Past Colloquia

DateSpeakerTitle / Abstract

Spring 2025

Jan 23, 2025
12:30pm-1:30pm
(UC 122)

Be'eri Greenfeld

University of Washington

Local smallness and global largeness: a quantitative approach
Jan 30, 2025
12:30pm-1:30pm
(UC 122)

Padmini Veerapen

Tennessee Tech University

Manin’s Universal Quantum Groups Through the Lens of Zhang Twists & 2-cocycle Twists, and Twisted Homogeneous Coordinate Rings of Quadrics

Video Recording

Feb 4, 2025
12:30pm-1:30pm
(UC 307)

Kent Vashaw

UCLA

A Tensor-Triangular Approach to Noncommutative Geometry

Video Recording

Feb 13, 2025
12:30pm-1:30pm 
(DWIRE 106)

Xumin Gu

Shanghai University of 
Finance and Economics

Well-Posedness And Low Mach Number Limit Of The Free Boundary Problem For The Euler-Fourier System
Apr 1, 2025
12:30pm-1:30pm
(OSB B136)

Pax Kivimae

Courant Institute of Mathematical Sciences

The Solutions of Random High-Dimensional Equations

Video Recording

Apr 3, 2025
12:30pm-1:30pm
(DWIRE 121)

Jeffrey Humpherys

Missouri S&T University

Distinguished Lecture Series

Learning to Care: Can AI/ML help fix the U.S. Healthcare System?
Apr 10, 2025
12:30pm-1:30pm
(CENT 102)

Ching Wei Ho

University of California, San Diego

The Model Deformation Phenomenon for Random Polynomials

Video Recording

May 9, 2025   

12:30pm-1:00pm

(OSB B134)

Lorenzo Zino

Polytechnic University of Turin

An adaptive-gain controller to solve the equilibrium selection problem

May 9, 2025   

1:00pm-1:30pm

(OSB B134)

Paolo Frasca

GIPSA Lab, France

A Coupled Friedkin-Johnsen Model of Popularity Dynamics in Social Media

Fall 2024

November 14, 2024

12:30pm-1:30pm

Robert Carlson

UCCS

An FFT for networks

Zoom Recording

November 21, 2024

12:30pm-1:30pm

(Columbine 136)

Gene Abrams

UCCS

A Whale of a Catch

Zoom Recording

Spring 2024

March 14, 2024

12:30pm-1:30pm

Alan Loper

The Ohio State University

Application of Regular Local Rings to Number Theory

April 11, 2024

12:30pm-1:30pm

Justin Cole

UCCS

Topological Insulators in Electromagnetic Systems

Zoom Recording

April 25, 2024

12:30pm-1:30pm

Ziad Musslimani

Florida State University

From space-time reflection symmetry to integrable nonlocal models

Zoom Recording

Fall 2023

September 21, 2023

12:30pm-1:30pm

Robert Carlson

UCCS

Using analysis and topology to count nonbacktracking walks in biregular graphs

Zoom Recording

September 28, 2023

12:30pm-1:30pm

Andrew Kelley

Colorado College/Colorado Engineering Inc.

Expected Runtime of Evolutionary Algorithms on Plateaus

Slides and Zoom Audio Recording

October 12, 2023

12:30pm-1:30pm

Bengt Fornberg

UC Boulder

Finite Difference Formulas and Numerical Contour Integration in the Complex Plane

Zoom Recording

October 26, 2023

12:30pm-1:30pm

Sergio Lopez-Permouth

Ohio University

Collaborations between binary operations

Zoom Recording

Nov 2, 2023

12:30pm-1:30pm

Bernard Deconinck

University of Washington (online talk)

Improving Archimedes, the water wave pressure problem

Zoom Recording

Nov 9, 2023

12:30pm-1:30pm

Yaning Liu

University of Colorado Denver

Randomized Quasi-Monte Carlo Methods for Global Sensitivity Analysis

Zoom Recording

Nov 16, 2023

12:30pm-1:30pm

Geraldo Soares de Souza

Auburn University, Al

 

Haar, Wavelets System, Multi-Resolutions and the special atom space in Higher Dimensions and its Analytic Characterizations

Zoom Recording

Spring 2023

February 23, 2023

12:30pm-1:30pm

Willy Hereman

Colorado School of Mines

Symbolic computation of solitary wave solutions and solitons through homogenization of degrees

