The University of Chicago Mathematics REU 2025
Interested in the REU but not at the University of Chicago?
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An essay about Chicago's REU and DRP programs (from 2014)
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2025 REU: Announcement and description of the program
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U of C students apply by Feb. 7 on Handshake: https://uchicago.joinhandshake.com/jobs/9507582/share_preview
Non U of C students apply by Feb. 7 on MathPrograms: https://www.mathprograms.org/db/login/ja
2025 REU: Application for non-University of Chicago students
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This is a suggested template for your Research Statement, an optional upload
to your application.
Links to past REUs
- Link to the 2024 REU
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- Link to the 2023 REU
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- Link to the 2022 REU
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- Link to the 2021 REU
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- Link to the 2020 REU
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- Link to the 2019 REU
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- Link to the 2018 REU
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- Link to the 2017 REU
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- Link to the 2016 REU
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- Link to the 2015 REU
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- Link to the 2014 REU
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PROGRAM LINKS
SCHEDULES, ABSTRACTS, and MENTORSHIP PAIRINGS
- FIRST and SECOND WEEK SCHEDULES, June 16-June 20 and June 23 June 27
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- FIRST and SECOND WEEK Abstracts
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- THIRD and FOURTH WEEK SCHEDULES, June 30-July 3 and July 7-July 11
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- THIRD and FOURTH WEEK ABSTRACTS
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- FIFTH and SIXTH WEEK SCHEDULES, July 14-July 18 and July 21-July 25
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- FIFTH and SIXTH WEEK ABSTRACTS
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- SEVENTH and EIGHTH WEEK SCHEDULES, July 28-Aug 1 and Aug 4-August 8
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- SEVENTH and EIGHTH WEEK ABSTRACTS
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- 8th week schedule of participant talks
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- REU: Table of mentorship pairings
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Notes and readings for talks
- Graphs and orthogonal polynomials (Web page for REU 2025 course taught by Laci Babai; ANSWER ITS QUESTIONNAIRE)
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- Finite Spaces Book Rough Draft (Parts in red may not be ready for reading)
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- Definitions: Operads, algebras, and modules
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- Operads, algebras, and modules
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- Operads, multerads, and bioperads
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- Glimpses of equivariant algebraic topology
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2025 REU: PARTICIPANT PAPERS -- FULL PROGRAM
Dead links are to papers under revision
- Dael Amzalag.
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- Claudio Bastiani-Fonck.
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- George Stanislaw Bayliss. On relative functors and simplicial localization.
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- Achyut Bharadwaj. Group cohomology and local class field theory.
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- Isaac Chang. From Brownian motion to Feynman-Kac: applications of stochastic differential equations to quantum mechanics.
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- Xiaoxian Chen. Phase transitions in random-cluster models.
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- Zhengfu Chen
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- Jalen Chrysos. The reverse mathematics of two combinatorial problems.
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- Maryam Contractor.
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- Leo Courbe. Non-parametric, data-driven hedging with generative models: from early attempts to Tailgan and Volgan.
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- Samuel Timothy Coyle. Finite cobordism.
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- William (Haolong) Duan. Bers' proof of Nielson-Thurston classification.
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- William M Easton. Automorphisms of $\mathbf{R}^n$, stable homeomorphisms, and Kirby's torus trick.
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- Liam Eifert.
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- Augustin Esteva. Random curves and Schramm-Loewner evolutions.
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- Ze Fan. The Lubin-Tate deformation theorem and the Morava $E$-theory.
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- Ezekiel Fleissner-Kates. The regularity and rigidity of the Burgers' equation.
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- William Flowers. Morphisms of finite $C_p$-Tambara field are free, \{e]tale, Galois.
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- Jeremy Forman-Duranona.
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- Avery Fox. Schramm-Loewner evolutions and percolation interfaces.
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- Pico Yeh Gilman
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- Eleanor Guha, (No title)
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- Andrew Hah.
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- Shravan Haribalaraman. Hausdorff dimension of random fractals.
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- Duke Hogan-Murphy.
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- Jeffrey Howard.
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- Qingcheng Hu.
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- Grayson (Grace) Jarboe. Hyperbolic surfaces, Teichm\"uller space, and the $9g-9$ theorem.
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- Joshua Johnson
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- Vaughn Komorech. Non-jumps in hypergraphs.
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- Ruize Lai. An Introduction to the Steinberg variety.
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- Seamus Lavine. Complexity methods in geometric measure theory.
