FALL SEMESTER 2014 

SPEAKER

TITLE/ABSTRACT



Mesoscopic Models for Flow in Spatial NetworksThe dynamics of flows in spatial networks, such as the pressuredriven blood flow in the human arterial network or the flow of cars in a traffic network, is most suitably described by PDEbased 'macroscopic' models. To cope with the computational complexity, often simplified models are employed, including at the level of individiual particle tracking, usually called 'microscopic' models. Here we describe a mathematical model for blood flow in vascular networks, and compare numerical solutions of the underlying system of PDEs with those of a simplified models, based on pulsetracking arguments (mesoscopic models). We then use these models to study flow optimization task, for variable size and/or topology of the network. Physiologically realistic control mechanisms are tested in the context of these simplified models.

Video Lecture

UCCS Department of Mathematics OSB A327

The ubiquity of the Fibonacci Sequence: It comes up in the study of Leavitt path algebras too!The majority of this talk should be quite accessible to math majors, to graduate students, even to math faculty: indeed, to anyone who has heard of the Fibonacci sequence ... Since its origin (more than eight centuries ago) as a puzzle about the number of rabbits in a (fantasmagorically expanding) colony, the Fibonacci Sequence 1,1,2,3,5,8,13,... has arguably become the most wellknown of numerical lists, due in part to its simple recursion formula, as well as to the numerous connections it enjoys with many branches of mathematics and science. Since its origin (less than ten years ago), the study of Leavitt path algebras (a type of algebraic object which arises from directed graphs) has been the focus of much research energy throughout the mathematical world (well, at least throughout the ringtheory world), especially here at UCCS. In this talk we'll show how Fibonacci's sequence is naturally connected to data associated with the Leavitt path algebras of a natural collection of directed graphs. No prior knowledge about Leavitt path algebras will be required. [But in fact we will show how to compute the Grothendieck group $K_0(L(E))$ of the Leavitt path algebra $L(E)$ for a directed graph $E$, by considering only elementarylevel properties of the graph. Those properties will lead us directly to Fibonacci. Plenty of easytosee examples will be given.] This is joint work with Gonzalo Aranda Pino of the University of Malaga (Spain). Many of you have met Gonzalo: he is a very frequent visitor to UCCS. 
Poster

UC 116A

Integrable Curve Flows: the solitary travels of a vortex filament
The Vortex Filament Equation, describing the selfinduced motion of a vortex filament in an ideal fluid, is a simple but important example of integrable curve dynamics. Its connection with the cubing focusing Nonlinear Schrodinger equation through the wellknown Hasimoto map allows the use of many of the tools of soliton theory to study properties of its solutions. I will discuss the construction of knotted solutions, their dynamics, and their stability properties. 
Poster

Jonathan Brown OSB A327

The center of rings associated to directed graphs
In 2005 Abrams and Aranda Pino began a program studying rings constructed from directed graphs. These rings, called Leavitt Path algebras, generalized the rings without invariant basis number introduced by Leavitt in the 1950's. Leavitt path algebras are the algebraic analogues of the graph C*algebras and have provided a bridge for communication between ring theorists and operator algebraists. Many of the properties of Leavitt path algebras can be inferred from properties of the graph, and for this reason provide a convenient way to construct examples of algebras with a particular set of attributes. In this talk we will explore how central elements of the algebra can be read from the graph. 
Poster

Jason Bell 
Game theory and the mathematics of altruism
Game theory is a branch of mathematics that deals with strategy and decision making and is applied in economics, computer science, biology, and many other disciplines as well. We will discuss some of the basic points of game theory and discuss the socalled iterated prisoner dilemma, a game that is of central importance in the study of cooperation between individuals. We will then describe various strategies to this game and explain why altruism is something that can evolve naturally.

Poster

Robert Carlson UC 122

Myopic Models of Population Dynamics on Infinite Networks
Population models In mathematical biology often use equations blending diffusion (for movement) with local descriptions of population growth and multispecies interactions (reaction diffusion models). A modern problem is how to make sense of such models on gigantic networks such as the human population or the World Wide Web. One approach is to work in a space of functions which 'look flat' at 'infinity'. A correct formulation of this idea supports a theory of reactiondiffusion models on infinite networks where the network is compactified by adding points at infinity, diffusive effects vanish at infinity, and finite dimensional approximations can be described. 

