# Seminars

All seminars meet from 11:00am-12:00pm in CAMS, Whitman room 183.

## Spring 2019

Tuesday, April 23, 2019

Chunhui Yu, Farmingdale State College

Quadratic Variation and Higher Order Realized Volatility

In this talk, we will briefly introduce properties of realized volatility and quadratic variation of a general Ito's process. And we will also derive an asymptotic distribution of a higher order realized volatility error.

Tuesday, April 16, 2019

Ronald Smith, William & Mary

Frogs, Fireflies and Other Fun Oscillators

The Kuramoto model is a mathematical model used to describe the behavior of coupled oscillators, that is, systems of objects with some time-periodic behavior, and whose phase dynamics are interdependent. Examples of such systems are many, and include the synchronized croaking of frogs, blinking of fireflies, and firing of neurons.

In this talk I'll give a high level introduction to the system, discuss a few real-world examples, and then show some results (i.e., pretty pictures!) obtained via numerical integration of a modified form of the model. As we will be focused more on the qualitative behavior rather than the analysis of the model, this talk will be appropriate (and fun) for a general mathematical audience at all levels.

Tuesday, April 9, 2019

Frank Sanacory, SUNY Old Westbury

Paul Revere's Ride and Meta Data

Paul Revere is famous for his midnight ride.  But mathematics and network theory can be used to show his importance to the revolutionary war.  Join us for a demonstration in mathematics, network theory, R and data analytics.

Tuesday, March 26, 2019

Steven Hoehner, Farmingdale State College

The intrinsic volume deviation of the Euclidean ball and a polytope

We provide sharp estimates for the asymptotic best approximation of the $n$-dimensional Euclidean unit ball by polytopes under a notion of intrinsic volume deviation. In the case of arbitrarily positioned polytopes, we generalize results on the symmetric volume difference and surface area deviation from papers of Hoehner, Ludwig, Kur, Sch\"utt and Werner. As a corollary, we show that in the case of the Euclidean ball, the random polytopes from papers of Affentranger, B\"or\"oczky, Fodor, Hug and Reitzner are optimal in high dimensions, up to an error term of the order $O(n^{-1}\ln n)$. We also introduce a notion of distance'' between convex bodies that is induced by the Wills functional, and we use it to derive asymptotically sharp bounds for approximating the ball. Interestingly, it turns out that there is a polytope which is best-approximating for the ball with respect to all intrinsic volumes simultaneously, up to absolute constants. Finally, we provide asymptotic formulas for best-approximation of smooth convex bodies by polytopes under a notion of dual volume deviation. This is joint work with Florian Besau (TU Wien) and Gil Kur (MIT).

Tuesday, February 19, 2019

Svetlana Tlupova, Farmingdale State College

Computing Nearly Singular Integrals for 3D Stokes Equations

The importance of boundary integral equations in Stokes flow models is well recognized. To develop robust numerical methods, it is imperative to address one of the main challenges arising in the solution, namely, evaluating the integrals accurately for points near the boundary, e.g., when two interfaces are close together. This is the most difficult case and remains a challenge today, despite significant efforts in recent years to construct accurate solutions. We have developed a numerical method for computing such integrals with high accuracy both on and near the surface. The accurate solution is obtained by regularizing the kernels and adding analytically derived correction terms to eliminate the largest error. This is joint work with Professor J.T. Beale of Duke University.

Tuesday, January 22, 2019

Ali Uncu, Research Institute for Symbolic Computation, Johannes Kepler University Linz

Polynomial Identities that Imply Capparelli's Partition Theorems and more

The theory of partitions has been a vibrant and highly active subject of study since Euler. The problems from this topic usually lie in between the number theory and combinatorics, and these problems have been a great source of research and progress in many fields spanning from algebraic geometry to modular forms and special functions.

