Untitled Document

Untitled Document




Radu Cascaval

UCCS Department of Mathematics

  September 4, 2014


 OSB A327 

Mesoscopic Models for Flow in Spatial Networks

The dynamics of flows in spatial networks, such as the pressure-driven blood flow in the human arterial network or the flow of cars in a traffic network, is most suitably described by PDE-based 'macroscopic' models.  To cope with the computational complexity, often simplified models are employed, including at the level of individual 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 pulse-tracking 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

Gene Abrams

UCCS Department of Mathematics

September 18, 2014


 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 well-known 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 ring-theory 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 elementary-level properties of the graph. Those properties will lead us directly to Fibonacci. Plenty of easy-to-see 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.


Annalisa Calini
College of Charleston

October 2, 2014


 UC 116A

Integrable Curve Flows: the solitary travels of a vortex filament

The Vortex Filament Equation, describing the self-induced 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 well-known 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.



Jonathan Brown
University of Dayton

October 9, 2014


 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.



Jason Bell
University of Waterloo
October 23, 2014

 Library APSE 
3rd floor

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 so-called 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.

Students are strongly encouraged to attend!


Video Lecture

Robert Carlson
UCCS Department of Mathematics

November 6, 2014

  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 reaction-diffusion models on infinite networks where the network is compactified by adding points at infinity, diffusive effects vanish at infinity, and finite dimensional approximations can behttp://cmes.uccs.edu/temp/colloquium110614.mov described. 

Video Lecture

Karen Livesey
UCCS Physics Department

November 20, 2014


 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
CU Boulder App Math Dept

December 4, 2014

 OSB A327

Experiments on Solitons, Dispersive Shock Waves, and Their Interactions

A 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 Korteweg-de 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 post-interaction as they had pre-interaction. 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 two-phase dynamics.



Gino Biondini


DATE:  February 6, 2014


A unified approach to boundary value problems:

Over the last fifteen years, A unified approach has recently been
developed to solve boundary value problems (BVPs) for integrable
nonlinear partial differential equations (PDEs).The approach is
a generalization of the inverse scattering transform (IST), which was
originally introduced in the 1970's to solve initial value problems for
such PDEs.Interestingly, this approach also provides a novel and
powerful way to solve BVPs for linear PDEs.This talk will discuss the
application of this method for linear PDEs. Specifically, we will look
in detail at the solution of BVPs on the half line (0<x<infty) for
linear evolution PDEs in 1 spatial and 1 temporal dimension.Time
permitting, two-point BVPs, multi-dimensional PDEs and BVPs for linear
elliptic PDEs will also be discussed.

Dr. Greg Morrow

DATE:  February 20, 2014

Distribution of Runs in Gambler's Ruin

John Villavert

Univ of Oklahoma
March 20, 2014

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

Dr. Kulumani Rangswamy
DATE:  April 3, 2014

The  Leavitt path algebras of
arbitrary graphs over a field

Mark Tomforde

University of Houston
 DATE:  May 1, 2014

Using results from dynamical systems to
classify algebras and



Zak Mesyan
University of Colorado at Colorado Springs

August 29, 2013

Evaluating Polynomials on Matrices:

A lassicaltheorem of Shoda from 1936 says that over any field K (of characteristic 0), every matrix with trace 0 can be expressed as a commutator AB-BA, or stated another way, that evaluating the polynomial f(x,y)=xy-yx on matrices over K gives precisely all the matrices having trace 0. I will describe various attempts over the years to generalize this result.

Robert Buckingham
University of Cincinnati

September 19, 2013

Large equilibrium configurations of two-dimensional fluid vortices

The point-vortex equations, a discretization of the Euler equations, describe the motion of collections of two-dimensional 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 knowledge of the asymptotic behavior of the rational Painleve II functions is useful in understanding critical phenomena in the solution of nonlinear wave equations.

Peter Perry
University of Kentucky

October 3, 2013

Solving non-linear dispersive equations by the method of inverse scattering:

The celebrated Korteweg-de 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 one-dimensional counterpart, are completely integrable.

Joseph Watkins
University of Arizona

Distinguished Lecture Series
October 17, 2013

Secrets From Deep Human History

Douglas Baldwin
University of Colorado-Boulder

October 31, 2013

Dispersive shock waves and shallow ocean-wave line-soliton 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 ocean-wave line-soliton 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 long-time asymptotic solution of the KdV equation for general step-like data is a single-phase 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 matched-asymptotic expansions. Ocean waves are complex and often turbulent. While most ocean-wave 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
Otterbein University-Western Ohio


November 7, 2013

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 function--that 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.

