MATHEMATICS AND COMPUTING RESEARCH EXPERIENCES FOR UNDERGRADUATES AT IOWA STATE UNIVERSITY
supported by the National Science Foundation through
DMS 0750986, DMS 0502354, DMS 0353880

ISU Math REU Summer 2011

We are proud of all of you who represented the ISU REU at Joint Mathematics Meetings. 

Congratulations to Shanise Walker, undergraduate poster award, Propagation Time for Zero Forcing of a Graph.

We are proud of all of you who represented the ISU REU at SACNAS. 
Congratulations to:
My Huynh and Shanise Walker, undergraduate poster award, Propagation Time for Zero Forcing of a Graph.
Angelica Gonzalez and George Shakan, undergraduate poster award, Automorphism Groups of Directed Strongly Regular Graphs.
Chetak Hussein, winner of Who Wants to be a Mathematician? contest.
Xavier Garcia and Georege Shakan, finalists in Who Wants to be a Mathematician? contest.



Thanks for a great summer!




Schedule July 23 - July 29

Symposium general schedule and  presentation schedule

M - F 9A-5P Do research except for scheduled activities below and lunch break (even when no group lunch).

Red = food, whole group.  Blue = whole group.

Saturday July 23

Sunday July 24
afternoon           Furman Aquatic Center

Monday July 25
9 AM               research
                          Zero forcing in 401
                          Dynamical systems in 390
                          Matrices over C[a,b] in 160
                         Algebraic graph  in 132
noon                  Union Drive Marketplace REU student lunch menu
                          REU business meeting in UDM at 12:20
1 PM                 t-shirt distrubution and group photo


Tuesday July 26

 
9 AM               research
                           Zero forcing in 401
                          Dynamical systems in 390
                          Matrices over C[a,b] in 160
                          Algebraic graph  in 132
by 3:45 PM        turn in Carver keys (can also be done Friday),
3:30 PM             sweet corn feed 400 Carver
  
Wednesday July 27
7:30 AM            depart Freddy for Iowa City
10 A - 8:30 P      Math REU symposium in Iowa City

Thursday July 28
8 A - noon           Math REU symposium in Iowa City
3:30 PM?             return to Freddy for Iowa City

Friday July 29
noon                   Final written reports due, turn in Carver keys if not done
all day                 clean apartments and pack
4:30                    depart Freddy for farewell dinner at Hickory Park restaurant
  
After the first week, as long as you attend your group meetings and REU scheduled activities, and get your work done, you can choose when/where to work unless instructed otherwise by your faculty mentor.  But you should always be reachable (e.g., by cell phone) during the work day if you are not in Carver.

Faculty mentors have authority to excuse students from any scheduled activity to avoid disruption of research, but someone should notify Leslie Hogben if a student is excused to miss a whole group activity during the workweek.

Weekend and evening activities are optional.

Participants

Photo gallery

Undergraduate Students
     
Anna Cepek               Bethany Lutheran College
Justin Cyr                   Syracuse University
Xavier Garcia            University of Minnesota - Twin Cities
Angelica Gonzalez    Whittier College
Chetak Hossain         University of California, Berkeley
My Huynh                 Arizona State University
Jennifer Kunze          St. Mary's College of Maryland
Kirill Lazebnik          State University of New York at Geneseo
Sarah Meyer              Smith College
Nathan Meyers          Bowdoin College
Crystal Peoples          Longwood University
Thomas Rudelius      Cornell University
Anthony Sanchez     Arizona State University
George Shakan         Worcester Polytechnic Institute
Sijing Shao               Iowa State University
Emily Speranza        Carroll College
Shanise Walker        University of Georgia
Charles Watts           Morehouse College

Graduate Students 
(all Iowa State University)
Kim Ayers
Jason Ekstrand
Nicole Kingsley
Michelle Lastrina
Oktay Olmez
Travis Peters
Chad Vidden

Faculty   (Iowa State University unless otherwise noted)
Leslie Hogben                     
Wolfgang Kliemann
Justin Peters
Sung-Yell Song
Michael Young
Minerva Catral                  Xavier College (Ohio)



Photo(s) of the week 





(for more pictures go to the photo URL)



T-shirt design

backfront


Ames Events

The following information is taken from the internet; these activites are not sponsored by the REU.
See http://www.visitames.com/events/ for more information.
Free unless noted otherwise.

All the time
Furman Aquatic Center (water park), $5 admission, 1-8 PM weather permitting
Ames/ISU Ice Arena $5 admission, $2.75 skate rental, see calendar for open times

Thursdays
5:30 PM Main Street (downtown) music
7 PM Ames Municipal Band concert in Bandshell park

Saturdays
8:00 a.m. - 1:00 pm Ames Main Street Farmers' Market, 400 block Main Street

Useful Links

LaTeX template    Figure for template     Beamer template

NSF REU sites

AMS Undergrad page

MAA Undergrad page

SACNAS National Conference 

Young Mathematicians Conference

Involve

SIAM Undergraduate Research Online (SIURO)

Rose-Hulman Undergraduate Math Journal

Journal of Young Investigators

Matlab Information has links to Matlab guides


Math Project Descriptions 2011

Algebraic Graph Theory Group  Dr. Sung-Yell Song
Existence and Nonexistence of (Directed) Strongly Regular Graphs

Strongly regular graphs are important objects in modern algebraic graph theory. The interest in strongly regular graphs has been stimulated by the development of the theory of finite permutation groups and the classification
of finite simple groups. The strongly regular graphs arise from various area of mathematics including group theory, association schemes, finite geometries, combinatorial designs and algebraic codes.

