Past Recipients

2024 Recipients

1. Emma Bohse
   Project title: Utilizing Neural Networks for Data-Driven Modeling of Alzheimer’s Disease
   Supervisor: Wenrui Hao
2. Opal Cieslak
   Project Title: Conformally Covariant Differential Operators
   Supervisor: Jeffrey Case

2023 Recipients

1. Lilith Loriinae
   Project Title: Modeling Resistance Selection Between Antibiotic Dosing Intervals to Discover Optimal Dosing Regimens
   Supervisor: Jessica Conway
2. Chenxi Ma
   Project title: An inverse problem for node-based epidemic models
   Supervisor: Amina Amassad

2022 Recipients

1. Isabelle Stepler
   Project Title: The Impact of Networks’ Topology on Epidemiological Models
   Supervisor: Pierre-Emanuel Jabin

2021 Recipients

1. Jaysa Grafton
   Project title: Solving Partial Differential Equations with Deep Neural
   Networks
   Time period: Summer-Fall 2021, Spring 2022
   Supervisor: Leonid Berlyand
2. Madison Pratt
   Project title: Oscillatory Behavior of a Multiple Recovery Phase SIRS
   Model
   Time period: Summer-Fall 2021
   Supervisor: Timothy Reluga

2019 Recipients

1. Erin Bevilacqua
   Project title: Study on Combinatorial Structure of Lecture Hall Partitions
   Time period: Fall 2019
   Supervisor: Ae Ja Yee
2. Colleen Conway
   Project title: A Critique of the Efficient Markets Hypothesis and Related Stock Price Models
   Time period: Fall 2019
   Supervisor: Jenny Li
3. Kristin Sickau
   Project title: Convergence of Iterative Methods for Quadratic Programing Problems
   Time period: Summer and Fall 2019
   Supervisor: Ludmil Zikatanov
4. Yiyang Wang
   Project title: An ODE in Geometric Scattering Theory
   Time period: Summer 2019
   Supervisor: Jeffrey Case

2018 Recipients

1. Sarah Guglielmi
   Project title: Asymptotic and Numerical Study of Nonlinear PDEs
   Time period: Summer 2018
   Supervisor: Leonid Berlyand
2. Alison Harris
   Project Title: Laboratory Models of Chaotic Systems
   Time period: Summer and Fall 2018
   Supervisor: Andrew Belmonte
3. Quanqi Hu
   Project title: Conservation Laws with Random Initial Data: A Numerical Study
   Time period: Summer 2018
   Supervisor: Luen-Chau Li
4. Pragnya Prabakaran
   Project title: Wind-Driven Surface Current at an Air-Water Interface
   Time period: Summer 2018
   Supervisor: Diane Henderson

2017 Recipients

1. Elena Cadenas
   Project title: Neural Activity in the Brain Using Mathematical Modeling
   Time period: 2017-2018 academic year
   Supervisor: Carina Curto
2. Sarah N. Fieger
   Project Title: Perceptions of Mathematics Educators on Diversity
   Time period: 2017-2018 academic year
   Supervisor: Nate Brown
3. Kaiyi Wu
   Project title: Markov Chain Monte Carlo method and Application
   Time period: 2017-2018 academic year
   Supervisor: Ludmil Zikatanov

2016 Recipients

1. Qianru Zhu
   Project Title: Evolutionary Games Dynamics
   Time period: Summer 2016
   Project Supervisor: Andrew Belmonte
2. Zhiyu Zhao
   Project Title: From Penrose to Escher — Visualization of Almost Periodic Structure
   Time period: 2016-2017 academic year
   Project Supervisor: Dmitri Burago

2015 Recipients

1. Hyun Jung Choi
   Project Title: Partitions with bounded largest parts
   Time period: 2015-2016 academic year
   Project Supervisor: George Andrews
2. Rachel Hoellman
   Project Title: Modeling the spread of influenza and vaccine distribution tactics
   Time period: 2015-2016 academic year
   Project Supervisor: Jessica Conway
3. Divya Jagadeesh 
   Project Title: Natural selection
   Time period: 2015-2016 academic year
   Project Supervisors: Michael DeGiorgio and Tim Reluga

2014 Recipients

1. Raquel Alvarez (junior)
   Project title: Normal forms and resonance
   Time period: Summer 2014
   Supervisor: Aissa Wade
2. Ailaura Donahoe (sophomore)
   Project title: Biology in Mathematics
   Time period: 2014-2015 academic year
   Supervisor: Tim Reluga
3. Allegra Inciardi (unior)
   Project title: Mathematical Modeling of Influenza at Penn State: A study of Incidence Patterns and Effect of Vaccination
   Time period: 2014-2015 academic year
   Supervisor: Tim Reluga
4. Eyan Su (sophomore)
   Project title: Geometry of Lie groups and Lie algebras
   Time period: Summer 2014
   Supervisor: Aissa Wade

