# Neel Patel

Tenure-Track Assistant Professor

University of Maine

Department of Mathematics and Statistics

## About Me

Background:

I am currently a tenure-track assistant professor of mathematics at University of Maine. Before arriving in Maine, I was a postdoctoral researcher at ICMAT (Instituto de Ciencias Matematicas) in Madrid, Spain. Prior to that, I was a Postdoctoral Assistant Professor in the Department of Mathematics at University of Michigan Ann Arbor working with Lydia Bieri and Sijue Wu. In 2017-2018, I was a postdoctoral researcher at Instituto de Matemáticas Universidad de Sevilla (IMUS) in Sevilla, Spain working with Francisco Gancedo. I completed my PhD in mathematics at University of Pennsylvania under Robert M. Strain in 2017. My thesis was entitled "Rigorous Results in Fluid and Kinetic Models" and was awarded The Carlitz-Zippin Prize, given to one finishing PhD student each year. My undergraduate education was in mathematics at University of Chicago.

Research:

My research is in the analysis of partial differential equations. In particular, I have worked on fluid free boundary problems, kinetic theory and currently, I am also working on a project in general relativity.

Teaching:

My primary goal in teaching is to empower students to be self-sufficient learners and to foster interest in mathematics for students of all backgrounds. In Spring 2020, I was nominated for the Golden Apple Award at University of Michigan. Previously, I was awarded the Moez Alimohamed Graduate Student Award for Distinguished Teaching in Mathematics (2014-2015), given to one graduate student annually, and two Good Teaching Awards (Fall 2013 and Spring 2014) during my time as a graduate student at UPenn.

Email: neelpatel.math@gmail.com

## Research

My research is in the analysis of partial differential equations. Below, are a list of my publications, grants and awards.

Links to papers by clicking on underlined titles.

### Papers

On Nonlinear Stability of Muskat Bubbles, with F. Gancedo, E. Garcia-Juarez and R. M. Strain; preprint (2024)

Rigidity of Acute Angled Corners For One Phase Muskat Interfaces, with S. Agrawal and S. Wu; Advances in Mathematics (2023)

Well-posedness for SQG Sharp Fronts with Unbounded Curvature, with F. Gancedo and H. Nguyen; Math. Models and Methods in App. Sci. (2022)

Global Results for the Inhomogeneous Muskat Problem, with N. Shankar; preprint (2021)

Global Regularity for Gravity Unstable Muskat Bubbles, with F. Gancedo, E. Garcia-Juarez and R. M. Strain; Memoirs of the AMS (2023)

On the local existence and blow-up for generalized SQG patches, with F. Gancedo; Annals of PDE; (2020)

On The Muskat Problem With Viscosity Jump: Global In Time Results, with F. Gancedo, E. Garcia-Juarez and R. M. Strain; Advances in Mathematics (2019).

Large Time Decay Estimates for the Muskat Equation, with R. M. Strain; Communications in PDE (2017)

Three New Results on Continuation Criteria for the 3D Relativistic Vlasov-Maxwell System, Journal of Differential Equations (2018)

On Fiber Diameters of Continuous Maps, with P. S. Landweber and E. A. Lazar; The American Mathematical Monthly (2015)

### Grants/Awards:

AMS-Simons PUI Faculty Grant (July 2023-July 2026)

AMS-Simons Travel Grant (July 1, 2019- June 30, 2021)

The Carlitz-Zippin Prize for best PhD Thesis (2017)

## Mathematical Activities

### Seminar/Conference Talks Given

Mathematical Research Institute of Oberwolfach; Deterministic Dynamics and Randomness in PDE (May 2022)

One World Meeting of Young Mathematicians in Fluid Dynamics (June 2021)

UC Davis; Partial Differential Equations Seminar (January 2021)

Invited Talk at SIAM Conference on Nonlinear Waves and Coherent Structures; Stability/Instability in Hydrodynamics Mini-symposium; Bremen, Germany (July 2020) CANCELLED

Brown University; Partial Differential Equations Seminar (February 2020)

University of Massachusetts - Amherst; Analysis and PDE Seminar (February 2020)

Invited Talk at SIAM PDE Conference 2019 - Recent Progress in Fluid Mechanics: Classical Flows, Geophysical Models and Complex Fluids Mini-symposium; La Quinta, California (December 2019)

Michigan State University; Applied Mathematics Seminar (December 2019)

CMSA (Center for Mathematical Sciences and Applications) Harvard University; Fluid Dynamics Seminars (April 2019)

University of Pennsylvania; Analysis Seminar (February 2019)

Princeton University; Analysis of Fluids and Related Topics Seminar (November 2018)

University of Michigan; Differential Equations Seminar (September 2018)

University of Pennsylvania; Analysis Seminar (May 2018)

Imperial College London; Analysis and PDE Seminar (January 2018)

Institute of Mathematical Sciences ICMAT, Madrid; Working Seminar on PDE and Fluid Mechanics (October 2017)

Instituto de Matematicas Universidad de Sevilla (IMUS University of Seville); Conversaciones Fluidas (Conversations about Fluids) (October 2017)

### Conferences

In collaboration with Francisco Gancedo and Eduardo Garcia-Juarez, I was an organizer of the MathFluids "Mathematical Analysis of Incompressible Fluids" conference in Sevilla, Spain during July 12-15, 2018.

In collaboration with Eduardo Garcia-Juarez and Annalaura Stingo, I was an organizer of the minisymposium "Recent Results in Incompressible Fluid Mechanics" at SIAM PDE 2019 in La Quinta, California during December 11-14, 2019.

### Outreach

FEMMES Saturday Sciences Capstone (Fall 2018): co-organized group activity for 4th-6th grade girls to learn about the Stable Matching Problem.

REU 2019: Advised Nikhil Shankar on a project on porous media flows with permeability jump

REU 2020: Advised Advika Rajapakse on a project on velocity growth bounds for collisionless plasmas

## Teaching

My primary goal in teaching is to empower students to be self-sufficient learners and to foster interest in mathematics for students of all backgrounds. In Spring 2020, I was nominated for the Golden Apple Award at University of Michigan. Previously, I was awarded the Moez Alimohamed Graduate Student Award for Distinguished Teaching in Mathematics (2014-2015), given to one graduate student annually, and two Good Teaching Awards (Fall 2013 and Spring 2014) during my time as a graduate student at UPenn.

Courses (UMaine):

MAT 453: Partial Differential Equations I

### Courses (at UMichigan)

Math 451: Advanced Calculus I (Winter 2021)

Math 289: Problem Solving (Putnam Preparation) (Winter 2021)

Math 555: Introduction to Complex Variables (Fall 2020)

Math 289: Problem Solving (Putnam Preparation) (Fall 2020)

Math 451: Advanced Calculus I (Winter 2020)

Math 286: Honors Differential Equations (Fall 2019)

Math 115: Calculus I (Fall 2019)

Math 555: Introduction to Complex Variables (Winter 2019)

Math 115: Calculus I (Fall 2018)