Welcome!

My name is Jared Marx-Kuo, and I am an instructor at Rice University. Broadly speaking, I'm interested in analysis, geometry, and mathematical physics. I completed my PhD at Stanford University, where I was co-advised by Rafe Mazzeo and Otis Chodosh.

Research

• "The p-widths of RP^2". January 2024.
• "Diameter, Area, and Mean Curvature": joint with Greg Chambers. December 2024. Submitted
• "Index, Intersections, and Multiplicity of Min-Max Geodesics": joint with Lorenzo Sarnataro, Douglas Stryker. October 2024. Submitted
• "The Isospectral Problem for p-widths: An Application of Zoll metrics": May 2024. Accepted at Comptes Rendus Mathematique
• "An Inverse Problem for Renormalized Area: Determining the Bulk Metric with Minimal Surfaces": January 2024. In revision
• Video of a talk on this paper at Banff 2024.
• "Second Inner Variations of Energy and Index of Codimension 2 Minimal Submanifolds": July 2023. Submitted
• "Geometric Variations of an Allen-Cahn Energy on Hypersurfaces": joint with Erico Silva, April 2023. Submitted
• "A Dirichlet-to-Neumann Map for the Allen-Cahn Equation on Manifolds with Boundary": January 2023 (update April 2023). Submitted
• "Variations of Renormalized Volume for Minimal Submanifolds of Hyperbolic Space": 2022. To appear in Communications in Analysis and Geometry 2025, Volume 33 No 1.
• Shortened version

• "Characters of Renner Monoids and Their Hecke Algebras": from the Minnesota Twin Cities REU 2018. Published in IJAC August 2020
• "Convolution Algebras for Finite Reductive Monoids": also from the Minnesota Twin Cities REU 2018.
• "Sandpile Groups of Cayley Graphs of $F^r_2$": also from the Minnesota Twin Cities REU 2018, accepted at Communications in Algebra, 2024
• The "Obstacle Problem" (Summary, Problem Set, Answers): Group summer reading from undergrad under Professor Luis Silvestre and Stephen Cameron
• "Odd Quadratic Residues Modulo Powers of 2": short write up of high school work on computing quadratic residues

Personal Notes

Here is a collection of notes I've taken

• My most recent talk: "Minimal Surfaces, Allen--Cahn, and Balanced Energy" at Rice University's Geometry Seminar, September 20th, 2023
• I gave a talk on the fractional laplacian and non-local minimal surfaces. For Student Analysis Seminar. Feb, 2023
• Notes on Ricci Flow: From Math 258 at Stanford, taught by Professor Yi Lai in Fall 2022
• Area Exam Files: My syllabus and talk notes for my Area Exam on March 17th, 2022
• Introduction to Renormalized Volume: Notes for talks at Stanford Student Analysis Seminar and Kiddie Colloquium (Fall 2021)
• Reading with Otis Chodosh: Personal notes and some solutions to problems from Otis Chodosh's notes on the Allen-Cahn equation and minimal surface. Written Spring 2020. Definitely incomplete and needing of edits!
• Math 210B Winter 2020: Very informal notes from Math 210B as taught by Ravi Vakil in Winter 2020.
• Student Analysis Seminar Fall 2019: A weekly Stanford seminar on Analysis. The topic this quarter was entropy, as organized by Cole Graham.
• I gave a talk about Entropy and The Central Limit Theorem on 11/22.
• Student Probability Seminar Fall 2019: A weekly Stanford seminar on Probability. The topic this quarter was mix of mixing times, spectral gaps, and log-sobolev inequalities, as organized by Kevin Yang.
• I gave a talk about Hypercontractivity and log-sobolev inequalities on 10-18.
• Math 257a - Intro to Symplectic Geometry Fall 2019: Notes from the class taught by Umut Varolgunes.
• I gave a talk for the student symplectic seminar (for which I don't take regular notes) on sobolev spaces.
• I gave a talk at the University of Minnesota Twin Cities Representation theory seminar on representation theory and quantum mechanics. This was geared towards mathematicians who had little to no background in quantum physics

Outreach

• See CV for all
• LIT Fellow 2023-2024
• SURIM 2020 Group Leader (Problem Sheet, Partial Answers, Write-Up) - I organized a project on the Allen-Cahn equation for a group of 3 incoming sophomore students through the Stanford Undergraduate Research Institute in Mathematics. The students I worked with were Wenqi Li, George Nakayama, and Gautam Manohar, and with their permission, I've included their work from the summer.
• TA for CAAP calculus - I was a teaching assistant for a summer class on calculus through the University of Chicago's "Chicago Academic Achievement Program" (CAAP) geared towards incoming FLI first year students. I also taught a few lectures on ODEs in mechanics.
• DRP - I'm an organizer and mentor in Stanford's Directed Reading Program. Topics that I've mentored on so far include measure theory, probability, fourier analysis, manifolds, geometry, quantum mechanics, differential forms, and point-set topology.
• Past mentees: Gautam Manohar, Francesca Fernandes, Drew Gao, Julian Bernado, William White, Oliver Miller, Owen Shen, Andrew Lee, Jake Hofgard, Rayhan Razzak
• Diversity and Inclusion in Mathematics - see this great write up by Abigail Ward about teaching in a diverse (Stanford) classroom
• Resources for Mathematicians from Underrepresented Backgrounds - working list of resources for mathematicians of all ages from underrepresented backgrounds. Please email me if you have anything to add

Credentials

Here is my CV

Contact Info

HBH 408. Email me at "jm"+"307"+"@"+"rice.edu"

Miscellaneous Info

• Originally from Maryland.
• I like soccer, frisbee, running, and volleyball
• I love music and play a few intstruments - below are some artists I enjoy listening to.
• Butcher Brown, see "Frontline"
• Anderson .Paak, see "Put Me Thru"
• D'Angelo, see "Voodoo"
• VULFPECK , see "Outro"