# 2017–2018 Mathematics Seminar

Please contact Johanna Franklin with any questions.

### Upcoming seminars

**Date**: Friday, February 23 at 3:30pm

**Room**: Roosevelt 213

**Speaker**: Fanny Shum, Courant Institute / NYU

**Title**: Brownian Motion: Its History and Application

**Abstract**: Brownian motion is used in many disciplines, such as mathematical physics, probability, and mathematical finance. We will look into the brief history of the development of brownian motion, also referred to as the Wiener process, and its significance in the mathematical field. In addition, we will discuss some of its applications.

**Date**: Wednesday, March 7 at 11:30am

**Room**: Roosevelt 213

**Speaker**: Jonathan Farley

**Title**: TBA

**Abstract**: TBA

**Date**: Wednesday, March 14 at 11:30am

**Room**: Roosevelt 213

**Speaker**: Josh Hiller, Adelphi University

**Title**: TBA

**Abstract**: TBA

**Date**: Wednesday, April 4 at 11:30am

**Room**: Roosevelt 213

**Speaker**: Taylor Ninesling, Hofstra University

**Title**: TBA

**Abstract**: TBA

**Date**: Wednesday, April 11 at 11:30am

**Room**: Roosevelt 213

**Speaker**: Stephen Melczer, University of Pennsylvania

**Title**: Lattice Path Enumeration and Effective Computation in Enumerative Combinatorics

**Abstract**: The problem of enumerating lattice paths in cones with a fixed set of allowable steps has a long history dating back at least to the 19th century. This talk focuses on the interaction between the kernel method, a powerful collection of techniques used extensively in the enumeration of lattice walks in restricted regions, and the relatively new field of analytic combinatorics in several variables (ACSV). In particular, the kernel method often allows one to write the generating function for the number of lattice walks restricted to certain regions as the diagonal of an explicit multivariate rational function, which can then be analyzed using the methods of ACSV. This pairing is powerful and flexible, allowing for results which can be generalized to high (or even arbitrary) dimensions, weighted step sets, and the enumeration of walks returning to certain boundary regions of the domains under consideration. In the process, we will survey some decidability results in asymptotic and enumerative combinatorics. There are no high-level prerequisites for the talk, which should be accessible to upper year undergraduates.

**Date**: Wednesday, April 25 at 11:30am

**Room**: Roosevelt 213

**Speaker**: David Rosenthal, St. John's University

**Title**: TBA

**Abstract**: TBA

**Date**: Friday, April 27 at 3:30pm

**Room**: Roosevelt 213

**Speaker**: Gent Gjonbalaj, Hofstra University

**Title**: TBA

**Abstract**: TBA

**Date**: Wednesady, May 2 at 11:30am

**Room**: Roosevelt 213

**Speaker**: Élise Vandomme, LaCIM / UQAM

**Title**: TBA

**Abstract**: TBA

**Date**: Friday, May 4 at 3:30pm

**Room**: Roosevelt 213

**Speaker**: Brian Zilli, Hofstra University

**Title**: TBA

**Abstract**: TBA

**Date**: Wednesady, May 9 at 11:30am

**Room**: Roosevelt 213

**Speaker**: Genevieve Maalouf, Hofstra University

**Title**: TBA

**Abstract**: TBA

### Previous seminars

**Date**: Wednesday, September 13 at 11:30 a.m.

**Room**: Roosevelt 213

**Speaker**: Catherine Pfaff, UC, Santa Barbara

**Title**: Symmetries, Outer Space, & the Outer Automorphism Group of the Free Group

**Abstract**: The symmetries of a polygon form a group. This group acts on the polygon by rotating it and flipping it. This basic idea of studying a group as symmetries of an object extends far beyond polygons. My favorite group is the outer automorphism group of the free group. Through a myriad of colorful pictures I will introduce this group and the object, Culler-Vogtmann Outer Space, that it acts on.

**Date**: Wednesday, September 27 at 11:30 a.m.

**Room**: Roosevelt 213

**Speaker**: Michael Cole, Hofstra University

**Title**: The Mathematics of Gravitation and Eclipses

**Abstract**: This talk will contain a mix of mathematics, physics, and astronomy. We begin with a derivation of Kepler's laws using vector calculus. Then tides will be discussed. There is a mathematical derivation of the basic facts about lunar tides that is quite simple and should be better known. Next astronomy: e.g. the layout of the solar system and some facts about the moon's rather complex orbital motion about the earth. We will study how periodicities of the moon's orbit about the earth and the orbit of the earth-moon system about the sun gives rise to the so-called "saros cycle" that describes the timing of lunar and solar eclipses.

**Date**: Wednesday, October 4 at 11:30 a.m.

**Room**: Roosevelt 213

**Speaker**: J. B. Nation, University of Hawai'i

**Title**: How Aliens Do Math

**Abstract**: We use a fanciful tour of the solar system to provide a gentle introduction to Universal Algebra. All major planets, plus a few Kuiper Belt objects, are included for the same low fare.

