UMD Department of Mathematics and Statistics

$Math and Stats$

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Phone: 218-726-8747 / 218-726-8254
Fax: 218-726-8399
Email: mathstat@d.umn.edu
Undergraduate Studies
Email: math.dus@d.umn.edu
Graduate Studies
Email: math.dgs@d.umn.edu
140 Solon Campus Center (map)
1117 University Drive
Duluth, MN 55812-3000

Home > Seminars and Colloquia

Seminar and Colloquia

Lecture The Department of Mathematics and Statistics offers a weekly colloquium series on Thursdays. Most colloquia begin between 3:00 and 3:30. Seminars alternate between those aimed at Undergraduate (type U) and Graduate (type G) audiences. Calendar of current events

Type	Date	Title	Speaker
G	2/23/12	Distance between consecutive entries in permutations	David S. Gunderson University of Manitoba
U	2/16/12	The Capture and Analysis of Aerial Photos of Lake Superior	Thomas Cameron UMD undergraduate math major
G	2/9/12	Ideas and Methods in Discrete Optimization	Uwe Leck University of Wisconsin Superior
U	2/2/12	Using Mathematics to Create Symmetry Patterns	Professor Joseph A. Gallian UMD Department of Mathematics & Statistics
G	1/26/12	An Ideal Schedule for Major League Baseball	Kristin Riesgraf MS Candidate: Program in Applied and Computational
G	12/22/11	Expression Patterns of Codon Usage and Homopolymers in the 13-Lined Ground Squirrel	Amy Virta MS Candidate: Program in Applied and Computational
G	12/19/11	An Investigation of Erdos' Method: A Schemefor Generating Carmichael Numbers	Trevor Brennan MS Candidate: Program in Applied and Computational
G	12/15/11	Stoichiometric Modeling of Nutrient and Biomass Flux in the Gulf of Mexico	Nathan L. Pollesch MS Candidate: Program in Applied and Computational
U	12/15/11	Neuroscience and the Mathematical Mind	Peter Baumgartner, UMD Mathematics and Mathematics Education major
G	12/12/11	Gracefule Kayak Paddles	Ann Litersky MS Candidate: Program in Applied and Computational Mathematics
G	12/8/11	On a Combinatorial Identity of J. Borwein	Steve Rosenberg Associate Professor, Department of Mathematics and Computer Science, University of Wisconsin-Superior
U	12/1/11	Undercover Symmetry	Frank A. Farris Santa Clara Unversity/Carleton College
G	11/17/11	Hearing Geometry	Marshall Hampton, Department of Mathematics & Statistics
U/G	11/10/11	A simple forced oscillator: Implications of KAM theory	Jim Walsh, Oberlin College
G	11/3/11	Magic squares and orthogonal arrays	Donald L. Kreher, Michigan Technological University
U	10/27/11	Knotted Arcs	Eric Rawdon, Mathematics Department, University of St. Thomas
U/G	10/20/11	Goshawk invasions and population cycles	Dick Green Department of Mathematics and Statistics
U	TBA	Julia Robinson and Hilbert's Tenth Problem	DVD
G	10/6/11	Perfect r-domination in the Kronecker products of cycles	Pranava K. Jha Department of Computer Science, St. Cloud State University
U	9/29/11	Breaking Driver's License Codes	Joe Gallian Department of Mathematics & Statistics
G	9/22/11	Tracking the three-dimensional evolution of mechanical percolation in nanocomposite materials	Sarah Baxter Department of Mechanical Engineering University of South Carolina

Tracking the three-dimensional evolution of mechanical percolation in nanocomposite materials
by

Sarah Baxter
Department of Mechanical Engineering
University of South Carolina

Abstract:
One mechanism, expected to play a large role in the sometimes novel, and often enhanced, properties of nanocomposites, is the formation of percolated or connected microstructures. While many novel properties are the direct result of the nano-scaled and closely packed microstructures, significant enhancements of traditional composite mechanical properties may also be due to mechanical percolation effects.