A strongly regular graph with parameters (v, k, λ, μ) is defined as an undirected regular graph G with v vertices satisfying the property: “the number of common neighbors of vertices x and y is k if x = y, λ if x and y are adjacent, and μ if x and y are non-adjacent vertices.” A loopless directed graph D with v vertices is called directed strongly regular graph with parameters (v, k, t, λ, μ) if and only if D satisfies the following conditions:
i) Every vertex has in-degree and out-degree k.
ii) Every vertex x has t out-neighbors that are also in-neighbors of x.
iii) The number of directed paths of length two from a vertex x to another vertex y is λ if there is an edge from x to y, and is μ if there is no edge from x to y.

There are many problems related to the characterization and classification of these graphs. We plan to settle some of the existence or non-existence problems for given parameter sets while we investigate various sources of (directed) strongly regular graphs. Sample problems that we might be tempted to explore include:
• How many strongly regular graphs with parameters (64, 28, 12, 12) are there?
• Is there a directed strongly regular graph with parameters (24, 10, 5, 3, 5)?
• Prove that there is no directed strongly regular graph with parameters (30, 7, 5, 0, 2).
• Characterize all tactical configurations that yield the directed strongly regular graphs with parameters ((n2 − 1)(n3 − 1)/(n − 1)2, n(n + 1), n, n − 1, n).


Dynamical Systems and Markov Chains 
Dr. Wolfgang Kliemann

Many ‘real world’ phenomena can be modeled mathematically via ordinary differential equations; this includes many engineering systems, reaction kinetics in chemistry, population dynamics in biology, market behavior in economics, etc. More often than not, these systems will be subjected to perturbations (cars traveling on roads, variations of influx into a chemical reactor, environmental conditions, etc) that need to be taken into account to obtain a workable model of the phenomenon.  If we have statistical information about the perturbation (such as spectra of road surfaces, weather predictions, or market volatility), a finite state Markov chain in discrete time is often the model of choice for the perturbation.

We are then faced with a (continuous time) differential equation (on a continuous state space) that is perturbed by a (discrete time) Markov chain (with finitely many, hence discrete states). How can one build a mathematical theory that studies these (hybrid) systems? What can be said about the behavior of such systems, and about our ability to control them (i.e. to make the system behave like we want it to behave)? How can we estimate from actual data the parameters of Markov chains that model specific perturbations well?

The project will address at least some of these questions; its focus will depend on the interest and backgrounds of participants. We will start looking at mathematical descriptions of such hybrid systems (including their simpler version, switched systems, that omit the probabilistic part) and at numerical methods that allow reliable simulations of system behavior. We will then study either control theoretic aspects, or more statistical questions of parameter estimation.


Matrices over C[a, b] Dr. Justin Peters

We will begin by looking at the basic notions of Banach space and Banach algebra. We will examine what the spectral radius formula and spectral mapping theorem tell us in the case of the familiar examples of C[a, b], the continuous complex-valued functions on the interval [a, b], and M_n, the complex n n matrices.

After reviewing central ideas from matrix theory (i.e., eigenvalues, eigenvectors, the Cayley-Hamilton theorem, diagonalization) we take up the major theme of this project: matrices over C[a, b], that is, matrices whose entries are in C[a, b]. This is a Banach algebra, which we denote M_n(C[a, b]), which combines the features of the two familiar examples in new and interesting ways. What are the appropriate notions of eigenvector and eigenvalue in this setting? How can the spectral radius be computed? How far can the analogy between M_n
and M_n(C[a, b]) be taken? For example, if A is an element of this Banach algebra such that for every t 2 [a, b] the matrix A(t) is diagonalizable by a unitary matrix in Mn, is A diagonalizable by a unitary
in M_n(C[a, b])?


Zero forcing/graph propagation  Dr. Leslie Hogben, Dr. Michael Young

Initially a subset Z of the vertices of a graph G are colored black and the remaining vertices are colored white.  The color change rule is that if a black vertex v has exactly one white neighbor w, then change the color of w to black.   The set Z is a zero forcing set if after applying the color change rule until no more changes are possible, all the vertices of G are black.  The zero forcing number is the minimum size of a zero forcing set.  Zero forcing arose in the study of determining the minimum rank/maximum nullity among real symmetric matrices having nonzero off-diagonal positions described by the edges of a given graph (the zero forcing number is an upper bound for maximum nullity, and independently in the study of control of quantum systems in physics, where it is called graph infection or propagation.   This project will investigate problems related to the zero forcing number.

Students involved in this project will be part the ISU Combinatorial Matrix Theory Research Group; more information is available on that page. This group regularly publishes its results.  The summer 2004, 2005, 2006, 2009, and 2010 groups all published papers (see list of papers).




Mathematics Department Homepage

Web page maintained by Leslie Hogben