Zoom Recording

March 2, 2023

12:30pm-1:30pm

Greg Oman

UCCS

From Ancient Egyptian Fractions to Modern Algebra

Zoom Recording

March 9, 2023

12:30pm-1:30pm

Jianke Yang

University of Vermont

Rogue wave patterns

Zoom Recording

March 16, 2023

12:30pm-1:30pm

Iddo Ben-Ari

University of Connecticut

Quasi-stationary distributions: existence uniqueness and characterization

Zoom Recording

March 23, 2023

12:30pm-1:30pm

Barbara Prinari 

University at Buffalo

Solitons and soliton interactions in the complex coupled short-pulse equation

Zoom Recording

April 6, 2023

12:30pm-1:30pm

Michael Calvisi

Mechanical and Aerospace Engineering UCCS

Modeling the complex dynamics of nonspherical microbubbles

Zoom Recording

Apr 13, 2023

12:30pm-1:30pm

Stephen Pankavich

Colorado School of Mines

Introduction to Kinetic Models of Collisionless Plasmas

Zoom Recording

Apr 20, 2023

12:30pm-1:30pm

Panayotis Kevrekidis

University of Massachusetts

On Some Select Klein-Gordon and Beam Problems: Internal Modes, Fat Tails, Wave Collisions and Beyond

Zoom Recording

Apr 27, 2023

12:30pm-1:30pm

Graduate Student Project(s)

Stephanie Klumpe

Equivalent Codes From Finite Fields

Spring 2022

February 17, 2022

12:30pm-1:30pm

Justin Cole

UCCS

Transverse Instability of Rogue Waves 

Video 

March 17, 2022

12:30pm-1:30pm

Taylor Klotz

University of Hawai'i

Cascade Feedback Linearization and Two-Legged Copepod Motion 

Video

March 31, 2022

12:30pm-1:30pm

Samy Wu Fung

Colorado School of Mines

Efficient Training of Infinite-Depth Neural Networks via Jacobian-Free Backpropagation

Video

April 21, 2022

12:30pm-1:30pm

Avadh Saxena

Los Alamos National Lab

 

Non-Hermitian Qubits and Photonic Lattices

May 5, 2022

12:30pm-1:30pm

Alberto Tonolo

University of Padova, Italy

The Mystery of Anatol Vieru’s Periodic Sequences Unveiled

Video

Fall 2021

September 23, 2021

12:30pm-1:30pm

Maziar Raissi

CU Boulder- Applied Math

Data-Efficient Deep Learning using Physics-Informed Neural Networks

Video

Slides

October 7, 2021

12:30pm-1:30pm

Dr. Daniel Bossaller

Baylor 

Ideal Extensions and Directly Infinite Algebras

Video

October 28, 2021

12:30pm-1:30pm

Dr. Sean Nixon

CU Boulder- Applied Math

Analytical study of Floquet topological insulators 

Video

November 4, 2021

12:30pm-1:30pm

Dr. Pavel Lushnikov

University of New Mexico

Conformal mappings and integrability of surface dynamics

Video

November 18, 2021

12:30pm-1:30pm

Dr. Pace Nielsen

BYU

Spoof odd perfect numbers

December 2, 2021

12:30pm-1:30pm

Michael Zowada

UCCS

Rational Solutions to the KPI Nonlinear Wave Equation and Their Connection to Partitions of Integers

Video

Spring 2020

January 23, 2020

12:30pm-1:30pm

Sergey Dyachenko

University of Washington, Seattle

The Singularities of 2D Fluid Flows with Free Surface

January 30, 2020

12:30pm-1:30pm

Justin Cole

UC Boulder 

Discrete Approximation of Topological Insulators in Magneto-optical Media

February 4, 2020

12:30pm-1:30pm

Ying Wang

University of Oklahoma


Mathematical Analysis and Numerical Methods for an Underground Oil Recovery Model

February 6, 2020

12:30pm-1:30pm

Sitai Li

University of Michigan 

Maxwell-Bloch and nonlinear Schrodinger systems with nonzero backgrounds

March 5, 2020

12:30pm-1:30pm

Mark Tomforde

University of Houston

Classification of Graph Algebras

March 10, 2020

12:30pm-1:30pm

Stefan Mancas

Embry-Riddle Aeronautical University

The Cosmological Vacuous Bubble Inside a Water Tank

Fall 2019

October 17, 2019
12:30pm-1:30pm
Room: University Center 309
Steven Lalley
University of Chicago
 