In this talk, we will start with a brief introduction to the theory of partitions. We will move on to a specific pair of combinatorics results (Capparelli's partition theorems) that is rooted from vertex operator algebras in the elementary frame of partitions and q-series. We will discuss recent developments on these theorems by Kanade--Russell and Kursungoz. Then we will move onto a refinement of their approaches to present the first group of polynomial identities that imply Capparelli's partition theorems. We will finish the talk by presenting multiple analytic implications of the results coming from this study and the developed techniques.

This research is partly joint with Alexander Berkovich.

## Fall 2018

Tuesday, December 4, 2018

Alex Kodess, Farmingdale State College

A Surprising Byproduct of the Isomorphism Problem for Monomial Digraphs

We present an example of a result in graph theory that is used to obtain a result in another branch of mathematics. More precisely, we show that the isomorphism of certain directed graphs implies that some trinomials over finite fields have the same number of roots.

Tuesday, November 20, 2018

The exponentiated gamma-Pareto distribution

There has been a renewed interest in developing more flexible statistical distributions in recent decades. In this talk, some methods of combination for generating statistical distributions are discussed. Then the exponentiated gamma-Pareto distribution is introduced and its properties are explored in detail. The maximum likelihood estimation method is used to estimate the model parameters and finally application of the model to real data set is presented to illustrate the usefulness of the proposed distribution.

Tuesday, October 23, 2018

Robert Abramovic, Farmingdale State College

The Spin Group, Spin Structures, and The Spin Connection (Part II from 9/18 talk)

Continuing my talk in September, I will use Clifford algebras to define the spin group and show that there is a natural two-fold covering map from this group to the group of rotations SO(n). The differential of this group turns out to be an isomorphism of Lie algebras! I will then define principal bundles and use these define a spin structure on a Riemannian Manifold. Spinor bundles are then defined as associated vector bundles of principle Spin(n)-bundles carrying a bundle morphism with Clifford bundles that restricts to a representation of the Clifford algebra on each fiber. I will explain how Spin(n) acts on spinor bundles and use this to define the spin connection induced from the connection on the Riemannian Manifold.

Tuesday, October 16, 2018

Steven Hoehner, Farmingdale State College

An extremal property of the sphere related to mean width

We prove that among all convex bodies of a given mean width, the $n$-dimensional Euclidean ball is hardest to approximate by inscribed polytopes with a restricted number of $k$-faces under the mean width difference. This generalizes a result of August Florian, extending it from dimension 2 to all dimensions. In the case $k=0$, our result is a ''dual" counterpart of a result of Rolf Schneider, who proved that among all convex bodies of a given mean width, the Euclidean ball is the hardest to approximate by circumscribed polytopes with a restricted number of facets under the mean width difference. (based on joint work with Ben Li, Tel Aviv University)

Tuesday, October 9, 2018

Florin Catrina, St. John's University

On the hypercontractivity of a convolution operator

We discuss a convolution operator which appears as an integral representation of the Wick product on $L^p(\mathbb{R}_+, \mu)$ spaces where the probability measure $\mu$ has a Gamma distribution. The hypercontractivity of this operator is tightly connected to inequalities of Brascamp-Lieb type.

Tuesday, September 25, 2018

Benjamin Russo, Farmingdale State College

$C$-algebras and the Category of Stochastic maps

Stochastic maps are a generalization of functions in that they assign to each point in the domain a probability measure on the codomain. In this talk we will discuss the category of stochastic maps. In particular, we will explore some generalizations of probabilistic concepts resulting from the existence of a contravariant functor from the category of stochastic maps into the category of $C$-algebras. (based on joint work with Arthur Pazygnat, UConn)