Yu Zhang
University of Colorado at Colorado Springs

November 14, 2013

Large Deviations in The Reinforced Random Walk Model on Trees

In this talk, we consider the linearly reinforced and the once-reinforced 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 once-reinforced random walk model. However,the lower tail is in polynomial decay
for the linearly reinforced random walk model.

Aug 23, 2012
Natasha FlyerNCAR (Boulder)

Improving Numerical Accuracy for Solving Evolutionary PDEs in the Presence of Corner Singularities

Sept 6, 2012

Greg OmanUCCS  An Independent Axiom System
for the Real Numbers

Sept 20, 2012
Distinguished Math Lecture

Jerry L. Bona

University of Illinois
at Chicago

and the Ocean

Oct 18, 2012

Keith Julien CU Boulder Convective flows under
strong rotational constraints

Nov 1, 2012

Gregory Beylkin CU Boulder

 Approximations and Fast
Algorithms for Green’s Functions

Nov 2, 2012

Brian Rider
CU Boulder

Extremal Laws the
Real Ginibre Ensemble

Nov 15, 2012

 Muge Kanuni Er
Boğaziçi University - Istanbul, Turkey

Visiting Fullbright scholar at UCCS 

Incidence Algebras
for Everyone

Nov 29, 2012
Yuji KodamaOhio State Univ

KP Solitons in shallow water:
Mach reflection and tsunami

Dec 6, 2012

David England

UCCS Math Department

Psudospectral Methods for Optimal Control 

Dec 6, 2012

Joshua Carnahan

UCCS Math Department

Nelder-Mead Method
and Applications

Dec 13, 2012

Geraldo De Souza

Auburn University

Atomic Decomposition of
Some Banach Spaces and Applications


January 26, 2012
Eric SullivanCU Denver

Development of Governing Equations for Unsaturated Porous Media
and An Overview of Hybrid Mixture Theory

February 16,2012
Sergio LopezOhio University Alternative Perspectives in Module Theory

March 8, 2012

Stefan Erickson

Colorado College Zeta Functions and L-Functions 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 CocliteUniversity of Bari, Italy Vanishing viscosity on networks


August 10, 2011
Jason BellSan Fraser UniversityPrimitivity in Leavitt Path Algebras
September 2, 2011
Yasunari Higuchi and Masato TakeiKobe University and Osaka Electro-Communication University Critical Behavior for percolation in the 2D high-temperature Ising model
Sept 27, 2011
Omer AngelUniversity of British Columbia 2011 Distinguished Math Lecture: Random Planar Maps

October 13, 2011

Robert Carlson University of Colorado - Colorado Spring Math Dpt After the Explosion:
An Analytical Look at
Boundary Problems for
Continuous Time Markov Chains

Oct 20, 2011


Willy Hereman

Colorado School of Mines Symbolic Computation of Conservation Laws of Nonlinear Partical Differential Equations
Oct 27, 2011
Hector Lomeli University of Texas- Austin Parameterization of Invariant Manifolds for Lagrangian
Systems with Long-range Interactions
Nov 3, 2011
Gino Biondini The State University of New York - Buffalo Solitons, boundary value problems and a nonlinear method of images
Nov10, 2011
Boaz Ilan University of California - Merced Luminescent solar concentrators, photon transport, and affordable solar harvesting
Nov 17, 2011
James MeissUniversity of Colorado - Boulder Transport and Mixing in Time-Dependent Flows
Dec 1, 2011
Ryan SchwiebertSlippery Rock University Faithful torsion modules and rings

December 8, 2011

Gregory LyngUniversity of Wyoming

Evans functions and the stability of viscous shock and detonation waves



January 27, 2011
Christopher Wade CurtisUniversity of Colorado - BoulderOn the Evolution of Perturbuations to Solutions of the KP Equation using the Benney-Luke Equation
February 3, 2011
Alexander Woo St Olaf College Local properties of Schubert varieties
February 10, 2011
Deena Schmidt Ohio State University Stochastisity and structure in biological systems: from the evolution of gene regulation to sleep-wake dynamics
February 15, 2011
Gregory OmanOhio University Jonsson Modules
February 28, 2011
Sandra CarilloUniversity of Rome Sapienza Baecklund transformations, Recursion Techniques and
Noncommutative soliton solutions

March 10, 2011

Bengt Fornberg University of Colorado - Boulder A Numerical Methodology for the Painlevé equations.