Classic percolation models assess connectivity by defining a percolation threshold, usually a volume fraction, at which the microstructure first appears as connected. This is the dominant mechanism in modeling, for example, composite electrical conductivity or porous media fluid flow. Analysis of the process is relatively binary, unconnected or connected. Mechanical percolation, however, necessarily occurs in tandem with other microstructural mechanisms and is perhaps better described as a continuous process. Thus, while percolation thresholds are still critical to characterization, the mechanical response may not be completely defined by this volume fraction. Mechanical response may depend on a combination of mechanisms enhanced or supported by a percolating microstructure. This is the challenge in modeling the effects of mechanical percolation.

Classic mean-field micromechanics models, with no specific description of microstructural arrangement, cannot capture the variability in effective properties due to a random microstructure or predict the onset of a percolated microstructure. In this work a unit cell micromechanics model was used to calculate the effective composite properties for simulated random microstructures. In this way we are able to track the onset and evolution of mechanical percolation by observing the relevant mechanical effects, which include observations of the range of variable properties, identification of distinct microstructural features associated with minimum and maximum properties, and following the changes in the probability density functions describing the distribution of properties.

Time: Thursday, September 22, 3:00PM
Location: 130 Solon Campus Center

Breaking Driver's License Codes
by

Joe Gallian
Department of Mathematics and Statistics

Abstract:
Many states use complicated algorithms or formulas to assign driver's license numbers but keep the method confidential. Just for the fun of it, I attempted to figure out how the states code their license numbers. In this talk I will discuss how I was able to break the original code for Minnesota (Minnesota changed it coding method in the early 2000s) and the current one for Missouri. The talk illustrates an important problem-solving technique used by scientists but is not emphasized in mathematics classes. It also teaches the lesson that sometimes things done just for the sake of curiosity can have applications. The talk is intended for a general audience. No advanced mathematics is needed.

Time: Thursday, September 29, 3:00PM
Location: 150 Chemistry

Perfect r-domination in the Kronecker products of cycles
by

Pranava K. Jha
Department of Computer Science, St. Cloud State University

Abstract:
The Kronecker product G x H of graphs G = (V, E) and H = (W, F) defined as follows: V(G x H) = VxW, and E = {{(a, x) , (b, y)}: {a, b} ∈ E and {x, y} ∈ F}. It is variously known as the direct product, tensor product and categorical product.

The present talk deals with perfect r-domination in the Kronecker product of k cycles. Under certain conditions on the lengths of the cycles, there exists a vertex partition of the graph into perfect r-dominating sets in each of the following cases: (a) r = 1 and k >2, (b) r> 2 and k = 2, and (c) r> 2 and k = 3. Areas of applications include efficient resource placement and error-correcting codes.

Time: Thursday, October 6, 3:00PM
Location: 130 Solon Campus Center

Julia Robinson and Hilbert's Tenth Problem

(DVD)

Abstract:
This one-hour biographical documentary film tells the story of an important American mathematician against a background of mathematical ideas. Julia Robinson, a pioneer among American women in mathematics, rose to prominence in a field where often she was the only woman. Julia Robinson was the first woman elected to the mathematical section of the National Academy of Sciences, and the first woman to become president of the American Mathematical Society. The film describes Robinson's major contribution to the solution of one of the most important theorems of the Twentieth century and some key events in the history of modern mathematics while conveying the motivations of mathematicians, and exploring the relationship between mathematical research and the development of computers.

Time: TBA
Location: 150 Chemistry

Goshawk invasion and population cycles

Dick Green
Department of Mathematics and Statistics

Abstract:
The Northern Goshawk is a large, fierce hawk of the north woods. It is seldom seen by birdwatchers outside of the migration period. Migrating hawks are observed at many sites across North America. Duluth is the best hawk watch site for observing migrating goshawks. Numbers fluctuate from several score to several thousand goshawks counted per year. Goshawk numbers show periodic fluctuations, with invasions occurring about every ten years. In this talk I will discuss the bird, hawk counts, goshawk numbers and population fluctuations. Of particular interest is the question of whether population fluctuations are cyclic or not.

