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Discrete Mathematics Seminar

Spring 2016 - Fridays at 11:00 a.m. in Lytle 203, unless otherwise noted

Friday, April 29 - Dr. Eric Landquist

"The Mathematics of Voting Theory"

Voting theory sounds simple enough, but there is quite a lot of deep mathematics there and some rather surprising results. I'll give an example to show that depending on the voting method used in the 2008 Presidential election, either Obama (D), McCain (R), or Barr (L) could have ended up with the electoral votes for Indiana. We'll discuss various voting methods and the philosophies and psychology behind them. The intent is not to debate politics, but to show how mathematics impacts and explains society.  

Friday, April 8 - Professor John Botzum

"It Does Matter How You Slice It: The Combinatorics of Pizza-Slicing"

Mathematics students are urged to recognize patterns and form general conclusions. However, Students of elementary mathematics are cautioned against assuming that conjectures formed inductively are necessarily true in the general case. A classic example of a reasonable conjecture that is false arises in the solution of the following problem : What is the maximum number of regions formed by pairwise connections of n points on the circle? We will employ elementary counting methods to solve this problem and more general problems.  

Friday, April 1 - Dr. Reinier Bröker, Brown University

"Constructing elliptic curves of prescribed order"

Elliptic curves have become increasingly important during the last 30 years, and made the front page of The New York Times for playing a key role in Wiles’ proof of Fermat’s last theorem. In this talk I will give an introduction to elliptic curves, and consider the problem of constructing an elliptic curve with a given number of points. Many examples will be given.  

Friday, March 25 at 3:00 p.m. - Dr. Gene Fiorini, Muhlenberg College

"Measuring Robustness of the Hudson River Food Web and Symmetric Class-0 Subgraphs"

Competition graphs and graph pebbling are two examples of graph theoretical-type games played on a graph under well-defined conditions. In the case of graph pebbling, the pebbling number pi(G) of a graph G is the minimum number of pebbles necessary to guarantee that, regardless of distribution of pebbles and regardless of the target vertex, there exists a sequence of pebbling moves that results in placing a pebble on the target vertex. A class-0 graph is one in which the pebbling number is the order of the graph, pi(G)=|V(G)|. This talk will consider under what conditions the edge set of a graph G can be partitioned into k class-0 subgraphs, k a positive integer. Furthermore, suppose D is a simple digraph with vertex set V(D) and edge set E(D). The competition graph G(V(G),E(G)) of D is defined as a graph with vertex set V(G)=V(D) and edge vw in E(G) if and only if for some vertex u in V, there exist directed edges (u,v) and (u,w) in E(D). This talk will present some recent results applying the competition graph concept of connectance to measure food web robustness.  

Friday, March 18 - Dr. Ju Zhou

"Integer Flows of Graphs and Graph Coloring - Part 2"

Friday, February 26 - Problem Session

Potential research problems for undergraduates!

Thursday, February 18 - Problem Session

Potential research problems for undergraduates!

Friday, February 5 - Dr. Ju Zhou

"Integer Flows of Graphs and Graph Coloring - Part 1"

In mathematics, the goals of researchers are to obtain new results and prove their correctness, create simple proofs for already established results, discover or create connections between different fields, construct and solve mathematical models for real world problems, and so on. In this talk, Dr. Zhou will talk about map coloring, integer flows, and group connectivity and their relationships. Also she will talk about some of the well-known conjectures and recent progress in each field. 

Friday, January 29 - Organizational meeting

Anyone who would like to speak is welcome to give a talk, students and faculty alike. Feel free to suggest topics to discuss or learn about, articles to read and discuss, etc.

Fall 2015 - Thursday or Friday at 11:00 a.m. in Lytle 136

Friday, November 20 - Dr. Fran Vasko

"Gurobi optimization software"

Dr. Vasko will tell us about an interesting talk he attended at Lehigh University about Gurobi optimization software.

Friday, October 30 - Math Movie!

"N is a number"

We will watch this film about legendary mathematician Paul Erdös!

