The University of Chicago Mathematics REU 2023

Interested in the REU but not at the University of Chicago? (pdf)

An essay about Chicago's REU and DRP programs (from 2014) (pdf)

2023 REU: Announcement and description of the program (pdf)

2023 REU: Application for University of Chicago students (pdf)

Completed U of C applications should be returned to E314 (slip under the door if nobody is there)

2023 REU: Application for non-University of Chicago students (pdf)

To apply, go to MathPrograms: https://www.mathprograms.org/db/login/ja

Links to past REUs

• Link to the 2022 REU (Go)
• Link to the 2021 REU (Go)
• Link to the 2020 REU (Go)
• Link to the 2019 REU (Go)
• Link to the 2018 REU (Go)
• Link to the 2017 REU (Go)
• Link to the 2016 REU (Go)
• Link to the 2015 REU (Go)
• Link to the 2014 REU (Go)

SCHEDULES, ABSTRACTS, and MENTORSHIP PAIRINGS

• FIRST WEEK SCHEDULE, June 12-16 (pdf)
• FIRST and SECOND WEEK SCHEDULES, June 12-16 and June 19-23 (pdf)
• FIRST WEEK Abstracts (pdf)
• SECOND WEEK ABSTRACTS (pdf)
• THIRD and FOURTH WEEK SCHEDULES, June 26-June 30 and July 3-July 7 (pdf)
• THIRD and FOURTH WEEK ABSTRACTS (pdf)
• FIFTH and SIXTH WEEK SCHEDULES, July 10-July 14 and July 17-July 21 (pdf)
• FIFTH and SIXTH WEEK ABSTRACTS (pdf)
• SEVENTH and EIGHTH WEEK SCHEDULES, July 24-July 28 and July 31-August 4 (pdf)
• SEVENTH and EIGHTH WEEK ABSTRACTS (pdf)
• REU: Table of mentorship pairings (pdf)

Notes and readings for talks

• Finite Spaces Book Rough Draft (Parts in red are not ready for reading) (pdf)
• Definitions: Operads, algebras, and modules (pdf)
• Operads, algebras, and modules (pdf)
• Glimpses of equivariant algebraic topology (pdf)
• Notes on condensed mathematics (pdf)