Return Probabilities of Random Walks on Non-Amenable Groups
October 31, 2019
12:30pm-1:30pm
Room: University Center 303
Edwin Jimenez
Caltech
High-order Numerical Methods for Boundary Integral Equations with
Applications to Acoustic and Electromagnetic Scattering
November 14, 2019
12:30pm-1:30pm
Room: University Center 116
Justin Lynd
University of Louisiana
Fusion Systems in Algebra and Topology

Spring 2019

March 7, 2019
12:30pm-1:30pm
Room: Osborne A327
Dr. Jason Boynton
NDSU
Factorization in rings of polynomials of the form D+M (and generalizations)
March 21, 2019
12:30pm-1:30pm
Room: Osborne A204
Daniel Herden
Baylor University
Local Automorphisms and Incidence Algebras 
April 4, 2019
12:30pm-1:30pm
Room: Osborne A204
Xinyi Li
University of Chicago
Natural parametrization for loop-erased random walk in three dimensions
April 18, 2019
12:30pm-1:30pm
Room: Osborne A327
Dr. John Lorch
Ball State University
Enlarging Franklin's Magic Squares

Fall 2018

September 6, 2018
12:30pm-1:30pm
Room: Osborne A327
Dr. Robert Carlson
UCCS 
Complex Analytic Functions and Differential Operators
September 20, 2018
12:30pm-1:30pm
Room: University Center 124
Dr. Katherine Stange
Univ. of Colorado, Boulder
From Farey Sequences to Apollonian Circle Packings
November 15, 2018
12:30pm-1:30pm
Room: University Center 122
Dr. Robert Jenkins
Colorado State University
Soliton Resolution for dispersive nonlinear wave equations
November 29, 2018
12:30pm-1:30pm
Room: Osborne A327
K.M. Rangaswamy
UCCS 
The multiplicative ideal theory of Leavitt path algebras-
Are Leavitt path algebras really commutative algebras in non-commutative clothing?

Spring 2018

February 1, 2018
12:30pm-1:30pm
Room: Osborne A204
Victor Ginting
University Wyoming
Multiscale Methods for Flow and Transport in Porous Media
February 15, 2018
12:30pm-1:30pm
Room: Osborne A327
Martin Mohlenkamp
Ohio University
The Hunt for the Swamp Monster
March 2, 2018
12:30pm-1:30pm
Room: University Center 302 
Benedetto Piccoli
Rutgers University (Joint with MAE)
Control methods for large groups: multi-scale models for social dynamics
March 15, 2018
12:30pm-1:30pm
Room: Osborne A327
Igor Rumanov
CU-Boulder 
Whitman modulation theory- developments and open problems
April 5, 2018
12:30pm-1:30pm
Room: Theater University Center 3027
Kathy Driver
University Pretoria

Distinguished Math Lecturer
Interlacing of zeros and Wendroff's Theorem
May 24, 2018
12:30pm-1:30pm
Room: Osborne A327
Stanislav Volkov
Lund University, Sweden
5x+1: how many go down?

Fall 2017

September 14, 2017
12:30pm-1:30pm
Room: Osborne A327
Robert Carlson
UCCS
Analytic problems of Sturm-Liouville type
September 28, 2017
12:30pm-1:30pm
Room: Osborne A327
Fritz Gesztesy 
Baylor University 
On factorizations of differential operators and Hardy-Rellich-type inequalities

Slides: Click here to view the PPT slides of this presentation
Tuesday
October 17, 2017
12:30pm-1:30pm
Room: Osborne A327
Michael Jay Stutzer
CU Boulder
The Statistical Theory of Large Deviations Way to Gamble or Invest...If You Must
October 26, 2017
12:30pm-1:30pm
Room: University Center 122
Dan Bossaller
Ohio University 
Associativity and Infinite Matrices
November 9, 2017
12:30pm-1:30pm
Room: Osborne A327
Dr. Alessandro Arsie
The University of Toledo
Bi-flat F-manifolds and Integrable Conservation Laws - an overview