**Date**: Friday, October 6 at 3:30pm

**Room**: Roosevelt 213

**Speaker**: J. B. Nation, University of Hawai'i

**Title**: A Primer of Quasivariety Lattices

**Abstract**: This talk develops the theory of lattices of quasivarieties in a very general context. The lattice of subquasivarieties of a quasivariety can be represented as the lattice of closed algebraic subsets of an algebraic lattice with operators. This representation is used to develop new restrictions on the equational closure operator. This is joint work with Kira Adaricheva, Jennifer Hyndman and Joy Nishida.

**Date**: Wednesday, October 18 at 11:30 a.m.

**Room**: Roosevelt 213

**Speaker**: Dan Turetsky, University of Notre Dame

**Title**: How hard is it to tell if two things are the same?

**Abstract**: If I have two groups, how hard is it to tell if they're isomorphic? If I know they're isomorphic, how hard is it to find an isomorphism between them? Is it easier if I look at fields instead of groups? How about linear orders? These are the sorts of questions computable model theorists think about.

This talk will provide a gentle introduction to the field of computable model theory. We will cover the necessary concepts to make sense of the above questions, and we'll discuss some of the answers.

**Date**: Wednesday, October 25 at 11:30 a.m.

**Room**: Roosevelt 213

**Speaker**: Neil J. A. Sloane, Rutgers University and The OEIS Foundation

**Title**: What Comes Next After 2, 4, 6, 3, 9, 12, 8, 10? - Confessions of a Sequence Addict

**Abstract**: The On-Line Encyclopedia of Integer Sequences (or OEIS, oeis.org) is a free web site that contains information about 300,000 sequences, and is often called one of the most useful mathematical sites on the Web. I will discuss some classic sequences (van Eck, Gijswijt, Queens in Exile, etc.) and some very recent sequences from geometry, number theory, and the theory of computing. There will be music, movies, and a number of unsolved problems.

**Date**: Wednesday, November 1 at 11:30 a.m.

**Room**: Roosevelt 213

**Speaker**: Genevieve Maalouf, Hofstra University

**Title**: Conjugacy Class Graphs of Dihedral and Permutation Groups

**Abstract**: In this talk, we combine the study of group theory and graph theory by generating a graph with a group. If we take a group, G, we construct the graph Γ(G) by computing the conjugacy classes of G–Z(G). A node is produced by every conjugacy class and labeled with the cardinality of the class, c_{i}. Lastly, an edge connects two vertices if gcd(c_{i},c_{j})>1. We say Γ(G) is the conjugacy class graph generated by G. The main focus of this talk is to classify all graphs of Γ(D_{2n}×D_{2m}) and to study the completeness of Γ(S_{n}×S_{m}). This work was done at the 2017 Missouri State REU and is joint with Taylor Walker (Tuskegee University) under the advisement of Les Reid (Missouri State University).

**Date**: Wednesday, November 15 at 3:00 p.m.

**Room**: Roosevelt 110

**Speaker**: John Goodrick, Universidad de los Andes

**Title**: Counting integer points in polytopes with an extension of Presburger arithmetic

**Abstract**: Fix some polytope P in R^{d} whose vertices have integer coordinates. Then for any positive integer t, one can ask to compute the number f_{P(t)} of points in the lattice Z^{d} that lie within the t-th dilate of P. By a theorem of Ehrhart, the function f_{P(t)} is always a polynomial. If the vertices of P are rational (i.e. in Q^{d} instead of Z^{d}), then the function f_{P(t)} is no longer necessarily polynomial but it is a quasi-polynomial: there is a number m and polynomials g_{1}, ..., g_{m} such that f_{P(t)} = g_{i(t)} whenever t is congruent to i modulo m.

In this talk, we will review the classic theory of Ehrhart polynomials and present a generalization (based on recent joint work with Tristram Bogart and Kevin Woods): if f(t) is the function which counts the number of integer points within a bounded region of R^{d} which is defined by a formula using addition, multiplication by the parameter t, inequalities, and quantifiers over variables from Z (but not over the domain of the variable t), then f(t) is quasi-polynomial for all sufficiently large values of t. We call such families "parametric Presburger families" in analogy with the logical theory of Presburger arithmetic. We will also present some new applications of this result.

**Date**: Wednesday, December 6 at 11:30 a.m.

**Room**: Roosevelt 213

**Speaker**: Zoran Sunic, Hofstra University

**Title**: Context-free orders on free groups

**Abstract**: We provide countably many orders on the free group such that, for each order, the set of positive words forms a context-free language. On the other hand, we show that there is no order on the free group with set of positive words that forms a regular language. Thus, as Einstein would say, things should be made as context-free as possible, but not regularer than that.

**Date**: Wednesday, February 14 at 11:30am

**Room**: Roosevelt 213

**Speaker**: Eric Rowland, Hofstra University

**Title**: Formulas for Primes

**Abstract**: Is there a formula that always produces primes? Fermat thought he found one; he conjectured that 2^{2n} + 1 is prime for all n ≥ 0, but he was wrong (this time). The answer depends on what we mean by a "formula". It turns out there is an expression for the nth prime using ordinary arithmetic functions! There are also simple functions/recurrences that generate primes. There is even a polynomial whose set of positive values is precisely the set of prime numbers. However, on closer inspection these formulas say less about prime numbers than they do about translating mathematical statements into others, and it's the clever translation that makes them interesting.