Binghamton University Math Graduate Student SeminarThe Mathematics Graduate Student Seminar seeks to strengthen communication among grad students at Binghamton University, thereby cultivating our community and fostering a friendly environment in which to do maths research. We provide a venue for grad student talks on interesting maths; we also hope to stimulate discussion around various topics--mathematical and otherwise--relevant to maths grad students.Presentations should be accessible to mathematics grad students, and all are encouraged to contribute a talk. Email Chris Eppolito or Matt Evans (math emails eppolito and evans resp) to schedule your talk! Spring 2019Usual Meetings: Wednesdays at 5pm in WH309Organizers: Chris Eppolito and Matt Evans For a list of talks from previous semesters, see the archives. Schedule of Talks23 JanuaryOrganizational Meeting 30 January Chris Eppolito (Binghamton University) Elementary Properties of the Chameleon Group Thompson's group F is an example of some importance in geometric group theory. We will construct Thompson's group F combinatorially and subsequently describe a number of seemingly paradoxical properties it enjoys. 6 February Samantha Wyler (Binghamton University) An introduction to polygonal numbers Polygonal numbers are number represented as dots or pebbles arranged in the shape of a regular polygon. We will look at a formula for computing them and some famous theorems they are involved in. 13 February BUGCAT General Interest Meeting 20 February Matt Evans (Binghamton University) Spectra of Commutative BCK-algebras BCK-algebras are algebraic structures that come from a non-classical logic. Mimicking a well-known construction for commutative rings, we can put a topology on the set of prime ideals; the resulting space is called the spectrum. I will discuss some results/properties of the spectrum, particularly when the underlying algebra is a so-called BCK-union. In some special cases, there is a strong connection to ring spectra. 27 February Uly Alvarez (Binghamton University) Judging a space by its cover Given a space X with a "nice enough" cover U, we can get close to knowing the homotopy type of X. In particular, it can be shown that the order complex of U is weakly homotopy equivalent to X. 6 March Changwei Zhou (Binghamton University) The Markov Chain Monte Carlo Revolution In 2000s, a psychologist from California state prison dropped in to consult with legendary statistician Persi Diaconis. They need someone to decode cryptic messages used by prisoners. The solution used the so called "MCMC" method from Bayesian statistics. In this talk I will review basics of Metropolis algorithm and discuss some of the applications in other fields like machine learning and algebraic geometry. 13 March John Brown (Binghamton University) A minor step toward proving a character theory conjecture In this talk we'll discuss a bit of the work done on a conjecture by Isaacs and others which states that the degree of any primitive character of a finite group G divides the size of some conjugacy class of G. We'll focus on the case that G is symmetric or alternating, with a view to showing that the result holds for every irreducible character of either group. The talk should be fairly easy to follow. 20 March NO SEMINAR--Spring Break :/ 27 March Yuan Fang (Binghamton University) A Review of Bayesian Approach to Model-based Clustering and Some Application Finite mixture models has been used to model heterogeneous data with a finite number of unobserved sub-population, hence are widely applied in clustering. Bayesian approach to parameter estimation for mixture models via Monte Carlo Markov Chain methods has been proven to possess many advantages over the classical approach. In this talk we will have a brief review of mixture models and Bayesian approach to model-based clustering. Recent research project as well as ongoing work related to this area will also be discussed. 3 April Jon Doane (Binghamton University) Restriction of Stone Duality to Generalized Cantor Spaces Stone duality is a correspondence between Boolean algebras (BAs) and Boolean/Stone topological spaces. Dualizing the free BA F(S) on set S yields a product space 2^{S}, where 2 = {0,1} is discrete. We call 2^{S} a generalized binary Cantor space (GCS_{2}), and similarly define the spaces GCS_{n} with n ≥ 2. This talk introduces Stone duality and then answers the question "what is dual to the class of GCS's?" 10 April Chris Eppolito (Binghamton University) Hopf Algebras of Matroids Hopf algebras are naturally arising algebraic objects, and matroids are interesting combinatorial objects. This talk is a selective introduction to these topics, with an eye to constructing and studying Hopf algebras from matroids. 17 April Zach Moltion (Binghamton University) Modern Methods of Primality Testing We will give the background for modern deterministic and probablistic primality testing for large integers, including Fermat, Lucas, Frobenius, and Baillie-PSW style tests, as well as some approximate bounds on their testing time. We will develop some modest field and character theory required to implement these tests. If time allows, I will present the Lucas-Lehmer algorithm for proving Mersenne numbers primarily used by GIMPS to find the record breaking large prime numbers. 24 April Kyle Bayes (Binghamton University) The Calculus of Variations
This talk will be an introduction to a powerful tool called the
calculus of variations along with some applications in Riemannian geometry.
1 May Kunle Abawonse (Binghamton University) Combinatorial vector bundle In finding a local combinatorial formula for characteristic classes of smooth manifolds, comes a theory of combinatorial differential manifold. We will discuss this and the corresponding bundle theory on oriented matroid and how it relates to the continuous case. 8 May Mike Gottstein (Binghamton University) Introduction to Kummer Theory A Kummer extension of exponent n is a Galois field extension L|K such that K contains n distinct roots of unity and the Galois group G is abelian of exponent n. In particular, every element of G has a finite order and the lcm of all these orders is n. When G is a finite group, the exponent of G divides |G|. Let K be a field that contains n distinct roots of unity. Adjoining to K the nth root of any element h of K creates a (finite) Kummer extension of degree d, where d divides n. Kummer theory is concerned with classifying all Kummer extensions L of K that have exponent n. To do this as stated, the machinery needed is more sophisticated than for the finite case. In this talk we will discuss the problem and the techniques involved so that we can see some of the first results in the theory. |
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