Spring 2017

February 9, 2017
12:30pm-1:30pm
Room: UC 122
Ben Dyhr
Metropolitan State University of Denver

The fractal geometry of Schramm-Loewner Evolution (SLE)

February 16, 2017
12:30pm-1:30pm
Room: OSB A327
Janos Englander 
University of Colorado Boulder

Turning A Coin Instead of Tossing It

March 16, 2017
12:30pm-1:30pm
Room: UC 126
Iddo Ben Ari
University of Connecticut

The Bak-Sneppen Model of Biological Evolution and Related Models

March 23, 2017
12:30pm-1:30pm
Room: UC 122
Diego Dominici
SUNY New Paltz

The Toda lattice and semiclassical orthogonal polynomials

April 6, 2017
12:30pm-1:30pm
Room: Osborne A327
Anna Weigandt
University of Illinois Urbana-Champaign

Partition Identities and Quiver Representations

April 20, 2017
12:30pm-1:30pm
Room: OSB A327
Boris Hanin
MIT

Pairing between zeros and critical points of random polynomials

 

May 4, 2017
12:30pm-1:30pm
Room: OSB A327
Dr. Wojciech Kossek
UCCS

Should you quit your job and start working on the
Twin Prime Conjecture?

Fall 2016

September 8, 2016
12:30pm-1:30pm
Room: OSB A327
Brandon Runnels
UCCS

Modeling grain boundaries in metals with optimal transportation theory, calculus of variations, and the phase field method.

September 22, 2016
12:30pm-1:30pm
Room: University Center 303
Dr. Bengt Fornberg
University of Colorado, Boulder

Numerical Solutions of the Painlevé Equations

October 6, 2016
12:30pm-1:30pm
Room: Osborne Center A204
Dr. Benjamin Steinberg
City College of New York

Representation Theory and Random Walks

October 13, 2016
12:30pm-1:30pm
Room: OSB A327
Dr. Cornelis van der Mee
University of Cagliari

Exact Solutions of Integrable Nonlinear Evolution Equations.

October 20, 2016
12:30pm-1:30pm
Room: Kraemer Family Library 3rd floor Apse
Dr. James Mitchell
University of St. Andrews

Distinguished Mathematics Lecturer

Mathematical Problems that Cannot be Solved

November 3, 2016
12:30pm-1:30pm
Room: OSB A327
Dr. Thomas Bothner
University of Michigan

Painlevé Functions in Statistical Physics

 

November 15, 2016
12:30pm-1:30pm
Room: OSB A204
Dr. David Aristoff
Colorado State University

Markov Chains, Metastability and Sampling

December 1, 2016
12:30pm-1:30pm
Room: OSB A204
Mr. Andrew Kelley
Binghamton University

Maximal Subgroup Growth of some Groups

Spring 2016

February 4, 2016
12:15pm-1:30pm
3rd Floor Library Apse
Mette Olufsen
North Carolina State University

Patient Specific Modeling of Cardiovascular System Dynamics

February 18, 2016
12:15pm-1:30pm
OSB A327
Jose Martell
Instituto de Ciencias Matematicas (Madrid)

The Dirichelt Problem for Elliptic Systems in the Upper-Half Plane

February 18, 2010
12:15pm-1:30pm
OSB A327
Dionyssios Mantzavinos
SUNY Buffalo

Initial Value Problems and Initial-Boundary Value Problems for Nonlinear Evolution Equations

March 3, 2016
12:15pm-1:30pm
OSB A327
Iddo Ben-Ari
University of Connecticut

Coupling for Brownian Motion with Redistribution

March 15, 2016
12:15pm-1:30pm
OSB A327
Damiano Fulghesu
Minnesota State, University Moorhead

Arithmetic Sets in Groups

March 17, 2016
12:15pm-1:30pm
OSB A327
Alessando Zampini
University of Luxembourg

Hodge-de Rham Operator on (some) Classical and Quantum Spheres

March 31, 2016
12:15pm-1:30pm
OSB A327
Paul Horn
University of Denver

The Geometry of Graphs

April 14, 2016
12:15pm-1:30pm
OSB A327
Vassilis Rothos
Aristotle University of Thessaloniki