Thursday, October 22 - Ms. Jiao Xu, Kutztown Mathematics Major


We will discuss an interesting coin-flipping game with a combinatorial flavor and a surprising result!

Friday, October 16 - Dr. Amy Lu

"The Teaching-Learning-Based Optimization Metaheuristic for Discrete Combinatorial Optimization Problems"

The Teaching-Learning-Based Optimization (TLBO) metaheuristic requires no parameter fine-tuning other than determining the population size and convergence criteria. In this paper, we enhance the performance of the TLBO method by introducing "a local neighborhood search on the best solution" before the teaching phase of TLBO. We use it to solve the problems from the literature for multiple-choice multidimensional knapsack problem (MMKP), and demonstrate that TLBO outperforms the best published solution approaches for the MMKP.

Thursday, September 24 - Dr. Brian Kronenthal

"An Immensely Interesting Integer Sequence"

Can you fill in the blanks in the following sequence of integers? No internet please!  

2, 6, 8, 10, 32, 84, 128, 186, _____, _____, 2048, 3172, 8192, 19816, ...  

In this talk, we will explain where this sequence comes from, along the way discussing some special polynomials and introducing you to incidence geometry (generalized quadrangles in particular) and algebraically defined graphs.  Don't worry, we will also fill in the blanks and give a formula to calculate every term of the sequence!

Friday, September 4 and Friday, September 11 - Faculty presentations

Ideas for student research, projects, and independent studies.

Friday, August 28 - Organizational meeting

Spring 2015 - Alternating Thursdays and Fridays at 11:00 a.m. in Lytle 203

May 1 - Wrap-up and plans for next semester

April 23 - Dr. Rajeev Kumar, College of Business

"A Smart Market of Personal Information."   

April 17 - Still more discussion on the graceful labeling problem!

April 10 (Lytle 226) - Kenneth Zyma (Masters Thesis Defense)

"Solving Medium-Scale Instances of the Cable-Trench Problem Applied to the Proposed LOFAR Super Station in Nancay France."

April 2 - Even more discussion on the graceful labeling problem.

March 27 - More discussion on the graceful labeling problem.

March 19 - The second half of the movie, "Counting from Infinity: Yitang Zhang and the Twin Primes Conjecture." 

March 6 - The first half of the movie, "Counting from Infinity: Yitang Zhang and the Twin Primes Conjecture." 

March 5 - Review of a proof that all binary trees can be labeled gracefully.

February 26 - Dr. Amy Lu

"Adapting the Teaching-Learning-Based Optimization Metaheuristic to the Weighted Set Covering Problem."

February 20 - The Graceful Labeling Problem (continued!)

February 12 - The Graceful Labeling Problem

February 6 - The Graceful Labeling Problem and the k-Equitable Labeling Problem

January 29 - k-equitable tree labelings and graceful labeling of trees

January 23 - Organizational meeting

Fall 2014 - Friday at 11:00 a.m. in Lytle 203

November 20 - Dr. Greg Schaper, Computer Science

"A Model of Computation for Teaching and Learning C++."

November 14 - Dr. Ge Xia, Department of Computer Science at Lafayette College

"The Stretch Factor of the Delaunay Triangulation is less than 1.998 ."

November 7 - Fixed-Parameter Tractable algorithms

October 31 - Dr. Yong Zhang, Computer Science

"Introduction to parametrized algorithms and complexity."

October 24 (Lytle 108) - Fun problem session

October 17 - Adib Farah, Computer Science

"Introduction to Big Data"

October 10 - Open Mic

October 3 - Problem-Solving Session

September 26 - Problem-Solving Session

September 19 - Dr. Eric Landquist

"Making Cryptanalysis Less Cryptic and Fried Eggs on Friday: Cracking early versions of the UberCrypt stream cipher"

In this talk, I'll give a quick overview of last week's talk and then poke around with pseudorandom number generators as a way of practically implementing a one-time pad, the only cryptosystem with perfect security. This provides the motivation for the stream cipher UberCrypt, developed by Mr. Joe Chiarella of Colloid, LLC, based in the Harrisburg area. UberCrypt aims to create a cryptographically secure pseudorandom number generator in order to provide perfect security. I'll describe the essential components of UberCrypt and show how one can crack earlier versions of the cipher via a chosen plaintext attack. The approach uses linear algebra with slightly more sophistication than you would see in a high school algebra course (the only difference is that all arithmetic is performed modulo 2, that is, over the binary field {0, 1}). The current version of UberCrypt has not been cracked as of the writing of this abstract, and so remains an open problem.