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- Michael Lee. The regularity and rigidity of the Burgers' equation.
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- Justin W Li.
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- Jikun Li. Twisting maps and Adams spectral sequence.
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- Jiasen Liu.
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- Yawen Liu.
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- Yinghan Liu.
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- Leo Long. Group actions on Boolean algebras.
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- Elijah Lowe.
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- Yuan Lu.
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- Yutong (Robin) Luo. Geometry and physics of black holes.
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- Kisna Matta.
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- Mirza Mehmedagic. Markov chain mixing and random walks on regular graphs.
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- Matteo Moessner. Convergence of the ground state energy of helium atom.
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- Maya Mustata. Amenability and the Folner criterion.
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- Brian Nguyen. L-Function and the class number formula.
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- Minh-Anh Nguyen-Dang. Mathematical models in biology.
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- Ryan O'Farrell. Gauge theory and the Chern-Simons action.
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- Pranav Padmanabhan. Approximation structures.
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- Nikhil Vinod Patel. The biggest open problem in Euclidean Ramsey theory.
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- Minh Pham. Highest weight theory.
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- Sofia Piccirillo
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- Hamshika Rajkumar
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- Aditya H Ramabadran. Ground states, concentration compactness, and blow-up dynamics in the nonlinear Schr\"odinger equation.
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- Otto Reed. Amenability and the Folner criterion.
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- Leonardo Rodrigues de Medeiros.
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- Kyle I Roke.
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- Julia Rychlik. Optimal stopping theorem & applications.
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- Desmond Saunders. An introduction to the modularity theorem.
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- Camille (Simon) Seignourel.
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- Morgan Sheehan.
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- Charles Shen. An exposition of Weil II.
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- Wenyuan (Selena) Shi. Frobenius algebras and cohomology rings with Poincar\'{e} duality.
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- Emory Sun. The levelwise finite generation of free Tambara functors.
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- Junfei Sun.
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- Bach Tran.
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- Vincent Tran. The enigmatic $Z/12Z$.
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- Soyoltoi Uranchimeg.
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- Alice Wang. The wandering exponent in first passage percolation.
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- Hanlei Wen. Local fields and $p$-adic numbers.
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- Yili Wen.
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- Siyuan Xing.
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- Tong (Ben) Yang.
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- Mufan Yao. Looking inside the gate of Chromatic Homotopy Theory.
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- Caleb Young.
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- Yao Yu. Condition for equivalence of random walk reflected off of infinity and random interlacements.
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- Angel Yuan. A generalized approach to cobordism.
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- Hongyi Zhang
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- Kaixu Zhang. Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants.
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- Jinchen Zhao
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- Wenshi Zhao. Galois representations and modularity theorems.
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- Keming Zhou
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- Rong Ping (Peter) Zhou.
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- Zhitong (Alexandra) Zhou.
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- Junrong Zhu.
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2025 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM
Dead links are to papers under revision
\item{$\bullet$} Nicole Abbott. Fundamental groups, covering spaces, and the Galois correspondence.
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\item{$\bullet$} Gavin An. An introduction to fractal dimension with applictions to Brownian motion.
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\item{$\bullet$} Jhon Lenin Acuna Arevalo. Mixing times and applications of finite Markov chains.
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\item{$\bullet$} Ariel Bishop. Topology and geometry of Teichm\"{u}ller space.
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\item{$\bullet$} Kabir Buch.
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\item{$\bullet$} Thomas Catalan. Arnold's proof of the Abel-Ruffini theorem.
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\item{$\bullet$} Atiwit (Miles) Chanbai.
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\item{$\bullet$} Finn Charest. Functional analytic and measure-theoretic proof of Radon-Nikodym.
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\item{$\bullet$} Lucas Chen.
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\item{$\bullet$} Dylan Cheng.
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\item{$\bullet$} Nicholas Chin. Introduction to geometric measure theory.
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\item{$\bullet$} Timothee F Collinet-Adler.
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\item{$\bullet$} Sizhong (Alan) Fang. Braid groups in configuration spaces and mapping class groups.
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\item{$\bullet$} Ruoxuan Feng.
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\item{$\bullet$} Carter Fleming.
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\item{$\bullet$} Anton Gaek. Constructions of irreducible representations of the symmetric group.
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\item{$\bullet$} Katherine Giffler. Topology and geometry of Teichm\"{u}ller space.
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\item{$\bullet$} Chenyu Gu. Error guarantees for k-means++ clustering.