Time: Thursday, October 20, 3:00PM
Location: 150 Chemistry

Knotted Arcs

Eric Rawdon
Mathematics Department, University of St. Thomas

Abstract:
Recently, some proteins have been classified as being knotted. However, proteins are open (i.e. they have free ends), and knotting, from a mathematical perspective, only is defined for closed curves (i.e. loops). Proteins are special in that the free ends typically lie on the "outside," so many of the protein knot detection techniques work fine for proteins but not so well in more ambiguous situations. How should we define the existence of knotting within open chains (like shoelaces and headphone cords)? We will discuss knotting in open chains and proteins, and search for knots within knots.

Time: Thursday, October 27, 3:00PM
Location: 150 Chemistry

Magic squares and orthogonal arrays

Donald L. Kreher
Michigan Technological University

Abstract:
A magic square is an n by n array of integers with the property that the sum of the numbers in each row, each column and the main back diagonals is the same. This sum is the magic sum.

Magic squares have had a long and colorful history. They have attracted the attention of Emperor's Statesman, hobbyists, magicians and yes even mathematicians. In this talk, we show how magic squares are connected with pairs of orthogonal Latin squares. This connection and recursive constructions are then used to show that a magic square exists for all n, except n = 2.

An investigation of the existence of pairs of orthogonal Latin squares is also included

Time: Thursday, November 3, 3:00PM
Location: 130 Solon Campus Center

A simple forced oscillator: Implications of KAM theory

Jim Walsh
Oberlin College

Abstract:
In this talk the dynamics of a simple model of three charged bodies interacting under an inverse square electrostatic force is presented. I will illustrate the manner in which fractals and chaos arise in the absence of damping when the forcing is periodic. The model easily serves as an alternative to the pendulum, the standard model of a periodically forced nonlinear oscillator. While not essential, having completed a multivariable calculus course will prove helpful in following along.

Time: Thursday, November 10, 3:00PM
Location: 130 Solon Campus Center

Hearing Geometry

Marshall Hampton
Department of Mathematics & Statistics

Abstract: Why do some instruments produce sounds with a characteristic pitch while others (such as drums) do not? What's the difference between an orchestral xylophone and a marimba? What would a square drum sound like? We will consider these and other questions in the context of "spectral geometry," which relates shapes to differential equations.

Time: Thursday, November 17, 3:00PM
Location: 150 Chemistry

Undercover Symmetry

Frank A. Farris
Santa Clara University/Carleton College

Abstract: Spend some time with the images shown, each a wallpaper pattern with six-fold symmetry. You can rotate 60 degrees about various points and the pattern is unchanged. You can spin 180 degrees about other points and 120 degrees around still others. A pattern with six-fold symmetry must have these additional three-fold and two-fold symmetries. But in the right-hand image, why do the red bowties seem to have mirror symmetry? Why are they set at such strange angles relative to the orientation of the red hexagons? These strange features led me to discover new types of symmetry in wallpaper patterns and find strange connections to number theory.

Joe Gallian

Time: Thursday, December 1, 3:00PM
Location: 150 Chemistry

On a Combinatorial Identity of J. Borwein

by
Steve Rosenberg
Associate Professor, Department of Mathematics and Computer Science,
University of Wisconsin-Superior

Abstract: Consider a pyramid made out of unit cubes arranged in square horizontal layers, with a ledge of one cube's length around the perimeter of each layer. For any natural number k,we can count the number of ways of choosing k unit cubes from the pyramid such that no two cubes are in the same horizontal layer; we can also count the number of ways of choosing k unit cubes from the pyramid such that no two cubes come from the same vertical slice or two adjacent slices.

In 2010, Jon Borwein and his co-authors made a conjecture equivalent to the statement that these two quantities are always equal.

In this talk, we prove Borwein's conjecture using standard ideas and facts from combinatorics, elementary algebra, and linear algebra.