April 12, 2011

Antonio Moro

SISSA Trieste- Italy Dispersive shock waves and Painleve' Trascendents
April 14, 2011
Harvey Segur University of Colorado - Boulder Tsunamis
April 28, 2011
Graduate Student PresentationsUCCS Various
May 5, 2011
James MitchellUniversity of St. Andrews Approximating permutations and automorphisms


August 26, 2010
Dr. Florian Sobieczky Friedrich Schiller UniversityAnnealed 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 AbramsUCCS Math DepartmentThe Graph Menagerie

October 14, 2010

October 21, 2010

November 4, 2010
Colorado College
November 11, 2010
Dr. Marek GrabowskiUCCS Physics Department Dynamics of a Driven Spin


January 19, 2010
Dr. Brian HopkinsSaint Peter's CollegeSequential Selection and the Symmetric Group

February 11, 2010

 Representations, quivers and periodicity

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
Ben-Gurion University, Israel
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



September 10, 2009

"Factorizations of rational matrix functions with applications to discrete integrable systems and discrete
Painlevé equations"

September 24, 2009
October 8, 2009
Dr. Mark
November 5, 2009
November 19, 2009

Dr. Juan G.

December 3, 2009
Dr. Wojciech Kosek


January 22, 2009
Dr. Herve Guiol
INP Grenoble
Almost sure scaling limit for monotone interacting particles  systems in one dimension.

January 29,2009
Fabio Machado
University of Sao Paulo
Non-homogeneous random
walks systems on Z

February 12, 2009
Mingzhong Wu

Excitation of chaotic spin waves through three-wave and four-wave interactions


February 17, 2009
 Scott Annin
 California State Univ.
Department of Mathematics
 Using Special Ideals to Illustrate a Research Philosophy in Ring Theory

February19, 2009
 Brigitta Vermesi
 University of Rochester
Department of Mathematics
 Critical exponents for Brownian
motion and random walk

February 26, 2009

Barbara Prinari

Dipartimento di Fisica
Università del Salento (Lecce)

Integrable Systems, Inverse
Scattering Transform and Solitons

March 12, 2009
Department of Physics
Colorado School of Mines

Emergent Time Scales in
Ultracold Molecules in Optical Lattices

[Joint Math/Physics Colloquium]

March 19, 2009
Bernard Junot
How Statistics Explain What Cancer Is

April 2, 2009
Bi-directional wave propagation in the human arterial tree

April 9, 2009
The uncanny resemblance between Leavitt path algebras and graph C*-algebras

April 17, 2009

Linear Algebra and Random Triangles

April 30, 2009
K-theory for Leavitt path algebras


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

Feynman diagrams, integrals,
and special functions

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 self-organization in cyclic
particle systems

October 23, 2008
Anca Radulescu Applied Mathematics
University of Colorado at Boulder
The Multiple Personality of Schizophrenia

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
Geometrical Multiscale Models of the
Cardiovascular System

 Jan 31, 2008 Robert Carlson Department of Mathematics
University of CO, Colo. Spgs.
Hunting for Eigenvalues of
Quantum Graphs
Feb 21, 2008 Radu Cascaval Department of Mathematics
University of CO, Colo. Spgs.
On the Soliton Resolution
Mar 6, 2008 Yu Zhang Department of Mathematics
University of CO, Colo. Spgs
Limit Theorems for Maximum Flows on a Lattice
Apr 3, 2008 Enrique Pardo Universidad de Cadiz (Spain) The Classification Question for Leavitt Path Algebras
Apr 17, 2008 Robert Carlson Department of Mathematics
University of CO, Colo. Spgs.
Bringing Matlab into Introductory Differential Equations
May 1, 2008 Tim Huber Iowa State University Parametric representations for Eisenstein series from Ramanujan's differential equations
May 6, 2008 Mercedes Siles Molina   Universidad de Málaga   (Spain)     Classification Theorems for Acyclic
Leavitt Path Algebras
May 8, 2008 John D. Lorch Ball State University Sudoku and Orthogonality