Andrew Baxter, Rutgers University
Title: Bijective Proofs in Partition Theory

Abstract: A partition of an integer N is a nonincreasing sequence of nonnegative integers which sum to N. In other words, a way to write N as the sum of other numbers without regard to order. The subject of partition theory counts the number of partitions of an integer. Things really get interesting when you start restricting the kinds of addends you're allowed to use, such as only using odd addends or requiring that all addends be distinct. While analytic proofs involving generating functions (which happen to be q-series) are common, the most satisfying proofs in the subject are bijective proofs. I will summarize some of the more interesting bijections, as well as known identities in need of bijective proofs.

Lisa Carbone, Rutgers University
Title: Trees and group actions

Abstract: We discuss symmetries of combinatorial objects named trees and their role in various branches of mathematics: algebra, number theory and Lie groups.

Fred Roberts, DIMACS
Title: Graph-theoretical Models of the Spread and Control of Disease and of Fighting Fires

Abstract: Mathematical models using graphs and networks are increasingly important in understanding ways to combat the spread of disease, whether due to natural outbreaks such as influenza or deliberate outbreaks caused by bioterrorists. We will discuss the role of the mathematical sciences in modeling the spread of disease and describe specific models that use the tools of graph theory to understand strategies for vaccination, quarantine, etc. We will describe recent work on abstract models of the control of fires that are mathematically analogous to the disease spread models. The talk will be self-contained. Background in graph theory, epidemiology, or firefighting is not required.

Joe Kilian, Rutgers University
Title: Secure Computation

Abstract: Secure computation is one of the most powerful cryptographic paradigms not being used in modern computer systems. It has applications to electronic commerce, voting, and dating. In this talk, I will give an undergraduate-level introduction to secure computation - what it is, what it can and cannot do, and its potential for use in real systems.

Stephen Greenfield, Rutgers University
Title:

Abstract: A nonlinear recurrence similar to the Fibonacci numbers (quadratic rabbits!) leads to some interesting results which are proved with ANALYSIS and ESTIMATION and not with COUNTING. The numbers in the title are a result of this work, and they are new real numbers (not known to such resources as the Inverse Symbolic Calculator).

I only can give one talk. If you have ever heard me talk before, then you will have heard this talk. Please do not get confused and hope to obtain further insight from me.

Daniel Král, Charles University, Prague
Title: The channel assignment problem models in graph theory

Abstract: I would like to provide an overview of various graph theory models for the problem of assigning radio frequencies to transmitters. Illustration of some basic techniques and approaches used in this area on examples accessible to a broad mathematical audience. I also aim to mention some recent results and trends in this area. The talk will focus on the mathematical theory of the models rather than the computational aspects.

Doron Zeilberger, Rutgers University
Title:

Abstract: I recently gave a talk entitled "n!", and I once gave a talk entitled "=" (without the quotes, of course). The lengths of these titles were 2 and 1 characters, respectively. So, as you can see, I am fond of short titles.

But, so far, I never gave a talk whose title has length 0. This is the first and last time in my life that I can give such a talk, since I never repeat a talk twice, and there is just a unique string in the English language (or any language for that matter) that has zero characters.

As the title suggests, the talk will be on Nothing. Paradoxically, Nothing is really something, and in fact, everything comes from nothing (and of course, comes to nothing, at the end).

Scott Schneider, Rutgers University
Title: TBA

Abstract: TBA
After Scott's talk, important information about your first REU presentations (June 19-20) will be provided.

Philip Matchett Wood, Rutgers University
Title: Origami: Elegant Mathematics and an Amazing Application

Abstract: Come learn the elegant mathematics of origami constructions in the plane! This talk will discuss the similarities between constructions with compass and straight-edge and constructions using origami. The focus, however, will be on some striking differences, in particular, how origami (and origami alone) can be used to solve the famous problem of trisecting an angle. Also, I would like this to be an applied talk, so please bring: (1) 2 or 3 blank sheets of paper (2) a dark marker (sharpie-style is best) I'll let you guess what the materials are for :-) ----just be sure to bring them along!