Adiabatic Perturbation Theory for Vector NLS and Application in BECs

Fall 2015

September 17, 2015
12:15pm-1:30pm
UC 122
Sean O'Rourke 
CU Boulder
Singular values and vectors under random perturbation
September 24, 2015
12:15pm-1:30pm
OSB A327
Anton Dzhamay
University of Northern Colorado
Bäcklund transformations, discrete Painlevé equations, and Sakai’s geometric classification scheme
October 8, 2015
12:15pm-1:30pm
Kraemer Family Library 3rd Floor APSE
James M. Keiser
Laboratory for Analytic Sciences National Security Agency (NSA)
Applied Mathematics and the Science of Analysis
October 22, 2015
12:15pm-1:30pm
OSB A327
Troy Butler
University of Colorado- Denver
End-to-end quantification of uncertainty using measure theory
November 5, 2015
12:15pm-1:30pm
OSB A327
John Wierman
Johns Hopkins University
A disproof of Tsallis’ conjecture for the exact bond percolation threshold of the kagome lattice
November 19, 2015
12:15pm-1:30pm
OSB A327
Greg Oman
University of Colorado -Colorado Springs
Turning automatic continuity around: automatic homomorphisms
December 3, 2015
12:15pm-1:30pm
OSB A327
Mei Yin
University of Denver
A gentle introduction to exponential random graphs

Spring 2015

January 29, 2015
12:30pm-1:30pm
OSB A327
Barbara Prinari
UCCS Math
Mathematical models for the ward atmosphere in a medical unit
February 24, 2015
12:30pm-1:30pm
OSB A327
Oksana Bihun
Concordia College
Goldfishing: Solvable N-Body Problems and Beyond
February 26, 2015
12:30pm-1:30pm
OSB A327
Matthew Johnston
University of Wisconsin
Recent Results in the Modeling of Chemical Reaction Systems
March, 3, 2015
12:30pm-1:30pm
OSB A327
Theodoros Horikis
University of Ioannina
Monsters of the Deep: Rogue Waves
March, 19, 2015
12:30pm-1:30pm
OSB A327
Sarbarish Chakravarty
UCCS Math
Nonlinear ODEs whose solutions are modular functions
March, 12, 2015
12:30pm-1:30pm
OSB A327
Anca Radulescu
SUNY New Paltz
Dynamic networks and templates: from hardwiring to temporal behavior
April 14, 2015
12:30pm-1:30pm
OSB A327
Mahadevan Ganesh
Colorado School of Mines
Random triangulations of genus g surfaces
April 9, 2015
12:30pm-1:30pm
OSB A327
Virgil U. Pierce
UTPA
Theoretical framework for the description of transmembrane receptor cluster coalescence in cells
April 23, 2015
12:30pm-1:30pm
OSB A327
Kathrin Spendier
UCCS Physics
Theoretical framework for the description of transmembrane receptor cluster coalescence in cells
April 30, 2015
12:30pm-1:30pm
OSB A327
Cristobal Gil
University of Malaga, Spain
Leavitt path algebras of Cayley graphs
May 7, 2015
12:30pm-1:30pm
OSB A327
Alberto Tonolo
University of Padova (Italy)
Equivalences between categories of modules

Fall 2014

September 4, 2014
12:30pm-1:30pm
OSB A327
Radu Cascaval 
UCCS Math

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 (archived)

September 18, 2014
12:30pm-1:30pm
OSB A327
Gene Abrams
UCCS Math

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.

Poster (PDF)

October 2, 2014
12:30pm-1:30pm
UC 116 A
Annalisa Calini
College of Charleston

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.

Poster (PDF)

Video Lecture (archived)

October 9, 2014
12:30pm-1:30pm
OSB A327
Jonathan Brown
University of Dayton

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 (PDF)

Video Lecture (archived)

October 23, 2014
12:30pm-1:30pm
Library APSE
Jason P. Bell
University of Waterloo

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.

Poster (PDF)

Video Lecture (archived)

November 6, 2014
12:30pm-1:30pm
UC 122
Robert Carlson
UCCS Math

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 be described

Video

November 20, 2014
12:30pm-1:30pm
OSB A327
Karen Livesey
UCCS Physics

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).

December 4, 2014
12:30pm-1:30pm
OSB A327
Mark Hoefer
CU Boulder App Math Dept

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.

Spring 2014

February 6, 2014Gino Biondini
SUNY Buffalo

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.

