# MATHEMATICS SEMINARS

**Conference on Financial Mathematics March 24, 2023**

Seminars

Dr. Douglas E Johnston, Coordinator Douglas Johnston

**Fall 2022**

Day: November 29, 2022 at 11:00 am, Whitman Hall Room 183

Speaker: Volvick Osse, Farmingdale State College

Title: Solving Diophantine Equations

Abstract:

Diophantine equations are very important mathematical tools that we make use of everyday. Fermat's last theorem states that x^n + y^n = z^n has no non-zero integer solutions where n is an integer larger than 2. While straight-forward to state, it was not until the 1990s when Andrew Wiles formally proved this result.

In today's presentation I am going to take us through Diophantine equations, specifically linear Diophantine equations. We will go over how these linear equations are solved, what methods we will use, and what kind of solutions we expect to get from these methods. By the end of this presentation, the listener should be able to solve and explain the process for solving linear Diophantine equations.

A linear Diophantine equation is an equation of the form ax + by = c, where a, b, and c are integers, and the solution (x, y) is also required to be an ordered pair of integers. Linear Diophantine equations are solvable if and only if c is a multiple of the greatest common divisor of a and b.

Day: October 6, 2022 at 11:00 am, Whitman Hall Room 183

Speaker: Dr. Douglas Johnston, Farmingdale State College

Title: Bayesian Forecasting of Dynamic Extreme Quantiles

Abstract: In this talk, we discuss a novel Bayesian solution to forecasting extreme quantile levels that are dynamic in nature. This is an important problem in many fields of study including climatology, structural engineering, and finance. We utilize results from extreme value theory to provide the backdrop for developing a state-space model for the unknown parameters of the observed time-series. To solve for the requisite probability densities, we derive a Rao-Blackwellized particle filter and, most importantly, a computationally efficient, recursive solution. Using the filter, the predictive distribution of future observations, conditioned on the past data, is forecast at each time-step, and used to compute extreme quantile levels. We illustrate the improvement in forecasting ability, versus traditional methods, using simulations and apply our technique to the S&P 500.

**Fall 2021****Day**: November 18th, 2021 at 11:00 am, Whitman Hall Room 183

**Speaker**: Dr. Carlos Marques, Farmingdale State College

**Title**: Understanding some Basic Arithmetic and Geometry Results from Strong Foundations

**Abstract**: The presentation will cover several topics, including an alternative proof of the
existence of an infinite number of prime numbers and the underlying structure of fractions.
This talk is suitable for all levels of math majors! New majors can see how one fundamentally
thinks about mathematics, and older majors will see interesting connections about
results that they have used without much thought.

**Spring 2022**

Day: April 14, 2022 at 11:00 am, Whitman Hall Room 183

Speaker: Dr. Carlos Marques, Farmingdale State College

Title: A Proof of the Irrationality of the Square Root of 2 via Inverses

Abstract: This talk will be accessible to all of our undergraduate majors! A proof that the square root of 2 is irrational has been around for millennia, but Dr. Marques will present a novel approach while also demonstrating the thought process mathematicians follow.

**Spring 2022: Student Presentations,** **Whitman Hall, room 183, on Thursday, May 12, from 11 am to 12 pm.**

**1. College Education Fund Planning: 529 vs. IUL**

By John Aguanno, Michael Brandon, Michal Piekarski, Brendan Stryska

Abstract: According to US News data, the average cost for tuition and fees has risen significantly in the past two decades. In this project, we will do a case study comparing two types of investments (529 and IUL) for a family saving for their children’s college education.

**2. A SIR Model for the Covid-19 Spread in New York City**

By Samantha Gervasi, Hamnah Teli, Juan Orellana, Michael Campbell

Abstract: In this project, we will use a SIR model to fit the Covid-19 Data in New York City. We will also discuss the effectiveness of vaccine, quarantine, and drug use in terms of ‘flattening the curve.’

**3. A Review of Multiple Proofs of the Multinomial Theorem**

By Christian Farkash, Michael Storm, Thomas Palmeri

Abstract: In this project, we will review different methods of proving the multinomial theorem.

**4. Computing the Adjoint Double Layer Potential**

By Michael Storm

Abstract: The adjoint double layer potential is the normal derivative of the single layer potential and is needed in solving Neumann problems. We use Taylor expansions to analyze the singularity in the integrand. We then propose a modification to the adjoint double layer to reduce its singularity.

## mathematics department

Whitman Hall, Room 180

934-420-2182

mathematics@farmingdale.edu

Monday-Friday 8:30am-4:30pm