Fall 2021

Covid plan The lab as a whole will operate in a hybrid capacity this fall: access to the physical space and resources will be available, but we will also make remote participation possible in all full-lab activities (orientation, mid-semester meeting, final day activities, and seminar). Individual projects will run based on the mentor’s preferences, shown below.

The stability of icebergs and other floating objects, led by Professor Daniel Anderson (hybrid)
Cores and hulls of ideals of commutative rings, led by Professor Rebecca R.G. (hybrid)
Mathematical Modeling, Analysis and Control for Understanding the Spread of infectious diseases, led by Professor Padhu Seshaiyer (hybrid)
Mathematical Outreach (paid internship), led by Professor Harrison Bray (mix of in-person and online activities expected)
Combinatorics of Cohomology Rings of Peterson Varieties, led by Professor Rebecca Goldin (hybrid)
Speed and Stability of Traveling Waves in Population Growth Models, honors thesis by Zach Richey, supervised by Professor Matt Holzer
Persistent Homology, honors thesis by Shrunal Pothagoni, supervised by Professor Sean Lawton
Vertex Algebras, honors thesis by George Andrews, supervised by Professor Sean Lawton

Faculty Mentor: Professor Daniel Anderson

Computing quantities like the center of mass, the center of buoyancy, and another quantity called the metacenter.  Archimedes’ Principle plays a role here.  This project will involve predicting stability and floating orientations of shapes with simple and complex geometries using numerical and analytical approaches  Some experimentation will likely be involved as well.

Background/Prerequisite: Math 213. Some numerical experience (or willingness to learn) will be useful.

Difficulty level: Entry Level

Faculty Mentor: Professor Rebecca R.G.

The integral core of an ideal of a commutative ring is used to determine key properties of the ideal and the ring. In this project, we will explore other types of cores and hulls, computing examples both by hand and in the programming language Macaulay2. We will work over commutative rings where we can describe most or all ideals in the ring. 

Background/Prerequisite: Completion of Math 300, Introduction to Advanced Mathematics, formerly Math 290. Preferred background: Math 321, small amount of programming experience in any programming language 

Difficulty level: Quite difficult

Faculty Mentor: Professor Padhu Seshaiyer

In this work, we plan to consider new compartmental models that will attempt to capture the dynamics of the spread of infectious diseases such as COVID-19 and its variants as well as impact of vaccination against the spread. Building on knowledge from the current nature of the spread, data available on transmission rates, seasonality, social behavior and infectious disease models our goal will be to come up with a family of models that help to provide deeper insight into the nature of the dynamics. Along with the development of these models the mathematical research will also focus on deriving rigorous mathematical expressions for basic reproduction number, performing mathematical stability analysis as well as conducting an optimal control applied to the infectious disease models. We also hope to validate the models against benchmark data and parameters available from the CDC and also use data of infected cases to estimate the parameters through parameter estimation techniques.  

Background/Prerequisites: Completion Math 214, Differential Equations.  

Difficulty level: Entry Level 

Faculty Mentor: Professor Harrison Bray

MEGL offers outreach activities to the community every semester. To fulfill our mission of outreach, we need your help. Participants will deliver, refine and help develop mathematical outreach activities which inspire a passion for mathematics. Check out our website for examples of MEGL outreach activities.

Background/Prerequisites: A passion for mathematics

Difficulty level: Entry Level

Faculty Mentor: Professor Rebecca Goldin

We will be looking at a ring map associated to the inclusion of the Peterson variety into the flag manifold, mainly the induced restriction in the S1-equivariant cohomology ring. We will study the restriction of geometrically represented classes called Schubert classes to the Peterson variety.

Background/Prerequisite: Completion of Math 321, Abstract Algebra.

Difficulty level: Challenging

Faculty Mentor: Professor Matt Holzer

Undergrad Research Assistants: Zach Richey

We study a reaction-diffusion PDE that models population growth and spread.  In particular, we are interested in solutions to this equation in the form of traveling wave fronts.  We seek to understand how the functional form of the reproduction rate, and the subsequent Allee effect, determine the speed and stability of these fronts.

Faculty Mentor: Professor Sean Lawton

Undergrad Research Assistants: Shrunal Pothagoni

The ability to interpret and understand rich data is more prevalent than ever. Topological Data Analysis (TDA) is a recently developed field that uses methods in topology to extract qualitative features from data sets. In particular, I will be studying how to use abstract simplical complex on point cloud data sets to study their geometry using computational homology. 

Faculty Mentor: Professor Sean Lawton

Undergrad Research Assistants: George Andrews

Vertex operator algebras provide an algebraic way to formalize quantum field theories. More specifically, I will be studying how to construct the vertex operator algebra associated with the affine Lie algebra corresponding to SL_2(C). When combined with the conformal blocks construction and the FRS theorem for constructing rational conformal field theories, this will result in a rigorous construction of the 3-dimensional SL_2(C) Chern-Simons theory as a topological string theory.