February 20, 2014Greg Morrow
UCCS Math
Distribution of Runs in Gambler's Ruin
March 20, 2014John Villavert
University of Oklahoma

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

April 3, 2014Dr. Kulumani Rangswamy
UCCS Math

The Leavitt path algebras of arbitrary graphs over a field

May 1, 2014Mark Tomforde
University of Houston

Using results from dynamical systems to classify algebras and C*-algebras

Fall 2013

August 29, 2013Zak Mesyan
UCCS Math

Evaluating Polynomials on Matrices:

A classical theorem 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.

September 19, 2013Robert Buckingham
University of Cincinnati

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.

October 3, 2013Peter Perry
University of Cincinnati

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.

October 17, 2013Joseph Watkins
University of Arizona

Secrets From Deep Human History

October 31, 2013Douglas Baldwin
University of Colorado-Boulder

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 Korteweg de 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.

November 7, 2013Ryan Berndt 
Otterbein University-Western Ohio

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. A recurring 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.

November 14, 2013Yu Zhang 
UCCS Math

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.

Spring 2013

Jan 13, 2013Robert Carlson
UCCS Math

Population Persistence in River Networks

February 14, 2013Sandra Carillo
University of Rome "La Sapienza" (ITALY)

Evolution Problems in Materials with Memory & Free Energy Functionals

March 21, 2013Murad Ozaydin
University of Oklahoma

The Linear Diophantine Frobenius Problem: An Elementary Introduction to Numerical Monoids

April 11, 2013Kenichi Maruno
University of Pan American Texas

Discrete Integrable Systems

April 25, 2013Graduate Student Presentations (M.S.)
UCCS Math

TBA

April 30, 2013Mercedes Siles Molina
University of Malaga

Graph algebras: from analysis to algebra and back

Fall 2012

August 23, 2012Natasha Flyer
NCAR (Boulder)

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

August 23, 2012Greg Oman
UCCS Math

An Independent Axiom System for the Real Numbers

Sept 20, 2012Jerry L. Bona
University of Illinois at Chicago

Mathematics and the Ocean

October 18, 2012Keith Julien
CU Boulder

Convective flows under strong rotational constraints

November 1, 2012Gregory Beylkin
CU Boulder

Convective flows under strong rotational constraints

November 2, 2012Brian Rider
CU Boulder

Extremal Laws the Real Ginibre Ensemble

November 15, 2012Muge Kanuni Er
Boğaziçi University - Istanbul, Turkey

Incidence Algebras for Everyone

November 29, 2012Yuji Kodama
Ohio State Univ

KP Solitons in shallow water: Mach reflection and tsunami

December 6, 2012David England
UCCS Math

Psudospectral Methods for Optimal Control

December 6, 2012Joshua Carnahan
UCCS Math

Nelder-Mead Method and Applications

December 13, 2012Geraldo De Souza
Auburn University

Atomic Decomposition of Some Banach Spaces and Applications

Spring 2012

January 26, 2012Eric Sullivan
CU Denver

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

February 16, 2012Sergio Lopez
Ohio University

Alternative Perspectives in Module Theory

March 8, 2012Stefan Erickson
Colorado College

Zeta Functions and L-Functions in Number Theory

March 22, 2012John Griesmer
Ohio State University

Inverse Theorems in Additive Combinatorics

April 5, 2012Cory Ahrens
Colorado School of Mines

Quadratures for the sphere, MRIs and radiation transport, what they have in common

April 19, 2012Patrick Shipman
Colorado State University

Patterns induced by nucleation and growth in biological and atmospheric systems

May 10, 2012Giuseppe Coclite
University of Bari, Italy

Vanishing viscosity on networks

Fall 2011

August 10, 2011Jason Bell
San Fraser University

Primitivity in Leavitt Path Algebras

September 2, 2011Yasunari Higuchi and Masato Takei
Kobe University and Osaka Electro-Communication University

Critical Behavior for percolation in the 2D high-temperature Ising model

September 27, 2011Omer Angel
University of British Columbia

2011 Distinguished Math Lecture: Random Planar Maps

October 13, 2011Robert Carlson
UCCS Math

After the Explosion: An Analytical Look at Boundary Problems for Continuous Time Markov Chains