Tuesday, September 18, 2018

Robert Abramovic, Farmingdale State College

Spinors, The Spin Connection, and The Dirac Operator

First, I will review definitions and properties of metric bundles on vector bundles and the Levi-Cevita connection on the tangent bundle of a Riemannian manifold and prove that the Levi-Cevita connection decomposes as the sum of the exterior derivative and an element of the Lie algebra of the special orthogonal group when realized as a metric connection on the tangent bundle. Then, I will define spin structures, the spinor bundle, the induced representation of the Clifford algebra of the tangent bundle, and show how the special orthogonal group (and its associated Lie algebra) act on spinor bundles. Using the action of this Lie algebra on the spinor bundle and the decomposition formula for the Levi-Cevita connection, we show how the Levi-Cevita connection induces a metric connection on the spinor bundle and express its formula in a given orthonormal frame for the tangent bundle. This connection satisfies a Liebniz rule with respect to Clifford multiplication and is used to define the Dirac operator once a given orthonormal frame is chosen. I will prove that the definition of the Dirac operator is independent from the choice of orthonormal frame and that this operators satisfies the Bochner-Lichnerowicz formula, which shows that it is a half-iterate of the conformal laplacian plus a (zero-order) scalar curvature term.

## Spring 2018

Tuesday, April 24, 2018

Chunhui Yu, Farmingdale State College

‘Most Likely Path’ of Shortfall Risk in Long Term Hedging with Short Term Future Contracts

In this talk, we will study the ‘most likely path’ problem that proposed by Paul Glasserman (2001)  when discussing the shortfall risk in long term hedging with short term future contracts. Based on a simple Winner process model, we are trying to find a path in the sense that when a shortfall occurs, it occurs with the Winner process staying close to this path.

Thursday, April 19, 2018

Ning (Patricia) Ning, UC Santa Barbara

Financial Machine Learning != Machine Learning on Finance: Challenges & Strategies

In this talk, I will first talk about the main reason why most of the standard machine learning tools fail when applied to the field of finance, and what's the fixing strategies currently being used by financial practitioners. Then I will focus on one working machine learning model: Multivariate Bayesian Structural Time Series Model, which is a machine learning technique used for feature selection, time series forecasting, nowcasting, inferring causal impact and other. (This talk is based on joint work with S. Rao Jammalamadaka and Jinwen Qiu)

Tuesday, April 17, 2018

Yajun Yang, Farmingdale State College

Using Secant Parabolas to Find Roots

Finding one or more roots of an equation f(x) = 0 is one of the more commonly occurring problems in applied mathematics. In this presentations, we propose a secant parabola method for solving the equation. We extend the secant method to a slightly more sophisticated approach that uses the secant parabola instead of the secant line used in the secant method. We show the empirical results and make comparisons with other well-known rootfinding methods including the secant method. We discuss the convergence of the method, its speed, and its dependence on the initial interval.

Tuesday, April 10, 2018

Douglas E. Johnston, Farmingdale State College

Modeling Extreme Risk-Events via Bayesian Processing

In this talk, we propose a new approach for analyzing extreme values such as large losses in financial markets. We apply a stochastic parametrization for a generalized extreme value distribution to model the asymptotic behavior of the block-maxima for the time series of interest. This allows for a relaxation of the i.i.d. assumption and the use of finer data blocks. By using a particle filter, with Rao-Blackwellization, we reduce the parameter space and provide a recursive solution. We use this to compute the conditional predictive distribution that is used to assess the probability of extreme events and risk-measures. We introduce a new risk-measure, p-VaR, that is a more robust estimate of the true nature of value-at-risk and illustrate our results using stock market data from 1928-2017.

Thursday, March 15, 2018

Wenjian Liu, Queensborough Community College

Spectral Methods and Ross Recovery

Steve Ross contributed a revolutionary breakthrough against the conventional wisdom by showing that along with a restriction on preferences, option prices forecast not only the average return, but also the entire return distribution. By placing the structure on the dynamics of the numeraire portfolio rather than Ross's restriction on the references of the representative agent, Carr and Yu have shown that the real-world transition probabilities of a univariate Markovian state in a bounded diffusion can be recovered by its risk-neutral transition probabilities. By means of the refined spectrum analysis of the elliptic operator, we build the general Ross Recovery under n driving state variables.