Karen Livesey OSB A327

Nonlinear magnetization dynamics in nanoparticles and thin films
Even the simplest magnetic system can undergo unusual nonlinear dynamics. In this talk I will discuss two magnetic systems that display unexpected nonlinear phenomena. Firstly, the magnetization dynamics in a nanoparticle will be detailed. It is found that the transient dynamics in this system can be made to persist for extremely long times when the nanoparticle is driven by oscillating magnetic fields at a very particular frequency and strength. [1] Secondly, thin magnetic films will be discussed and a perturbative expansion of nonlinear dynamic terms will be presented. In thin films, the threshold above which the system is driven nonlinear depends sensitively on the thickness of the film. [2] Connections to experiments will briefly be mentioned. [1] M.G. Phelps, K.L. Livesey and R.E. Camley, in preparation (2014). [2] K.L. Livesey, M.P. Kostylev and R.L. Stamps, Phys. Rev. B. 75, 174427 (2007). 

Mark Hoefer OSB A327

Experiments on Solitons, Dispersive Shock Waves, and Their InteractionsA soliton is a localized traveling wave solution to a special class of partial differential equations (integrable equations). A defining property of solitons is their interaction behavior. In his seminal work of 1968 introducing a notion of integrability (the Lax pair), Peter Lax also proved that the Kortewegde Vries (KdV) equation admits two soliton solutions whose interaction behavior is quite remarkable. Two solitons interact elastically, i.e., each soliton maintains the same speed and shape postinteraction as they had preinteraction. Moreover, Lax classified the interaction geometry into three categories depending on the soliton amplitude ratio. This talk will present a physical medium (corn syrup and water) modeled by the KdV equation in the weakly nonlinear regime that supports approximate solitons. Numerical analysis and laboratory experiments will be used to show that the three Lax categories persist into the strongly nonlinear regime, beyond the applicability of the KdV model. Additionally, a wavetrain of solitons called a dispersive shock wave in this medium will be described and investigated using a nonlinear wave averaging technique (Whitham theory) and experiment. Interactions of dispersive shock waves and solitons reveal remarkable behavior including soliton refraction, soliton absorption, and twophase dynamics. 

SPRING SEMESTER 2014 

DATE/SPEAKER

TITLE/ABSTRACT


A unified approach to boundary value problems:


Distribution of Runs in Gambler's Ruin 

Sharp existence and Liouville type theorems for a class of weighted integral equations 



Using results from dynamical systems to classify algebras and C*algebras 
FALL SEMESTER 2013 

DATE/SPEAKER

TITLE/ABSTRACT

Zak Mesyan 
Evaluating Polynomials on Matrices:

Robert Buckingham 
Large equilibrium configurations of twodimensional fluid vortices The pointvortex equations, a discretization of the Euler equations, describe the motion of collections of twodimensional fluid vortices. The poles and zeros of rational solutions to the Painleve II equation describe equilibrium configurations of vortices of the same strength and mixed rotation directions.There is an infinite sequence of such rational solutions with an increasing number of poles and zeros.In joint work with P. Miller (Michigan), we compute detailed asymptotic behavior of these rational functions with error estimates.Our results include the limiting density of vortices for these configurations.We will also describe how knowlege of the asymptotic behavior of the rational Painleve II functions is useful in understanding critical phenomena in the solution of nonlinear wave equations. 

Solving nonlinear dispersive equations by the method of inverse scattering: The celebrated Kortewegde Vries (KdV) equation and the nonlinear Schrodinger (NLS) equations are partial differential equation that describe the motion of weakly nonlinear long waves in a narrow channel. They predict "solitary waves" which do not disperse, which have been observed in nature, and used in many applications.In this lecture we'll talk about the "KdV miracle" of complete integrability that explains the solitary waves and establishes a remarkable connection between these equation and quantum mechanics. We will also discuss work in progress involving generalizations of the KdV and NLS equations to two space dimensions that describe surface waves and, like their onedimensional counterpart, are completely integrable. 
Joseph Watkins 

