2016 Past Seminar Talks

Fall 2016 Semester

Wednesday, December 7
Speaker: Sam Carolus
Title: Blokus
Abstract: An exploration of the geometry in the game Blokus.

Wednesday, November 30
Speaker: Logan Opperman
Title: P-systems, D-systems and Why You Should Love Them
Abstract: We define p-systems and d-systems and explore their uses. 

Wednesday, November 16
Speaker: Jordan Bounds
Title: Commuting Maps Over a Nilpotent Ring
Abstract: We will characterize the commuting linear maps over the ring of strictly upper triangular matrices.

Wednesday, November 9
Speaker: Dave Walmsley
Title: What Universal Elements Can Look Like in a Semigroup
Abstract: 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 2
Speaker: Todd Romutis
Title: A Universal Entire Function
Abstract: 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 26
Speaker: Serge Phanzu
Title: The Approximation Problem
Abstract: 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 19
Speaker: Mark Medwid
Title: Limits of Sequences of Metric Spaces
Abstract: 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 12
Speaker: Tom Tuberson
Title: Vertex Replacement Rules Generate Post Critically Finite Self-Similar Sets
Abstract: 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 5
Speaker: Garrett Ebbers
Title: An Exploration of Perfect and Not So Perfect Numbers
Abstract: 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 28
Speaker: Sam Hokamp
Title: Introduction to Banach Space Theory: Examples and the Banach-Steinhaus Theorem

Wednesday, September 21
Speaker: Kevin Stoll
Title: Recreating the Missing Data Mechanism Via Bootstrapping and Missing Iteration
Abstract: 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 14
Speaker: Paul Schrader
Title: Bialgebras and Tensor Categories
Abstract: 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 7
Speaker: Jake Laubacher
Title: Ramsey Numbers
Abstract: 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 31
Speakers: John Haman and James Munyon
Title: Graduate Internships in Math and Stats
Abstract: 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 28
Speaker: Dave Walmsley
Title: Universal Taylor Series
Abstract: 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 Ebbers
Title: 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 14
Speaker: Sam Carolus
Title: The Poincare Conjecture
Abstract: 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 7
Speaker: Jeff Norton
Title: 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 Dechow
Title: K0 Group of Dedekind Domains
Abstract:  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 Bresnahan
Title: Elliptic Curve Cryptography
Abstract: 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 Mailloux
Title: Introduction to Mapping Class Groups
Abstract: 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 Haman
Title: Collaborating With Git
Abstract: 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 Romutis
Title: Pell's Equation
Abstract: We will discuss Pell's equation, its history, and some classical methods for finding solutions.

Thursday, February 18

Speaker: Rob Kelvey
Title: 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 Medwid
Title: It's Knot Unusual
Abstract: 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 4th
Speaker: Sam Hokamp
Title: Closed Knight's Tours on Rectangular Prisms: The Existence of Closed Tours on 3-D Chessboards
Abstract: 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 28th
Speaker: Logan Opperman
Title: Detecting change points in a simple linear regression model: An SIC approach
Abstract: 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 21st
Speaker: James Munyon
Title: 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 14th
Speaker: Jake Laubacher
Title: The mathematics behind the game Spot It!