## Fall 2017

Tuesday, November 28, 2017

Steven Hoehner, Farmingdale State College

Approximation of convex bodies by random polytopes and the connection to sphere covering (joint with Gil Kur, Weizmann Institute of Science)

Tuesday, November 21, 2017

Steven Hoehner, Farmingdale State College

Best and random approximation of convex bodies by polytopes

How well can a convex body be approximated by a polytope? This is a fundamental question not only in convex geometry, but also in view of applications in stochastic geometry, complexity, computer vision, medical tomography, geometric algorithms, and many more. Typically, side conditions are imposed on the approximating polytopes, such as a prescribed number of vertices, facets, or more generally k-dimensional faces. Moreover, various notions of approximation can and have been considered. In this talk we will focus on two such notions: the symmetric difference metric and the surface area deviation. We will present background material and some results on best and random approximation.

## Spring 2017

Tuesday, May 2, 2017

Carlos Marques, Farmingdale State College (joint work with Loucas Chrysafi)

Continuously but Discretely Looking at Sums

Some thoughts derived from the soon to be submitted paper "Sums of Powers of Consecutive Integers via Matrices" (Chrysafi, Marques) highlighting some continuous-discrete interplay.

Thursday, April 27, 2017

Paul Macciarone and James Denino, St. John's University

Information session for Applied Mathematics students regarding the Actuarial Science Master's program at St. John's University. James is a Master's student in St. John's actuarial science program and an FSC Applied Math alumnus.

Tuesday, April 25, 2017

Yajun Yang, Farmingdale State College

Introducing Polynomial Interpolation through Modeling Parabolas

There are two well-known approaches to the interpolating polynomial – Lagrange's formula and Newton's formula. We will introduce and derive these formulas by examining how we model a parabola. Through modeling parabolas, we bring the most powerful and useful tools of numerical analysis to the attention of lower division students while simultaneously building on and reinforcing some of the fundamental ideas in precalculus mathematics.

Thursday, April 20, 2017

Dipendra Regmi, Farmingdale State College

Global regularity for the 2D magneto-micropolar equations with partial dissipation

We study the global existence and regularity of classical solutions to the 2D incompressible magneto-micropolar equations with partial dissipation. The magneto-micropolar equations model the motion of electrically conducting micropolar fluids in the presence of a magnetic field. When there is only partial dissipation, the global regularity problem can be quite difficult. We are able to single out three special partial dissipation cases and establish the global regularity for each case. As special consequences, the 2D Navier-Stokes equations, the 2D magnetohydrodynamic equations, and the 2D micropolar equations with several types of partial dissipation always possess global classical solutions.

Tuesday, April 18, 2017

Chunhui Yu, Farmingdale State College

Shortfall risk in long term hedging with short-term future contracts on multi-commodity case

We study strategies to reduce shortfall risk in long-term hedging with short-term futures contracts on multi-commodity case. We re-evaluate these strategies in Glasserman's work and introduce some new hedging strategies. We will also introduce "most likely path" associated with some of these strategies.

Thursday, March 30, 2017

Ron Smith, Ph.D. candidate at College of William & Mary and FSC Applied Math alumnus

Likelihood ratio tests for Homeolog Expression Bias

Duplicated genes are common in eukaryotes and a likely contributor to the diversity of life on earth. There are several ways that a gene can be duplicated. In this talk we'll focus on Whole Genome Duplications (WGD), common to all plants, especially all major crops (corn, potato, rice,...). It is not well understood how duplicated genes evolve in function over time or in different tissues. In this talk I'll present a statistical method, using RNA-seq data, that can be used to measure "homeolog expression bias" (HEB) and HEB-shift (HEBS). Results from the monkeyflower Mimulus Luteus (a tetraploid) will be shown, and we will also discuss the broad applicability of this approach. These techniques should be of interest to any researcher interested in the fate of duplicated genes.