2011-2012 Recipients

1. Bingqian Lu, Supervisor: Anna Mazzucato.
   Title: Monte Carlo simulations and option pricing.
   Description: Monte Carlo simulation is a legitimate and widely used technique for dealing with uncertainty in many aspects of business operations. The purpose of this paper is to explore the application of this technique to the stock volality and to test its accuracy by comparing the result computed by Monte Carlo Estimate with the result of Black-Schole model. In addition, we used Mathematica, a mathematical computer software application, we tested the relationship between the sample size and the accuracy of Monte Carlo Simulation and provide numerical and geometrical evidence for our conclusion.
2. Paige Carlton, Supervisor: Andrew Belmonte.
   Title: Saffman-Taylor Fingering.
   Description: Researching Saffman-Taylor Fingering. Injecting liquids of different densities and observing the patterns of fingering. Later will infuse particles into the liquids and observe how the particles affect fingering and the air bubbles formed.

2010-2011 Recipients

1. Jacquelyn Kirchner, Superviser: Jason Morton.
   Title: Petascale Experimental Mathematics.
   Description: Jacquelyn will study approaches for using supercomputer hardware such as the Blue Waters machine, as well as commodity clusters, to solve problems in computational algebraic geometry. Specifically, she will be attempting to solve computationally certain implicitization problems that have resisted both mathematical and small-scale computational approaches.
2. Yixuan Shi, Junior, Supervisor: Jenny Li.
   Title: Mathematical models on monetary policy and open market operation analysis.
   Description: Many countries now face the economical crisis problem. A very powerful tool for government to balance their economy is using monetary policy. A well-build mathematical model will provide a decisive help on formulating proper policy. Bubble problem, hyper deflation problem, and many economic issues can be well presented and fixed via mathematical models. I hope to development a certain way to solve those economic problems. Moderate adjusting the interest rate and the amount of liquidity in a nonlinear way may achieve equilibrium in a dynamic economic and a steady positive growth rate. Project Report

2007-2008 Recipients

1. Paige Elizabeth Pfeffer, Junior, Supervisor: Jenny Li.
   Title: Optimization problems arising from economics and finance
   Description: Economics and finance are concerned with decisions making, i.e. making a choice among alternatives in a way to maximize or minimize something. For example, a company wants to maximize their profit while minimizing cost with consumers maximizing there utility (represents happiness) and financial intermediaries maximizing their investment returns. The corresponding mathematical model can be an optimization problem with many variables; stochastic and dynamic with equality or inequality constraints. Professor Jenny Li and I are going to investigate a particular problem arising from a banking firm model from economics.
2. Amber L. Reardon, Junior, Supervisor: Alexei Novikov.
   Title: Front propagation in reaction-diffusion equations
   Description: The objective of this project is to understand the behavior of solutions of the reaction-diffusion equations. The project comprises two parts: rigorous analytical study of the Kolmogorov-Petrovsky-Piskunov-Fisher equations and numerical simulations of reaction-diffusion equations in 1-dimensional heterogeneous media using MATLAB. Project Report

2006-2007 Recipients

1. Anna Auker , Freshman, Supervisor: James Sellers.
   Title: Properties of recurrent Sequences
   Description: As part of a small group, Anna will participate in a study of recurrences and related properties (such as divisibility of Fibonacci numbers and related families.
2. Kristina Colladay, Senior, Supervisor: Andrew Belmonte.
   Title: Mathematical modeling of biodiesel production
   Description:Biodiesel is a fuel esentially interchangeable with petroleum diesel, produced by chemical reaction from mo0st vegetable oils. We are studying the coupled Oridnary Differential Equations models for this reaction, and comparing it with our own biodiesel production experiments in the Pritchard Fluid Lab.
3. Christine Cushwa, Senior, Supervisor: Diane Henderson and Victor Nistor.
   Title: Numerical look at Mathieu’s equation.
   Description: We studied differential equations with non-constant coefficients, concentrating on the Mathieu equation for which we conducted a numerical investigation.
4. Fara Delitsky, Freshman, Supervisor: Anna Mazzucato and Victor Nistor.
   Title: Numerical methods for elliptic equations and linear algebra
   Description: We study the properties of the stiffness matrix associated to the discretization of the Laplace equation. Our approximation space is defined in terms of a partition of unity. We want to obtain a fast method for solving the resulting linear system. We will consider the effect of changing the basis of the Finite Element space.
5. Noopur Pathak, Sophomore, Adviser: Luen-Chau Li.
   Title: Zero-preserving isospectral flows
   Description: We plan to construct isospectral flows on symmetric matrices which preserve zero patterns and which converge to diagonal matrices. We hope to be able to use such flows to compute the eigenvalues of some classes of structured matrices.