Fall 2016 SemesterWednesday, December 7Speaker: Sam CarolusTitle: BlokusAbstract: An exploration of the geometry in the game Blokus.Wednesday, November 30Speaker: Logan OppermanTitle: P-systems, D-systems and Why You Should Love ThemAbstract: We define p-systems and d-systems and explore their uses. Wednesday, November 16Speaker: Jordan BoundsTitle: Commuting Maps Over a Nilpotent RingAbstract: We will characterize the commuting linear maps over the ring of strictly upper triangular matrices.Wednesday, November 9Speaker: Dave WalmsleyTitle: What Universal Elements Can Look Like in a SemigroupAbstract: In 1952, MacLane showed there is an entire function whose successive derivatives are dense in the space of all entire functions in the compact-open topology. In this talk, we will define universality and provide some examples, and we will discuss what universal elements can look like in a few semigroups of functions. Wednesday, November 2Speaker: Todd RomutisTitle: A Universal Entire FunctionAbstract: We review Maclane's proof of the existence of a function such that the set of all derivatives is dense in the space of entire functions. Wednesday, October 26Speaker: Serge PhanzuTitle: The Approximation ProblemAbstract: The approximation problem is a well known problem of functional analysis (Grothendieck 1955). It asks to determine whether every compact operator T from a Banach space X to a Banach space Y is the uniform operator topology of a sequence of operators with finite rank. This question was answered in the negative by Enflo (1973), who provided a deep counterexample to this problem. Wednesday, October 19Speaker: Mark MedwidTitle: Limits of Sequences of Metric SpacesAbstract: In this talk we first develop a notion of a metric between compact metric spaces, the Gromov-Hausdorff distance. This naturally leads to the idea of a limit of a sequence of metric spaces. We will discuss some applications and basic theory before moving on to the more general concept of ultrafilters, ultraproducts, ultralimits and the asymptotic cone of a metric space X. These concepts have surprising and "exciting" applications to group theory. Wednesday, October 12Speaker: Tom TubersonTitle: Vertex Replacement Rules Generate Post Critically Finite Self-Similar SetsAbstract: This talk was based off of research that I did during my time as an undergraduate at Penn State Behrend. This research blends together topics from graph theory, topology, analysis and fractal geometry. In the talk, we make use of famous self-similar sets to help the audience gain an intuition for the subject.Wednesday, October 5Speaker: Garrett EbbersTitle: An Exploration of Perfect and Not So Perfect NumbersAbstract: This talk will discuss perfect numbers and the following doppelgangers: quasiperfect numbers, almost perfect numbers, multiply perfect numbers, hyperperfect numbers, semiperfect numbers, unitary perfect numbers and weird numbers. We will start by introducing the divisor function and its relation to perfect numbers. Then for the rest of the talk we will explore some properties of these numbers as well as open questions. Wednesday, September 28Speaker: Sam HokampTitle: Introduction to Banach Space Theory: Examples and the Banach-Steinhaus TheoremWednesday, September 21Speaker: Kevin StollTitle: Recreating the Missing Data Mechanism Via Bootstrapping and Missing IterationAbstract: Currently, there are four main genres used to estimate the true population mean of a response variable that is subject to missingness. Those genres are inverse propensity weighting, regression imputation, stratification, and empirical likelihood. First, this talk will briefly discuss the aforementioned genres. Then, a modified boostrap estimator that assumes a propensity model is correctly specified and uses weighted bootstrap sampling and iteration will be introduced as a fifth genre for estimating the population mean of a response variable that is subject to missingness. This method will be examined in a small simulation study.Wednesday, September 14Speaker: Paul SchraderTitle: Bialgebras and Tensor CategoriesAbstract: As a prequel to my upcoming talk in the department's Algebra/Topology seminar later this month, this talk will review some foundational concepts concerning my current research. First we will recall the notions of an associative k-algebra, a coassociative k-algebra, a bialgebra and a module over a k-algebra. Next we will review some basic concepts from categoroy theory pertaining to these algebraic structures. These include categories, tensor categories and braided tensor categories. Finally, we will discuss a known result about bialgebras and tensor categories showing how algebraic structures fit into a categorical framework. Wednesday, September 7Speaker: Jake LaubacherTitle: Ramsey NumbersAbstract: In this talk we will present Ramsey's theorem, as well as a consequence: Ramsey numbers. We will discuss how many people to invite to a party. Wednesday, August 31Speakers: John Haman and James MunyonTitle: Graduate Internships in Math and StatsAbstract:
We will talk about our experiences applying for internships in
statistics and working at our respective jobs. We intend to address some
of the challenges at work, the skills that we found to be useful from
graduate school, and some resources that were useful for obtaining a
good internship program. We hope to convince more graduate students to
consider summer internships and to ease the process of finding an
internship.Spring 2016 Semester Thursday, April 28Speaker: Dave WalmsleyTitle: Universal Taylor SeriesAbstract:
We will talk about some poorly behaved (formal) real power series and
construct an example of one which diverges in the worst possible way.Thursday, April 21 Speaker: Garrett EbbersTitle: It’s Only Logical Abstract: This talk will explore some of the basic concepts of deductive logic, and will be structured such that after covering necessary material, the audience will be asked to help prove conclusions of symbolized arguments. First we’ll start off by briefly exploring truth tables as a tool to justify certain conclusions about statements and arguments. Next we’ll discuss the eighteen rules of inference as well as the usefulness of conditional and indirect proofs. Lastly we’ll use what we’ve covered to complete proofs for the remaining amount of time.Thursday, April 14Speaker: Sam CarolusTitle: The Poincare ConjectureAbstract: I
will discuss the history and eventual solution to one of the most
famous problems in mathematics, the Poincare conjecture. Conceived in
1904, it wasn't until 2006 that Grigory Perelman finally proved the
conjecture to be true. I'll start with some basic topology and sprinkle
in some comments on the famous folks who have worked on the conjecture.