September 12 - Dr. Eric Landquist

"Making Cryptography Less Cryptic"

In this talk, I will give an overview of cryptography and go over enough mathematical background to help everyone follow next week's talk on how to crack a stream cipher. We'll talk about private key versus public key cryptography, but will focus on different kinds of private key cryptosystems. We'll then get into different kinds of attacks on a cryptosystem and the attributes of a secure cipher.

Spring 2014 - Friday at 11:00 a.m. in Lytle 136

April 25 - Professor John Botzum

"Don't Stand So Close to Me or: How I Learned to Stop Worrying and Love the Twin Prime Conjecture"

Number theory -- the most easily accessible, but possibly the least penetrable of branches of mathematics has intrigued professional and amateur mathematicians for centuries. In honor of the monumental paper published by Yiteng Zhang last April 17th, I will present an introduction to the Twin Prime Conjecture and discuss Zhang's work and the work of Polymath 8a, an international group of renowned mathematicians led by Terrence Tao.

April 14 - Combinatorical Problems (continued)

April 11 - Combinatorical Problems

  1. The Cable-Trench Problem
  2. Analyze the game Flow Free - For a board of a given size and a given number of dots, how many different games are there? How many give you a unique solution or no solution?

April 4 - Dr. Greg Schaper

Problem-Solving Processes

The key to success isn't knowing what to think, but knowing how to think.  Dr. Schaper will give an overview of the process that he uses to solve problems and how different brances of Math, Computer Science, and other disciplines factor into this problem-solving process.

March 28 - Dr. Fran Vasko

Dr. Vasko will explain how he has applied the matching problem in graph theory to the problem of determining optimal cuts of rectangular pieces of stock.  This work was successfully implemented for Bethlehem Steel and published the Journal of the Operational Research Society in 2000.

March 14 - Bitcoin Part 4

Computer Science undergraduates discuss cryptocurrency.

March 7 - Bitcoin Part 3

Hacks of the Online Cryptocurrency Exchange Mt. Gox

February 28 - Bitcoin Part 2

February 19 (Wednesday) - Dr. Brian Kronenthal

"Two Perspectives on Generalized Quadrangles"

February 7 - Bitcoin

Bitcoin is a decentralized digital currency whose security relies on various cryptographic protocols and mathematically and computationally hard problems.  It is a fascinating protocol in many regards.

Fall 2013 - Alternating Thursdays and Fridays at 11:00 a.m. in Lytle 109

December 6- Dr. Amy Lu

"Homogeneous structures and their reducts."

November 22- Dr. Tony Wong

"A problem on matroid theory by Dominic Welsh."

November 14- Dr. Joshua Goodson

"Orbits of an Action Involving Extra-special Groups."

November 8- Dr. Eric Landquist

"The Hunt for Primes and Perfection and How You Can Win $3000."

October 31 - Dr. Greg Schaper, Computer Science

"Conjecture: (P = NP) and (P ≠ NP)."

October 24 - Dr. Ju Zhou

"Pancyclicity of Claw-free Graphs."

October 11 - More interesting problems in discrete mathematics

October 3 - Dr. Tony Wong

"Some interesting problems in combinatorics."

September 26 - Dr. Brian Kronenthal

"Generalized quadrangles, algebraically defined graphs, and permutation polynomials: an introduction."

September 19- Faculty presentations of interesting discrete mathematics (research?) problems

September 12- Dr. Eric Landquist

"What is Discrete Math? Making Discrete Math Less Discreet!"