October 20, 2011Willy Hereman
Colorado School of Mines

Symbolic Computation of Conservation Laws of Nonlinear Particle Differential Equations

October 27, 2011Hector Lomeli
University of Texas- Austin

Parameterization of Invariant Manifolds for Lagrangian Systems with Long-range Interactions

November 3, 2011Gino Biondini
The State University of New York - Buffalo

Solitons, boundary value problems and a nonlinear method of images

November 10, 2011Boaz Ilan
University of California - Merced

Luminescent solar concentrators, photon transport, and affordable solar harvesting

November 17, 2011James Meiss
University of Colorado - Boulder

Transport and Mixing in Time-Dependent Flows

December 1, 2011Ryan Schwiebert
Slippery Rock University

Faithful torsion modules and rings

December 8, 2011Gregory Lyng
University of Wyoming

Evans functions and the stability of viscous shock and detonation waves

Spring 2011

January 27, 2011Christopher Wade Curtis
University of Colorado - Boulder

On the Evolution of Perturbations to Solutions of the KP Equation using the Benney-Luke Equation

February 3, 2011Alexander Woo
St Olaf College

Local properties of Schubert varieties

February 10, 2011Deena Schmidt
Ohio State University

Stochastisity and structure in biological systems: from the evolution of gene regulation to sleep-wake dynamics

February 15, 2011Gregory Oman
Ohio University

Jonsson Modules

February 28, 2011Sandra Carillo
University of Rome Sapienza

Baecklund transformations, Recursion Techniques and Noncommutative soliton solutions

March 10, 2011Bengt Fornberg
University of Colorado - Boulder

A Numerical Methodology for the Painlevé equations.

April 12, 2011Antonio Moro
SISSA Trieste- Italy

Dispersive shock waves and Painleve' Trascendents

April 14, 2011Harvey Segur
University of Colorado - Boulder

Tsunamis

April 18, 2011Graduate Student Presentations
UCCS

Various

May 5, 2011James Mitchell
University of St. Andrews

Approximating permutations and automorphisms

Fall 2010

August 26, 2010Dr. Florian Sobieczky
Friedrich Schiller University

Annealed bounds for the return probability of Delayed Random Walk on finite critical percolation clusters

September 9, 2010Dr. Yi Zhu
University of Colorado - Boulder

Unified description of Bloch envelope dynamics in the 2D nonlinear periodic lattices

September 23, 2010Geraldo Soares de Souza
Auburn University

A New Proof of Carleson's Theorem

September 30, 2010Dr. Gene Abrams
UCCS Math

The Graph Menagerie

October 14, 2010Dr. William Kath
Northwestern University

2010 Distinguished Math Lecture: Computational Modeling of Neurons

October 21, 2010Janos Englander
University of Colorado - Boulder

An interacting branching particle model

November 4, 2010Andrea Bruder
Colorado College

The Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators

November 11, 2010Dr. Marek Grabowski
UCCS Physics Department

Dynamics of a Driven Spin

Spring 2010

January 19, 2010Dr. Brian Hopkins
Saint Peter's College

Sequential Selection and the Symmetric Group

February 11, 2010Alex Dugas
University of California, Santa Barbara

Representations, quivers and periodicity

February 18, 2010Manuel Reyes
University of California, Berkeley

Theorems of Cohen and Kaplansky: from commutative to noncommutative algebra

February 25, 2010Dr. Zachary Mesyan
Ben-Gurion University, Israel

Conjugation of injections by permutations

March 4, 2010Dr. Mark Hoefer
North Carolina State University

Supersonic Dispersive Fluid Dynamics

March 18, 2010Dr. Boaz Ilan
University of California, Merced

Soliton Dynamics in Inhomogeneous Media

April 1, 2010Dr. Michael Dorff 
BYU

Convex combinations of harmonic mappings

April 15, 2010Theodoros Horikis
University of Colorado - Boulder

Excited Bose-Einstein Condensates: Quadrupole Oscillations and Dark Solitons

April 22, 2010Dr. Mihai Bostan
University of Besancon

High Field Limits for magnetized plasmas

April 29, 2010Dr. Bob Carlson
Department of Mathematics, UCCS

Nonconservative Transmission Line Networks, or Jordan normal form for some differential equations

Fall 2009

September 10, 2009Dr. Anton Dzhamay
School of Mathematical Science, Univ of Northern Colorado

