# Opportunities

**Summer 2022 UW-Madison REU in analysis: **

In Summer 2022 the Mathematics Department will offer an (in-person) NSF supported research experience for undergraduates (REU). Students will work in small groups under the guidance of a mentor to solve non-trivial research problems in pure mathematics. The primary goal of the program is to give students a sense of what research in pure mathematics is like.

**Project Topics:**

**Computational Geometry****(Burkart):**In this project, we will study some problems related to the geometry of Jordan curves in the plane. We will focus on studying and implementing certain algorithms on “wild” Jordan curves, looking to provide evidence for possible (or impossible) improvements of certain theoretical problems. A solid background in 3D Calculus and Linear Algebra will be helpful, as will programming experience in a language like MATLAB or Python.- Harmonic Analysis (Jesurum and Stovall): We will focus on inequalities in harmonic analysis that relate to curves in higher dimensional space and related geometric objects. A solid background in 3D calculus and a proof-based course will be helpful.
- Complex Analysis (Zimmer): In this project, we will use non-Euclidean geometry to study problems in complex analysis. More precisely, students will learn about and use hyperbolic geometry to prove results about holomorphic functions. For this project it will be helpful to have familiarity with epsilon/delta proofs - the rest can be learned over the course of the project.

No background in or prior knowledge of these areas is required, but it would be helpful to have taken an introductory analysis course (Math 421 or 375-376), or a proof-based linear algebra course (Math 341), or to have some programming experience (e.g. Matlab, Python, or Java).

**Program Details:**

*Program dates:* July 11 - August 19, 2022. During the program period, students are expected to be in-person and work full time on their project.

*Eligibility:* Any current undergraduate student at UW-Madison who expects to continue enrollment in the 2022-2023 academic year.

*Stipend: * Eligible students will receive a stipend of $3,000 for the 6-week program.

*Organizers:* Jack Burkart, Michael Jesurum, Betsy Stovall, Andrew Zimmer.

*Contact information:* For questions, please contact the organizers at this email address, rtg-reu-2022-admin@g-groups.wisc.edu

*Funding:* This program is supported by NSF grants DMS-2037851, DMS-1653264, and DMS-2105580.

**Application Details: **

If interested please submit an application by March 11, 2022 (applications thereafter considered on a rolling basis) using the following Google form: application form