem of Calculus

**Date:** 4/15/2015**Time:** 4:30PM-5:30PM**Place:** 422 Armstrong Hall

John Thompson

Abstract: Learning physics concepts often requires the ability to interpret and manipulate the underlying mathematical representations and formalism (e.g., equations, graphs, and diagrams). Physics students are expected to be able to apply mathematics concepts to find connections between various physical quantities that are related via derivatives and/or integrals. Our own research into student conceptual understanding of physics has led us to investigate how students think about and use prerequisite, relevant mathematics, especially calculus, to solve physics problems. This is a rapidly growing research area in physics education.

Based on responses to questions administered in thermodynamics, we developed or adapted questions related to definite integrals and the Fundamental Theorem of Calculus (FTC), specifically with graphical representations, that are relevant in physics contexts, including some integrals that result in a negative quantity. Questions were administered in written form and in individual interviews; some questions had parallel versions in both mathematics and physics. Eye-tracking experiments provided additional information on visual attention during problem solving. Our findings are consistent with much of the literature in undergraduate mathematics education; we also have identified new difficulties and reasoning in students’ responses to the given problems.

## Gexin Yu 4/13/2015

On path cover of

regular graphs

**Date:** 4/13/2015**Time:** 3:30PM-4:30PM**Place:** 315 Armstrong Hall

Gexin Yu

Abstract: A path cover of a graph is a set of disjoint paths so that every vertex in the graph is contained in one of the paths. The path cover number p(G) of graph G is the cardinality of a path cover with minimum number of paths. Reed conjectured that a 2-connected 3-regular graph has path cover number at most $\lceil n/10\rceil$. In this paper, we confirm this conjecture.

## Xiangwen Li 4/13/2015

Forbidden graphs and

group connectivity

**Date:** 4/13/2015**Time:** 4:30PM-5:30PM**Place:** 315 Armstrong Hall

Xiangwen Li

Abstract: Here

## Arthur T. Benjamin 4/9/2015

Combinatorial Trigonometry (and a method to DIE for)

**Date:** 4/9/2015**Time:** 2:30PM-3:30PM**Place:** 315 Armstrong Hall

Arthur T. Benjamin

Abstract: Many trigonometric identities, including the Pythagorean theorem, have combinatorial proofs. Furthermore, some combinatorial problems have trigonometric solutions. All of these problems can be reduced to alternating sums, and are attacked by a technique we call D.I.E.

(Description, Involution, Exception). This technique offers new insights to identities involving binomial coefficients, Fibonacci numbers, derangements, and Chebyshev polynomials.

## Guantao Chen 3/6/2015

Lovasz-Plummer Conjecture on Spanning Halin Subgraphs

**Date:** 3/6/2015**Time:** 3:30PM-4:30PM**Place:** 315 Armstrong Hall

Guantao Chen

Abstract: Here

## Lijiang Wu 2/4/2015

Non-local Interaction Equations in Heterogeneous Environment With Boundary

Date: 2/4/2015

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

Lijiang Wu

Abstract:We discuss biological aggregation in a heterogeneous environment and on noncovex, nonsmooth domains. We model the heterogeneous environment as a Riemannian manifold with boundary and develop gradient flow approach in the space of probability measures on the manifold endowed with Riemannian 2-Wasserstein metric. We use the gradient flow structure to show the well-posedness of a class of nonlocal interaction equations. We discuss how heterogeneity of the environment leads to new dynamical phenomena. We also present a result on generalizing the well-posedness of weak measure solutions to a class of nonlocal interaction equations on nonconvex and nonsmooth domains. We use particle approximations, solve the discrete ODE systems and pass to the continuum limit by stability property. The novelty here is that under mild regularity conditions on space(i.e. prox-regularity), we can show the well-posedness of the ODE systems and the stability properties with explicit dependence on the geometry of the space(prox-regular constant). The talk is based on collaborations with J. A. Carrillo and D. Slepcev

## Seyfi Turkelli 1/14/2015

Expander graphs and

arithmetic applications

Date: 1/14/2015

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

Professor Seyfi Turkelli

Abstract: In this talk, I will first introduce expander graphs, gonality of curves and the arithmetic objects that we are interested in. Then, I will talk about several recent expansion results and their applications to number theory.

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