Douglas Baldwin 
Dispersive shock waves and shallow oceanwave linesoliton interactions: Many physical phenomena are understood and modeled with nonlinear partial differential equations (PDEs). A special subclass of these nonlinear PDEs has stable localized waves  called solitons  with important applications in engineering and physics. I'll talk about two such applications: dispersive shock waves and shallow oceanwave linesoliton interactions. Dispersive shock waves (DSWs) occur in systems dominated by weak dispersion and weak nonlinearity. The Kortewegde Vries (KdV) equation is the universal model for phenomena with weak dispersion and weak quadratic nonlinearity. I'll show that the longtime asymptotic solution of the KdV equation for general steplike data is a singlephase DSW; the boundary data determine its form and the initial data determine its position. I find this asymptotic solution using the inverse scattering transform (IST) and matchedasymptotic expansions. Ocean waves are complex and often turbulent. While most oceanwave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these nonlinear interactions look like an X or a Y or an H from above; much less frequently, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. I'll show photographs and videos of such interactions, which occur every day,close to low tide, on two flat beaches that are about 2,000 km apart.These interactions are related to the analytic, soliton solutions of the Kadomtsev Petviashvili equation, which extended the KdV equation to include transverse effects. On a much larger scale, tsunami waves can merge in similar ways. 
Ryan Berndt 
Weight Problems in Harmonic Analysis, Especially the Fourier Transform: Three important operators in harmonic analysis include the maximal operator, the singular integral operator, and the Fourier transform. Arecurring problem in studying these operators is measuring the ''size"of an output function given some knowledge of the size of the input functionthat is, finding the mapping properties of the operator. A further complication is introduced by using weighted measures of size.Determining whether an operator maps a weighted space into another weighted space is sometimes referred to as a ''weight problem" for the operator. The weight problem is completely solved for the maximal operator,mostly solved for the singular integral operator, but unsolved for the Fourier transform. This is peculiar, since the Fourier transform is, in fact, the most widely used and oldest of the operators. In this talk I will review weight problems, their solutions, and focus especially on recent progress on the weight problem for the Fourier transform. 

Large Deviations in The Reinforced Random Walk Model on Trees In this talk, we consider the linearly reinforced and the oncereinforced random walk models in the transient phase on trees.We show the large deviations for the upper tails for both models.We also show the exponential decay for the lower tail in the oncereinforced random walk model. However,the lower tail is in polynomial decay for the linearly reinforced random walk model. 
SPRING SEMESTER 2013 

DATE

SPEAKER

AFFILIATION/INSTITUTION

TITLE/ABSTRACT


Robert Carlson 
University of Colorado atColorado Springs 
Population Persistence in River Networks 

Sandra Carillo  University of Rome "La Sapienza" (ITALY) 
Evolution Problems in Materials with Memory & Free Energy Functionals 

Murad Ozaydin  University of Oklahoma  The Linear Diophantine Frobenius Problem: An Elementary Introduction to Numerical Monoids 

Kenichi Maruno  University of Pan American Texas 


Graduate Student Presentations (M.S.) 
UCCS Dept of Mathematics 
TBA 

Mercedes Siles Molina  University of Malaga  Graph Algebras: From Analysis to Algebra and Back 
FALL SEMESTER 2012  

DATE  SPEAKER  AFFILIATION  TITLE 
Aug 23, 2012
 Natasha Flyer  NCAR (Boulder) 
Improving Numerical Accuracy for Solving Evolutionary PDEs in the Presence of Corner Singularities 
Sept 6, 2012
 Greg Oman  UCCS  An Independent Axiom System for the Real Numbers 

Jerry L. Bona

University of Illinois at Chicago 
Mathematics

Oct 18, 2012 
Keith Julien  CU Boulder  Convective flows under strong rotational constraints 
Nov 1, 2012

Gregory Beylkin  CU Boulder  
Nov 2, 2012

Brian Rider 
CU Boulder  
Nov 15, 2012
 Muge Kanuni Er 
Boğaziçi University  Istanbul, Turkey


Nov 29, 2012  Yuji Kodama  Ohio State Univ 
KP Solitons in shallow water:

Dec 6, 2012 
 UCCS Math Department  
Dec 6, 2012 
Joshua Carnahan  UCCS Math Departmen  
Dec 13, 2012  Auburn University 
Atomic Decomposition of