Time: Thursday, December 8, 3:00PM
Location: 130 Solon Campus Center

Graceful Kayak Paddles
by
Ann Litersky
MS Candidate: Program in Applied and Computational Mathematics

Advisor: Dalibor Froncek

Abstract: A kayak paddle is a graph made of two cycles joined by a path. We can define KP(r,s,l) as two cycles of lengths r and s joined by a path of length l. If a graph G has m vertices and n edges, then a general vertex labeling of the graph is a one-to-one mapping of the vertex set of G into the set of all non-negative integers. If we have two vertices, say x and y joined by an edge xy, then we can define the edge length as min{x – y, y – x}, where the subtraction is performed in Z2n+1. A b- or graceful labeling is a labeling where all the vertex labels must come from {0,1,…,n}, and the set of edge lengths must be equal to {1,…,n}. If a graph can be labeled using a b-labeling, then it can cyclically decompose K2n+1. In this thesis we investigate the existence of graceful labelings of kayak paddles.

Time: Thursday, December 12, 10AM
Location: 130 Solon Campus Center

Neuroscience and the Mathematical Mind
by
Peter Baumgartner
UMD Mathematics and Mathematics Education major

Abstract: Do we have an innate number sense, or do we develop it as we mature? Is there a part of the brain dedicated to doing mathematics? Can other animals do math? How much math do infants really know? What impact does math-anxiety and performance pressure have on the brain's ability to do math? What happens in the brain when we solve 5 + 2? The emerging field of educational neuroscience can guide us towards answering these questions, as well as direct the way we might teach math in the future. We'll delve into the science behind how the brain does arithmetic and more in this colloquium for a general audience.

Time: Thursday, December 15, 3:00PM
Location: 150 Chemistry

Stoichiometric Modeling of Nutrient and Biomass Flux in the Gulf of Mexico

by
Nathan L. Pollesch
MS Candidate: Program in Applied and Computational
Advisor: Harlan Stech

Abstract: The purpose of this thesis is to explore the connections between agricultural runoff influx, oil influx, and oxygen levels in a near-coastal marine environment. The creation of oxygen deficient conditions is investigated through the use of a stoichiometric modeling approach that utilizes a system of ordinary differential equations. Agricultural runoff is modeled as a source of a limiting nutrient for algae. Oil influx is modeled as a carbon source for bacterial consumption. The investigation is motivated by the Gulf of Mexico-ecosystem in the wake of the Deepwater Horizon oil rig incident of 2010, which contributed large amounts of oil (carbon) to the Gulf system. The model consists of an algal class with flexible stoichiometry that utilizes the nutrient for growth and a bacterial class with fixed stoichiometry that assimilates the carbon. A consumer class with fixed stoichiometry that is dependent upon the oxygen present in the system is modeled and is used to indicate oxygen deficient conditions. Equilibrium, time series, and stability analysis of this five-dimensional system are presented. Through the analyses presented and simulations, it is found that this model reproduces the behavior of the biological processes associated with nutrient enrichment and the creation hypoxic areas, or ‘dead zones’.

Time: Thursday, December 15, 3:00PM
Location: 130 Solon Campus Center

An Investigation of Erdös' Mdoethod: A Schemefor Generating Carmichael Numbers

by
Trevor Brennan
MS Candidate: Program in Applied and Computational
Advisor: John Greene

Abstract: In 1956 Paul Erdös’ outlined a method for calculating a large number of Carmichael numbers. Fermat’s little theorem states; if p is a prime then for any integer a, a^p = a (mod p). A Carmichael number is a composite number, as defined by Korselt’s criterion, which will also satisfy Fermat’s little theorem for an infinite number of bases. For example, the smallest Carmichael number is 561 = 3*11*17 and a⁵⁶¹ = a (mod 561) for any positive integer a. In this project we have explored Erdös’ method in the effort to understand how well it works in producing a large number of Carmichael numbers. In addition, we established some underlying constructions and behaviors of the method.

