Friday, December 4Title: The Gerrymandering ProblemSpeaker: John MaddreyFriday, November 20Title: A Little Something on Game TheorySpeaker: Sam CarolusAbstract: We will define and discuss some basic game theory concepts and calculations. I will also talk about the guys who turned game theory into what it is today and how people use it. There will be examples for all to enjoy!Friday, November 13Speaker: Kelly BresnahanTitle: How to play distant poker with cheatersAbstract: Many games such as card games can be difficult, if not impossible to play fairly and securely over distance. With growing need for telecommunications, there needs to be a way to ensure fairness without using a trusted third party. In this talk, I am going to outline two procedures: fair coin flips and distance poker that produces an fair game, even when one or more parties are actively trying to cheat.Friday, November 6Title: EMACSSpeaker: John HamanAbstract: I'm going to be talking about Emacs, which is a text editor you can use to type papers and computer code. I'm going to outline the advantages to using Emacs over your usual suite of applications, and some of the cool things Emacs can do that save you a lot of time when writing or coding.The talk will benefit statistics folks the most, but really anyone who generates text can benefit from using Emacs. Friday, October 30Title: The Mathematics of the Perfect ShuffleSpeaker: Mike HughesAbstract: There is a card shuffling technique used by card sharks and magicians called the perfect shuffle. With a little dexterity and knowledge of permutation groups these skilled people can successfully stack any deck with 2n cards in it. I will be discussing an article that gives a mathematical background on the perfect shuffle.Friday, October 23Title: On the Knight's Closed Tour: The Existence of Closed Tours on m x n chessboards.Speaker: Samuel HokampAbstract: The Knight's Tour Problem has long been analyzed by notable mathematicians and chess players alike, and the practice of finding open and closed tours on a standard chessboard remains an excellent practice for budding enthusiasts. However, a firm statement categorizing which mxn chessboards admit a closed tour remained unproven until 1991, when the classification was formalized by Allen Schwenk. The purpose of this talk is to give an appropriate introduction to the Knight's Tour, discussing its graph-theoretic relevance, and to explore Schwenk's result, which is a logically-simple yet elegantly-crafted proof.Friday, October 16Title: The Brachistochrone ProblemSpeaker: Todd RomutisAbstract: I will present the solution to this problem first posed by Johann Bernoulli in 1696. Friday, October 9Title: Algebras, Co-algberas, Bi-algebras, Hopf AlgebrasSpeaker: Paul SchraderAbstract:As a prequel to my talk on the Center Construction Z(C) in the Algebra /Topology seminar later this semester, we will explore the fundamental objects of associative algebras which will be captured by the categorical notions of the Center Construction. These will include diagrammatic equivalent of an algebra A over a field k(i.e., as a ring together with a ring homomorphism mapping the elements of the field k to the center of A), its dual notion the coalgebra C, the bialgebra B which is both an algebra and a coalgebra in a compatible way and the Hopf algebra H which is a bialgebra together with an endomorphism S called the antipode. All of these objects will be described in terms of commutative diagrams involving the tensor product which we will also briefly review. Friday, September 25Title: Groups Acting on Twin TreesSpeaker: Rob KelveyAbstract: We
will define twin trees and discuss an example. Given time, we may
discuss more general theory of Kac-Moody groups and Twin Buildings.
Don't worry, this talk is completely introductory and there will be
pictures! Friday, September 18Title: Introduction to QI RigiditySpeaker: Mark MedwidAbstract:Come learn a thing or two about QI rigidity! We'll talk about word metrics on groups, Cayley graphs, quasi-isometries, the QI rigidity problem, along with some basic tools of study about the subject. Some algebra and analysis! Friday, September 11Title: Examples of UniversalitySpeaker: David WalmsleyAbstract:Some historical examples of universal phenomena will be given. Friday, September 4Title: Devil's NumberSpeaker: Jake Laubacher Abstract: We will use group theory and combinatorics to analyze properties of the Pocket Cube. Friday, August 28thTitle: Organizational Meeting for Fall 2015Speaker: Rob Kelvey Thursday, April 30Title: CombinatoricsSpeaker: Taylor BelcherAbstract:We'll talk about some interesting things! There might even be proofs Random Walks (with R)Thursday, April 23 Title: Speaker: Brandon HillSymmetric and asymmetric random walks. Gambler's wealth, particle motion, etc. Some use of R to generate sample paths.Abstract: Thursday, April 16 Untangling the Eternal Golden BraidTitle: Speaker: Jeff NortonAbstract: We will discuss a topological proof of the general insolubility of the quintic by radicals, originally by Arnold, using basic covering space theory. We will relate the content of the proof to the other three topics in the title in fun and surprising ways. Thursday, April 9Title: Hadamard MatricesSpeaker: Logan OppermanAbstract: Come learn about the generation and application of some useful matrices! Thursday, April 2Title: Chapter 7: Flows in NetworksSpeaker: Sam CarolusAbstract: Want to know what a flow in a network is? Come find out. Thursday, March 26Title: De Bruijn SequencesSpeaker: Todd RomutisAbstract: We will discuss k-ary De Bruijn sequences of order n and their construction, some examples for small values of k and n, and applications. Thursday, March 19Title: Introduction to Latin SquaresSpeaker: Kelly BresnahanAbstract: We'll discuss how Latin squares relate to orthogonal arrays, quasi-groups, and sodoku puzzles, as well as when a partial Latin square can be completed. Thursday, March 5Title: Groups of Graphs of GroupsSpeaker: Dave WalmsleyAbstract:We classify all groups of color preserving automorphisms (isometries) of edge colored complete graphs derived from finite groups. Thursday, February 26Introduction to Connected GraphsTitle: Speaker: Mike Hughes Abstract: We are going to discuss what rank and nonseparability mean for Connected Graphs and take a look at Menger’s Theorem. Thursday, February 19Algebraic and Error Correction Coding (ECC) Theory: An IntroductionTitle: Paul SchraderSpeaker: Abstract: This talk will explore the fundamentals of ECC and general coding theory emphasizing its foundations within the subject of algebra. We will begin with basic definitions of coding theory and examples of ECC, the linear and Hamming codes. From these examples we will discuss the fundamental tradeoff in ECC, reliability verses efficiency. Next we will introduce the linear algebra representations over finite fields of such codes. Finally, we will explore the Hamming distance, the construction of the metric space of ECC code words and some combinatorics on the objects that occupy this space. Thursday, Feburary 12Title: Projective and Combinatorial GeometriesSpeaker: Rob KelveyAbstract:We shall explore what we can of Chapter 23 in Lint & Wilson's Combinatorics. There will be definitions and Theorems galore (proofs?). There might even be pictures! Thursday, February 5 Title: Dilworth's Theorem and Extremal Set TheorySpeaker: Mark MedwidAbstract:We will examine chapter 6 from van Lint and Wilson's "A Course in Combinatorics." Here we will state and prove Dilworth's theorem about partially ordered sets and talk through some easy examples of extremal set theory. Thursday, January 29Title: Elementary Counting: Stirling NumbersSpeaker: Jacob LaubacherThursday, January 22Organizational Meeting for Spring 2015 Title: Speaker(s): Rob Kelvey and friends?Abstract: This semester we are hoping to work our way through a specific special topic in Math and Stats. Each week someone will give a talk covering a section of a textbook/lecture notes. This allows us to collectively learn something interesting that lies outside the scope of our general coursework, while still practicing giving talks. Come to this meeting to find out more juicy details! |