There will be some pictures, and I'll try to break your mind as we think about too many dimensions. Thursday, April 7Speaker: Jeff NortonTitle: Who kneads math anyway?Abstract:
Few things have nourished humanity as much as bread and mathematics
have. In this talk we will briefly discuss the history of bread, and its
impact on the development of mathematics and human society in general.
We will then begin to explore the mathematics of bread making. A
standard example arises from kneading dough, and modeling the dynamics
with so called bakers transformations, well known in ergodic theory. We
will also explore some more abstract mathematical questions related to
bread and dough. All ideas presented will be accompanied by numerous
examples, some of which will be edible!Thursday, March 31 Speaker: Luke DechowTitle: K0 Group of Dedekind DomainsAbstract: I'll
introduce a special type of ring called a Dedekind domain, talk a bit
about some important properties and related concepts (fractional ideals
and ideal class groups of integral domains), then go on to state (and
prove, if you're lucky) a few results about their (finitely generated,
projective) modules, resulting in a characterization of the K0 group of
Dedekind domains. Thursday, March 24 Speaker: Kelly BresnahanTitle: Elliptic Curve CryptographyAbstract: Elliptic Curve Cryptography (ECC) is the newest member of established
public key algorithms of practical relevance today. Introduced in the
1980s, it has gained enormous popularity and provides a significantly
more secure foundation than other public key cryptography systems like
RSA. However, it is one of the least understood types of cryptography in
wide use. In my talk, we will introduce
the idea of elliptic curves, its structure, and various elliptic curve
algorithms such as Identity Based-Encryption.Thursday, March 17 Speaker: Mike MaillouxTitle: Introduction to Mapping Class GroupsAbstract: Have
you ever asked yourself one of the following questions: What is a
mapping class group? What are some examples of mapping class groups? Why
do people care, and what kinds of questions are people working on with
them? The aim of this talk is to begin to formulate some basic notions
of the answers to some of these questions. Thursday, March 3 Speaker: John HamanTitle: Collaborating With GitAbstract: I'll introduce a version control system called Git, which allows a group of people to
collaborate efficiently on a project. Math and statistics students can
use Git to easily make and distribute changes to LaTeX papers or any
other files.Thursday, February 25 Speaker: Todd RomutisTitle: Pell's EquationAbstract: We will discuss Pell's equation, its history, and some classical methods for finding solutions. Thursday, February 18 Speaker: Rob KelveyTitle: FH Implies FA.Abstract: For
a topological group G, property FH says: "every action of G by affine
isometries on a real Hilbert space has a fixed point." Essentially, the
'F' stands for "fixed point" and 'H' for "Hilbert Space." Property FA
means the same thing, but where the action is on a tree (the 'A' stands
for tree...because French). It turns out that, if a group G has property
FH, then it must have property FA. The converse is not true. We will
give a proof of this implication and discuss how these properties relate
to a similar notion: the infamous Kazhdan property (T). Thursday, February 11 Speaker: Mark MedwidTitle: It's Knot UnusualAbstract:
A gentle introduction to knot theory. We'll draw some pictures of knots
and discuss Reidemeister moves. We may prove something. Finally, we'll
discuss some basic knot invariants such as tricolorability. Thursday, February 4thSpeaker: Sam HokampTitle: Closed Knight's Tours on Rectangular Prisms: The Existence of Closed Tours on 3-D ChessboardsAbstract: The
knight's tour is a problem that involves using legal moves to visit
every square of the chessboard exactly once. In 1991, Allen Schwenk
solved the problem for closed tours by stating which boards fail to
admit such a tour, and providing an elegant method for creating closed
tours on those that do. The purpose of this talk is to develop a like
theorem on boards that are rectangular prisms. A result from a paper by
DeMaio and Mathew will be discussed, as well as relevant research by the
speaker. Thursday, January 28thSpeaker: Logan OppermanTitle: Detecting change points in a simple linear regression model: An SIC approachAbstract: We will discuss what is meant by a change point, what is meant by SIC, and how we can use the SIC to detect a change point. Come listen!January 21stSpeaker: James MunyonTitle: R Matey.Abstract: I think that all stats students should know R. It's a great tool that I'm better for knowing. More flexible than SAS, more reproducible than Minitab. Plus it's free. Topics can/ will include: getting R, RStudio, R Markdown, the Monty Hall problem simulation, basic/common things you'd do in R, etc.January 14thSpeaker: Jake LaubacherTitle: The mathematics behind the game Spot It! |