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

September 24, 2009Dr. Bob Carlson
Department of Mathematics, UCCS

Harmonic Analysis for Star Graphs and the Spherical Coordinate Trapezoidal Rule

October 8, 2009Dr. Mark Ablowitz
Department of Applied Math University of Colorado, Boulder

Extraordinary Waves: From Beaches to Lasers

November 5, 2009Dr. Luca Gerardo Giorda
Department of Mathematics, Emory University

Modeling the Electrical Activity of the Heart

November 19, 2009Dr. Juan G. Restrepo
Department of Applied Mathematics, Univ of Colorado at Boulder

Synchronization of Oscillators with Noisy Frequency Adaptation

December 3, 2009Dr. Wojciech Kosek
Department of Mathematics Colorado Technical University

What do stock market and positive L1 operators have in common?

Spring 2009

January 22, 2009Dr. Herve Guiol
INP Grenoble

Almost sure scaling limit for monotone interacting particles systems in one dimension.

January 29,2009Fabio Machado
University of Sao Paulo

Non-homogeneous random walks systems on Z

February 12, 2009Mingzhong Wu
Department of Physics Colorado State Univ.

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

February 17, 2009Scott Annin
California State Univ. Department of Mathematics

Using Special Ideals to Illustrate a Research Philosophy in Ring Theory

February 19, 2009Brigitta Vermesi
University of Rochester Department of Mathematics

Critical exponents for Brownian motion and random walk

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

Integrable Systems, Inverse Scattering Transform and Solitons

March 12, 2009Lincoln Carr
Department of Physics Colorado School of Mines

Emergent Time Scales in Ultracold Molecules in Optical Lattices [Joint Math/Physics Colloquium]

March 19, 2009Bernard Junot
UCLA

How Statistics Explain What Cancer Is

April 2, 2009Radu Cascaval
Department of Mathematics UCCS

Bi-directional wave propagation in the human arterial tree

April 9, 2009Gene Abrams
Department of Mathematics UCCS

The uncanny resemblance between Leavitt path algebras and graph C*-algebras

April 17, 2009Gilbert Strang
Department of Mathematics MIT

Linear Algebra and Random Triangles

April 30, 2009Pere Ara
Universidad Autonoma de Barcelona

K-theory for Leavitt path algebras

Spring 2008

Jan 31, 2008Robert Carlson
Department of Mathematics UCCS

Hunting for Eigenvalues of Quantum Graphs

Feb 21, 2008Radu Cascaval
Department of Mathematics UCCS

On the Soliton Resolution Conjecture

Mar 6, 2008Yu Zhang
Department of Mathematics UCCS

Limit Theorems for Maximum Flows on a Lattice

Apr 3, 2008Enrique Pardo
Universidad de Cadiz (Spain)

The Classification Question for Leavitt Path Algebras

Apr 17, 2008Robert Carlson
Department of Mathematics UCCS

Bringing Matlab into Introductory Differential Equations

May 1, 2008Tim Huber
Iowa State University

Parametric representations for Eisenstein series from Ramanujan's differential equations

May 6, 2008Mercedes Siles Molina
Universidad de Málaga(Spain)

Classification Theorems for Acyclic Leavitt Path Algebras

May 8, 2008John D. Lorch
Ball State University

Sudoku and Orthogonality

Fall 2008

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

Feynman diagrams, integrals, and special functions

September 25, 2008Kulumani Rangaswamy
University of Colorado Department of Mathematics

On Leavitt path algebras over infinite graphs

October 10, 2008Steve Krone
University of Idaho Department of Mathematics

Spatial self-organization in cyclic particle systems

October 23, 2008Anca Radulescu
Applied Mathematics University of Colorado at Boulder

The Multiple Personality of Schizophrenia

November 6, 2008Chihoon Lee
Department of Statistics Colorado State University

Diffusion Approximations to Stability and Control Problems for Stochastic Networks in Heavy Traffic

November 20, 2008David Bortz
Applied Mathematics Univ of Colorado at Boulder

Mathematics and Biology in the 21st Century (joint math and biology colloquium)

December 11, 2008Alessandro Veneziani 
Mathematics & Comp Sci Emory University

Geometrical Multiscale Models of the Cardiovascular System