Tuesday, March 28, 2017

Ron Smith, Ph.D. candidate at College of William & Mary and FSC Applied Math alumnus

My Experiences as a Graduate Student

After getting my bachelor's degree, I was uncertain about whether or not I should go to grad school. The whole thing was a bit of a mystery to me. In this talk I'll give an overview of what the last 3 years as a grad student have been like, including some really hard tests, canoe trips in Canada, trying to explain to my family what I do, and getting to meet some really neat people from various disciplines. This talk should be of interest for any students considering pursuing a graduate degree. I will also give a brief introduction into the field of mathematical biology, what types of problems are studied, and various opportunities for employment that might follow from such a degree.

Tuesday, February 28, 2017

Svetlana Tlupova, Farmingdale State College

Fast and accurate solutions of coupled free/porous media flow

An interface between fluids partly flowing freely and partly coursing through a permeable matrix is a fundamental feature of all living systems comprised of more than one cell. Such problem is modeled by a coupled Stokes-Darcy system with carefully chosen interface conditions. In this talk, I will present a numerical solution based on a boundary integral formulation, where the Green's function is regularized and correction terms are added for high accuracy. I will also address the cost of computing the discretized sum of the particle-particle interactions, using a treecode algorithm to compute the sum rapidly.

## Fall 2016

Thursday, November 17, 2016

Worku Bitew, Farmingdale State College

A Bio-economic Model of Externalities and Foreign Capital in Aquaculture Production in Developing Countries

Most developing countries are increasingly depending on fresh water based aquaculture (cage culture) to supplement the declining catch from capture fisheries. Yet the competition for space between capture fisheries and cage culture, pollution generated by cage culture, and fish markets interaction effects are hardly conceptualized in a bioeconomic framework. Furthermore, the economic viability of cage culture depends on substantial investment thresholds, engendering foreign direct investment in the industry. This paper develops a conceptual model for fresh water based aquaculture that account for (1) space allocation, pollution, and interaction of markets for fish from aquaculture and capture fisheries; and (2) foreign capital financing aquaculture production. We found that a Pigouvian tax (optimum ad valorem tax) that corrects the externalities depends on economic and biological parameters in aquaculture and capture fisheries. Furthermore, if the aquaculture is financed with foreign capital, then the Pigouvian tax equal the ratio of net to total benefit from aquaculture. Numerical values are used to illustrate the results. (Joint work with Wisdom Akpalu, UNU-WIDER)

Tuesday, October 11, 2016

Steven Hoehner, Farmingdale State College

The Surface Area Deviation of the Euclidean Ball and a Polytope

While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices or facets in the symmetric surface area deviation. (Joint work with Carsten Schuett, Christian-Albrechts-Universität zu Kiel and Elisabeth Werner, Case Western Reserve University)

# Student Presentations

## Spring 2019

Thursday, May 2, 2019

Students: Victoria Brown, James Prasad, Jordan Rebolini and Kevin Stanis

On the Road to Ultimate Ruin

Natural, and man-made, disasters are inherent risks for insurance companies. Capitalization, premiums charged, and the claims paid out are important factors that determine solvency. Our research involves understanding the probability of a hypothetical insurance company paying out more capital than they have by a point in time, i.e. the probability of ruin. To start, we use the method of Laplace transforms and derive the solution for the aggregate claims, which is a compound Poisson distribution, and then analyze and test two numerical methods for its computation. We prove the validity of the methods for both the exponential (small claims) as well as Pareto (large claims) and then investigate our approach using real-world data; auto and fire insurance claims. This result allows us to compute the probability that the total claims, at a point in time, exceed a certain level and, therefore, value at risk. Finally, we derive the solution for the probability of ultimate ruin, which is the probability of becoming insolvent at any point in time in the future. This is critical for determining an adequate initial capital level and the premiums to be charged. We derive the analytical solution for the thin-tailed case of exponential tails and use numerical methods for the heavy-tailed Pareto claims. We then utilize the real-world claims, as a mock insurance company, to perform a Monte-Carlo simulation and analyze the risk-reward trade-offs to determine the appropriate mix of capital, premiums, and dividends.