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\item{$\bullet$} Sagar Gupta. A combinatorial proof of Brouwer's fixed point theorem via Sperner's lemma.
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\item{$\bullet$} Ilan Haas. An introduction to singular homology and the hairy ball theorem.
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\item{$\bullet$} Charles Hammack.
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\item{$\bullet$} Joshua Hikida. Finite-sample concentration inequalities: Hoeffding, Bernstein, and a Kelly sizing appendix.
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\item{$\bullet$} Eliot Huang. Markov chain Monte Carlo: the Metropolis-Hastings algorithm.
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\item{$\bullet$} Julian Huang.
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\item{$\bullet$} Charles (Bingde) Jiang. Usage of the probabilistic method in combinatorial games.
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\item{$\bullet$} Lingyue Jiang.
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\item{$\bullet$} Gavin Johnson. An introduction to category theory.
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\item{$\bullet$} Gregory Karaev. A Glimm-Effros dichotomy for countable groups.
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\item{$\bullet$} Vedesh Kodnani.
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\item{$\bullet$} Ryan Kotamraju. A measure-theoretic foundation for conditional expectation.
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\item{$\bullet$} Victoria Kurakata.
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\item{$\bullet$} Badis Labbedi. Geometric gauge field theory.
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\item{$\bullet$} Souhoon Lee. The weak and strong law of large numbers.
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\item{$\bullet$} Ethan Li. Symmetry and the Cauchy identity.
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\item{$\bullet$} Vanessa Lowder. Measure theoretical nullsets and diophantine equations.
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\item{$\bullet$} Matthew Lund. Optimal stopping theory and the binomial option pricing model.
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\item{$\bullet$} Zachary McCarthy. The Banach-Tarski paradox.
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\item{$\bullet$} Johnathan McDow.
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\item{$\bullet$} Abishek Mukherjee.
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\item{$\bullet$} Sarah Nagarkatti.
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\item{$\bullet$} Cavan Gabaldon O'Neill. On the symplectic representation of mapping class groups of surfaces.
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\item{$\bullet$} Panav Pallothu.
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\item{$\bullet$} Neal Pannala. An introduction to basic properties of Markov chains.
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\item{$\bullet$} Matthew Paraboschi. Stochastic calculus and financial applications.
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\item{$\bullet$} Daniel Pressman. An introduction to algebraic number theory.
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\item{$\bullet$} Julian Quinonez. An introduction to algebraic number theory.
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\item{$\bullet$} Dylan Sparrow. Clique number and random graphs.
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\item{$\bullet$} Isaac Spiller.
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\item{$\bullet$} Shuyuan (Julie) Sun. Haar measure, spectral theory and the Peter-Weyl theorem.
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\item{$\bullet$} Sheldon Tan. The character table of $GL(2,q)$.
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\item{$\bullet$} Ian Teo.
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\item{$\bullet$} Aman Thawani. Measure theory and convergence in $L^p$.
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\item{$\bullet$} Filippos Tsoukis
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\item{$\bullet$} Kavya Vaidyanathan.
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\item{$\bullet$} Leah Vashevko. An overview of quasirandom graph sequences.
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\item{$\bullet$} Luoqian (Ocean) Wang.
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\item{$\bullet$} Jack Whelan. Some spectral bounds on graph invariants.
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\item{$\bullet$} Claire Wong. Fundamental groups, covering spaces, and the Galois correspondence.
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\item{$\bullet$} Qihong (Kevin) Wu. An introduction to persistence homology: theory with an application.
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\item{$\bullet$} Mel Xiao. The Cauchy integral.
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\item{$\bullet$} Zerlina Yau. Extension and the 0-1 law on the countable random graph.
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\item{$\bullet$} Chengyue Zhang. Representation of braid group.
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\item{$\bullet$} Enze Zheng. The. Euler characteristic.
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\item{$\bullet$} Aeres Zhou.
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\item{$\bullet$} Jiale (Jasper) Zhou.
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\item{$\bullet$} Oliver Ray Wang. Counting with symmetries; Burnside's lemma and P\'{o}lya's enumeration.
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Tex Help
- Template for texing REU papers: \underline{YOU MUST USE THIS TEX FILE}
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- An excellent latex web page (with an REU template with more examples)
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- LaTeX -- A document preparation system
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(web page)
- LaTeX -- A document preparation system
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Guides to writing papers (Steve Kleiman and Dan Kleitman, MIT)
- Writing a math paper (two formats): READ THIS CAREFULLY
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- Another useful guide: READ THIS TOO
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