SPRING SEMESTER 2012  

DATE  SPEAKER  AFFILIATION  TITLE 
January 26, 2012  Eric Sullivan  CU Denver  
February 16,2012  Sergio Lopez  Ohio University  Alternative Perspectives in Module Theory 
March 8, 2012 
Colorado College  Zeta Functions and LFunctions in Number Theory  
March 22, 2012 
John Griesmer  The Ohio State University  Inverse Theorems in Additive Combinatorics 
April 5, 2012 
Cory Ahrens  Colorado School of Mines  Quadratures for the sphere, MRIs and radiation transport, what they have in common 
April 19, 2012 
Patrick Shipman  Colorado State University  Patterns induced by nucleation and growth in biological and atmospheric systems 
May 10, 2012  Giuseppe Coclite  University of Bari, Italy  Vanishing viscosity on networks 
FALL SEMESTER 2010  

DATE  SPEAKER  AFFILIATION  TITLE 
August 26, 2010
 Dr. Florian Sobieczky  Friedrich Schiller University  Annealed bounds for the return probability of Delayed Random Walk on finite critical percolation clusters 
September 9, 2010  Dr. Yi Zhu  Unified description of Bloch envelope dynamics in the 2D nonlinear periodic lattices  
September 23, 2010 
Geraldo Soares de Souza  Auburn University  A New Proof of Carleson's Theorem 
September 30, 2010  Dr. Gene Abrams  UCCS Math Department  The Graph Menagerie 
October 14, 2010 

October 21, 2010 

November 4, 2010


November 11, 2010
 Dr. Marek Grabowski  UCCS Physics Department  Dynamics of a Driven Spin 
SPRING SEMESTER 2010  

DATE  SPEAKER  AFFILIATION  TITLE 
January 19, 2010
 Dr. Brian Hopkins  Saint Peter's College  Sequential Selection and the Symmetric Group 
February 11, 2010 

February 18, 2010 
Manuel Reyes  University of California, Berkeley  Theorems of Cohen and Kaplansky: from commutative to noncommutative algebra 
February 25, 2010

Dr. Zachary Mesyan


March 4, 2010


March 18, 2010


April 1, 2010


April 15, 2010

Theodoros Horikis  
April 22, 2010 
Dr. Mihai Bostan  University of Besancon  High Field Limits for magnetized plasmas 
April 29, 2010


Department of Mathematics, UCCS  Nonconservative Transmission Line Networks, or Jordan normal form for some differential equations 
FALL SEMESTER 2009  

DATE  SPEAKER  AFFILIATION  TITLE 

"Factorizations of rational matrix functions with applications to discrete integrable systems and discrete
Painlevé equations"  
September 24, 2009  
October 8, 2009 
Dr. Mark
Ablowitz 

November 5, 2009 

November 19, 2009 
Dr. Juan G.
 
December 3, 2009 
Dr. Wojciech Kosek


SPRING SEMESTER 2009  

DATE  SPEAKER  AFFILIATION  TITLE 
January 22, 2009 
Dr. Herve Guiol

INP Grenoble
 
January 29,2009 
Fabio Machado
 
February 12, 2009 

February 17, 2009

Scott Annin

California State Univ.
Department of Mathematics 

February19, 2009

Brigitta Vermesi

University of Rochester
Department of Mathematics 

February 26, 2009 
Barbara Prinari 
Dipartimento di Fisica
Università del Salento (Lecce) 

March 12, 2009 
Emergent Time Scales in 

March 19, 2009 
Bernard Junot


April 2, 2009 

April 9, 2009 

April 17, 2009 

April 30, 2009 
FALL SEMESTER 2008


DATE

SPEAKER

AFFILIATION/INSTITUTION

TITLE

September 11, 2008 
Mark W. Coffey  Colorado School of Mines Department of Physics 

September 25, 2008 
Kulumani Rangaswamy  University of Colorado Department of Mathematics 
On Leavitt path algebras over infinite graphs 
October 10, 2008 
Steve Krone  University of Idaho Department of Mathematics 
Spatial selforganization in cyclic particle systems 
October 23, 2008 
Anca Radulescu  Applied Mathematics University of Colorado at Boulder 

November 6, 2008 
Chihoon Lee  Department of Statistics Colorado State University 
Diffusion Approximations to Stability and Control Problems for Stochastic Networks in Heavy Traffic 
November 20, 2008 
David Bortz  Applied Mathematics Univ of Colorado at Boulder 
Mathematics and Biology in the 21st Century (joint math and biology colloquium) 
December 11, 2008 
Mathematics & Comp Sci Emory University 