Jared Marx-Kuo

Welcome! I am an NSF Postdoctoral Fellow at the University of Chicago. I was previously a G.C. Evans Instructor and NSF Postdoctoral Fellow at Rice University, and before that, I completed my PhD at Stanford University under the supervision of Rafe Mazzeo and Otis Chodosh.

I am broadly interested in geometric analysis, with my recent work focusing on the Allen--Cahn equation, min-max constructions of minimal hypersurfaces, and Gromov's "p-widths." My past work has also focused on conformal geometry and asymptotically hyperbolic manifolds.

Research

1. "Equivariant Allen--Cahn Solutions and the Existence of Cohomogeneity 2 Minimal Surfaces": July 2026.
2. "The p-widths of the Hemisphere": March 2026. Submitted
3. "Mountain Pass Critical Points of the Volume Constrained Area Functional": Joint with Gregory Chambers. September 2025. In Revision
4. "Almgren's Three-Legged Starfish": Joint with Christos Mantoulidis. April 2025. In Revision
5. "Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface": Joint with Pedro Gaspar. February 2025. Submitted
• Slides of a talk on this paper at UTK, March 2025.
6. "The p-widths of RP^2". January 2025. Proceedings of the AMS, Vol 153, No. 12 (2025) 5385 -- 5396 .
7. "Diameter, Area, and Mean Curvature": joint with Greg Chambers. Differential Geometry and Its Applications, Vol 103
8. "Index, Intersections, and Multiplicity of Min-Max Geodesics": joint with Lorenzo Sarnataro, Douglas Stryker. October 2024. Advances in Mathematics. Volume 502, Part C. Article 111193.
9. "The Isospectral Problem for p-widths: An Application of Zoll metrics": May 2024. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 565-570.
10. "An Inverse Problem for Renormalized Area: Determining the Bulk Metric with Minimal Surfaces": January 2024. New Zealand Journal of Mathematics, Vol 56. (2025)
• Video of a talk on this paper at Banff 2024.
• Slides from the above talk.
11. "Second Inner Variations of Energy and Index of Codimension 2 Minimal Submanifolds": July 2023. Journal of Geometric Analysis, Vol 35, No. 290 (2025)
12. "Geometric Variations of an Allen-Cahn Energy on Hypersurfaces": joint with Erico Silva, April 2023. Calculus of Variations and Partial Differential Equations, Vol 64, No. 180 (2025).
• Slides of a talk on this paper at Scuola Normalie online seminar, February 2024.
13. "A Dirichlet-to-Neumann Map for the Allen-Cahn Equation on Manifolds with Boundary": January 2023. Interfaces and Free Boundaries, Vol 27, No. 4 (2025) 575 -- 618
14. "Variations of Renormalized Volume for Minimal Submanifolds of Hyperbolic Space": Communications in Analysis and Geometry 2025, Vol 33, No. 1 (2025) 17 -- 29.
• Shortened version

1. "Sandpile Groups of Cayley Graphs of $F^r_2$": joint with Jiyang Gao, Vaughan McDonald, Chi Ho Yuen. Communications in Algebra, Vol 52, No. 10 (2024), 4459 -- 4479
2. "Characters of Renner Monoids and Their Hecke Algebras": Joint with Andy Hardt, Vaughan McDonald, John M. O'Brien, Alexander Vetter International Journal of Algebra and Computation, Vol 30, No. 7 (2020), 1505 -- 1535
3. "Convolution Algebras for Finite Reductive Monoids": Joint with Vaughan McDonald, John M. O'Brien, Alexander Vetter.

Rice Dynamics and Geometry Conference 2026

I co-organized the 2026 Rice Geometry and Dynamics Conference along with F. Arana-Herrera, D. Fisher, and C. Mantoulidis.

Teaching

• Rice University: Instructor for Math 355 (Linear Algebra) and Math 354 (Honors Linear Algebra)
• Stanford University: Teaching/Course Assistant for Math 53 (ODEs and Linear Algebra), Math 62CM (Modern Mathematics: Continuous Methods), Math 171 (Fundamentals of Analysis)
• Miscellaneous
• Leland Scholars Program, Stanford University. Instructor for bridge program for incoming FGLI students
• SUMAC TA, Stanford University. TA for summer course in algebraic topology for advanced high schoolers

Outreach

• Rice SURF mentor 2025 (Problems + Solutions) - I organized a summer reading on chapters 1-7 of Stein and Shakarchi's Complex Analysis. My mentee, Oscar Pan, completed a length list of problems, which I've included.
• 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 was an organizer and mentor in Stanford's Directed Reading Program, as well as Rice's DRP. 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
• I have also mentored Ben Schussler, Ben May, and Alejandro Lopez at Rice through an analogous DRP
• 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

Personal Notes

Here is a collection of notes I've taken

• A 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
• The "Obstacle Problem" (Summary, Problem Set, Answers): Group summer reading from undergrad under Professor Luis Silvestre and Stephen Cameron

Credentials and Contact

Here is my CV.

HBH 408. Email me at "jmarx"+"kuo"+"@"+"gmail.com".

Miscellaneous Info

• I'm originally from Maryland.
• I enjoy running, playing soccer, and watching basketball!
• 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"