Mentor: Dr. Douglas Johnston

## Fall 2018

Thursday, December 13, 2018

Student: Tunisia Solomon

Evaluation of Fission Data for Reactor Applications

Mentor: Dr. Worku T. Bitew

Student: Matthew Spindler

Surface area approximation of the Euclidean ball by polytopes with a restricted number of edges

Mentor: Dr. Steven Hoehner

Thursday, December 6, 2018

Students: Melissa Gander, Joseph Valentine, Doreen O’Hara, Joseph Bunster

Applications of Optimal Control Theory in Retirement Portfolio Management

Mentor: Dr. Worku T. Bitew

Students: Nicholas Gonzalez, Horton Denis

Optimal Retirement Financial Planning by Maximizing a Discounted Utility Function

Mentor: Dr. Worku T. Bitew

Students: Erick Elias, Austin Curran, Yasman Mustafa, Azeem Islam

Optimal Production Plan to Fulfill Inventory

Mentor: Dr. Worku T. Bitew

## Spring 2018

Thursday, May 10, 2018

Students: Venkat Ganesh, Carmeline Jean-Francois, Mark D. Valerie, Joseph R. Yackel

Random Number Generators and European Option Pricing

Mentor: Dr. Chunhui Yu

## Fall 2017

Tuesday, December 12, 2017

Students: Brian Galligan and Steven Maiorca

The Glider

Mentor: Dr. Irina Neymotin

Students: Sean Alexander, Demetra Gouvoussis, Nicole Ladoucer, and Joseph Napoli

Modeling Epidemics

Mentor: Dr. Irina Neymotin

Monday, December 11, 2017

Students: Jonathan Rendon and Lilibeth Torres

Pendulum

Mentor: Dr. Irina Neymotin

Student: Hung A. Nguyen

Pendulum Clock

Mentor: Dr. Irina Neymotin

Student: Gary Hagen

Chemical Oscillator

Mentor: Dr. Irina Neymotin

Thursday, December 7, 2017

Student: Christopher Marchelos

The Effect of Deductible Options in Auto Insurance Premiums

Mentor: Dr. Worku T. Bitew

Students: Emily Giordano, Erik Markowski, Giang Nguyen, Tunisia Solomon

Optimal Control in Oil Extraction

Mentor: Dr. Worku T. Bitew

## Spring 2017

Thursday, May 4, 2017

Student: Tammy Avolese

The Lorenz Equations: Non-Linear System Used to Model Weather Patterns

A study of the Lorenz Equations and their meteorological application. The behavior of the solutions, and their sensitivity to the perturbations of the initial conditions, is studied for different values of the Rayleigh Number, a parameter that determines the convective flow in the physical problem that is being modeled.

Mentor: Dr. Irina Neymotin

## Fall 2016

Tuesday, December 6, 2016

Students: James Breinlinger, Jenna DeCordova, and Donald Romard

An Introduction to Actuarial Present Value

Students introduce the concept of actuarial present value for several probability survival models.

Mentor: Dr. Chunhui Yu

Energy Evolution Fitting Software using Six-Order Harmonic Polylogarithms

Mentor: Dr. Chunhui Yu

# Past Seminars

• Apr 19, 2016: Gerald Flynn
• Apr 5, 2016: Loucas Chrysafi & Carlos Marques
• March 17, 2016: Nathaniel Prince (Farmingdale class of 2010), Ph.D. candidate at RPI "The Energy Method and Corresponding Eigenvalue Problem for Navier Slip Flow"
• Mar 8, 2016: Chunhui Yu
• Feb 25, 2016: Dipendra Regmi
• Dec 3, 2015: Yajun Yang
• Nov 12, 2015: Worku Bitew

# Past Conferences

## Conference Schedule

The Third Biennial Conference on Financial Mathematics was held at Farmingdale State College on March 1, 2019. The conference included presentations on both theoretical and applied financial mathematics, guest speakers, a moderated panel discussion on the state of the quantitative finance industry, and a student poster session.

Second Biennial Conference in Financial Mathematics, March 24, 2017 Call for abstract submission

Conference on Mathematics of Signals, Friday, September 23, 2016

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