Time: Monday, December 19, 3:00PM
Location: 130 Solon Campus Center

Stoichiometric Modeling of Nutrient and Biomass Flux in the Gulf of Mexico

by
Amy Virta
MS Candidate: Program in Applied and Computational
Advisor: Marshall Hampton

Abstract: The 13-lined ground squirrel is particularly interesting to study because of the extremes their bodies go through during hibernation. Their bodies do amazing physical feats, such as dropping their core temperature to around 0°C, that would be fatal to humans. It is these physical feats that make the study of their DNA interesting. This project used data from Dr. Andrews’ biology lab and biostatistical methods to analyze squirrel DNA sequences. The hope is to find genetic explanations in the codon usage or avoidance of homopolymers that might help shed light on the genes expressed during hibernation.

Time: Thursday, December 22, 3:00PM
Location: 130 Solon Campus Center

An Ideal Schedule for Major League Baseball

by
Kristin Riesgraf
MS Candidate: Program in Applied and Computational
Advisor: Dalibor Froncek

Abstract: Intense competition exists not only on Major League's baseball diamonds but also behind the scenes. Scheduling for the MLB season is an outsourced job. Contenders receive the format and the restrictions for the next year's schedule and submit a proposal. The contract is awarded to the group whose schedule is closest to ideal. In this project, I wrote my own schedule for the 2012 MLB regular season using concepts of Graph Theory. The schedule that I created is ideal in a world where no time, travel, or financial constraints exist.

Time: Thursday, January 26, 3:00PM
Location: 130 Solon Campus Center

Using Mathematics to Create
Symmetry Patterns

by
Professor Joseph A. Gallian
UMD Department of Mathematics & Statistics

Abstract: We use video animations to illustrate how mathematics can be used to create computer generated symmetry patterns. Discrete math, exponential functions, logarithms and modular arithmetic are used to transform basic images into symmetry patterns. These methods were used to create the image for the 2003 Mathematics Awareness Month poster. The talk is intended for a general audience.

Time: Thursday, February 2, 3:00PM
Location: 120 Solon Campus Center

Ideas and Methods in Discrete Optimization
Symmetry Patterns

by
Uwe Leck
University of Wisconsin Superior

Abstract: We survey some of the main ideas used to solve discrete optimization problems and give examples illustrating them. This includes exact methods like complete enumeration, exchange methods, greedy algorithms, partial enumeration as well as non-exact heuristics and approximation algorithms.

Time: Thursday, February 9, 3:00PM
Location: 130 Solon Campus Center

The Capture and Analysis of Aerial Photos of Lake Superior

by
Thomas Cameron
UMD undergraduate math major
Advisor: Dr. Jay Austin

Abstract: Although satellite imagery is the optimal method for capturing aerial photos of Lake Superior, photos can only be taken once a day and cloud cover ruins any photo opportunities. The bluffs in Duluth provide an opportunity to employ a more versatile method for capturing aerial photos of Lake Superior. In a proof of method, the process for capturing and analyzing aerial photos of Lake Superior using a single digital camera will be described. The experimental process used to find the numerical values of the parameters necessary to establish projection equations between world measurements and image geometry and an algorithm that map points of interest from a digital photograph to a map of Lake Superior will be explained.

Time: Thursday, February 16, 3:00PM
Location: 120 Solon Campus Center

Distance between consecutive entries
in permutations

by
David S. Gunderson
University of Manitoba

Joint work with P. Ballister and B. Bollobas, University of Memphis

Abstract:

Given a permutation S on {1, 2,..., n}, define its distance set to be {|S(i+1) – S(i)|: i=1, 2,..., n–1}. For example, when n=5, the permutation (S(1),..., S(5))=(5,1,4,2,3) has distance set {1,2,3,4} with all possible differences, however the permutation (1,2,3,4,5) has distance set {1}. On average, how large is the distance set of a random permutation?

This question was loosely motivated by a famous open problem in graph theory called "the graceful tree conjecture."

Time: Thursday, February 23, 3:00PM
Location: 130 Solon Campus Center