2023 REU: PARTICIPANT PAPERS -- FULL PROGRAM

Dead links are to papers under revision

• Abdalla Aboarab (pdf)
• Gabriel Aguilar. Comparison and rigidity statements in geometry. (pdf)
• Raman Aliakseyeu. Integral currents and Plateau's problem. (pdf)
• Michael Barz. Singularities, Milnor fibrations, and vanishing cycles. (pdf)
• Chad Berkich. An introduction to knot polynomials. (pdf)
• Pedro Bernal (pdf)
• Patrick Borse (pdf)
• Cameron Chang. Images of morphisms: Chevalley's theorem and applications. (pdf)
• Daniel Chen. Regularity of elliptic PDEs. (pdf)
• Hang Chen. An introduction to Shimura varieties. (pdf)
• Ruoyu Chen. Category theory and the van Kampen theorem. (pdf)
• Yanbo Chen. On equivariant $S$-modules and orthogonal spectra. (pdf)
• Yankai Chen (pdf)
• Isaiah Wayne Dailey. An axiomatic approach to the Adams spectral sequence. (pdf)
• Adam Joseph Earnst. Artin reciprocity. (pdf)
• Daniel Espejo. The Riesz-Markov-Kakutani representation theorem. (pdf)
• Brian Fu. Linear Representations of $GL_2(F_p)$. (pdf)
• Noah Geller (pdf)
• Tyler Groshong. Minimal surfaces from the differential viewpoint. (pdf)
• Zhuohan Gu. A study in Markov chains, loop-erased random walk and loop soups. (pdf)
• Federico Guglielmotti. An introduction to It\u{o} calculus. (pdf)
• Robert Hale. Dynamical systems and Birkhoff's ergodic theorem. (pdf)
• James Henry Harbour. Asymptotics of fractional Sobolev norms and $s$-perimeter (pdf)
• William Houston. Vector bundles and Stiefel-Whitney classes. (pdf)
• William Hu. Graph partitioning and multi-way Cheeger inequalities. (pdf)
• Logan R. Hyslop. Whitehead filtrations for computations in topological Hochschild homology. (pdf)
• Daniel Katari (with William Spencer). High conductance expander graphs: constructions and bounds. (pdf)
• Dhruv Kohli. An introduction to Galois theory and the Abel-Ruffini theorem. (pdf)
• Owen Kolean. Schemes and the Riemann-Roch theorem. (pdf)
• Dow Lafevers. Relationship between expansion and the unique games conjecture. (pdf)
• Haoda Li (pdf)
• Yutong (Elena) Li. Behavior of growth for first passage percolation. (pdf)
• Zhenpeng Li. Generalized Landweber exact functor theorem. (pdf)
• Astrid Olivia Lilly. The Brauer group and obstructions to the Hasse principle. (pdf)
• Jeffrey Lu. The springer correspondence via convolution. (pdf)
• Rushil Mallarapu. A motivic approach to the height one telescope conjecture. (pdf)
• Nico Marin Gamboa (pdf)
• Zachary Marks. An introduction to Lie algebras. (pdf)
• Thomas Matheos. Shadowing and structural stability of hyperbolic sets. (pdf)
• Sam Mayo. Hodge-Lefschetz theory, perverse sheaves, and semismall maps. (pdf)
• Hugh Turner McLaurin. Chromatic homotopy theory and spectral algebraic geometry. (pdf)
• Shreya Mukherjee. On the Patterson-Sullivan measure for convex cocompact groups. (pdf)
• Ethan Naegele. It\u{o}'s formulat with applications. (pdf)
• Matthew A. Niemiro. Semi-additivity and ambidexterity. (pdf)
• Mark O'Shea. Lebesgue spaces and the Riesz-Fisher theorem. (pdf)
• Michael Panner. Topological field theory and finite gauge theory. (pdf)
• Mahnav Petersen. An introduction to measure-theoretic probability. (pdf)
• Hadi Rihawi. The prime geodesic theorem. (pdf)
• Liam Rust (pdf)
• Nathaniel Selub. Conway's 99-graph problem: a Boolean satisfiability approach. (pdf)
• Yunhan (Alex) Sheng. Cofreeness of Lubin-Tate theory.
• Thomas Sheppard (pdf) (pdf)
• Shiv Seshan (pdf)
• Hejing Shi. On Mordell-Weil theorem. (pdf)
• Ben Slater. Clifford algebras and Bott periodicity. (pdf)
• Rohan Soni. A course in complex analysis via Brownian motion. (pdf)
• William Spencer (with Daniel Katari). High conductance expander graphs: constructions and bounds. (pdf)
• Sidney Stanbury. The discrete spectrum of the automorphic Laplacian. (pdf)
• Dante Strollo (pdf)
• Baichen Tan. Introduction to linear dimensionality reduction methods. (pdf)
• Sammy Thiagarajan. Concentration and compensated compactness techniques in PDE. (pdf)
• Lauren Tsai. The Riemann-Roch theorem. (pdf)
• Lucas Tucker. Dimensionality reduction and the Fenchel game. (pdf)
• Yuanzheng Wang. Notes on conformal welding of Liouville quantum gravity surfaces. (pdf)
• Annie R. Wei. Nash-Moser iteration. (pdf)
• Jake Wellington. Critical site percolation on the triangular lattice. (pdf)
• Conrad Wichmann. An introduction to de Rham cohomology. (pdf)
• Zongjin (Tracy) Wu. Introduction to Gaussian free field and Liouville quantum gravity. (pdf)
• Colin Yao. Monge-Kantorovich and transportation theory (pdf)
• Richard Ye. Bourgain’s Embedding Theorem, Johnson-Lindenstrauss Lemma, and the Sparsest Cut Problem. (pdf)
• Dino Zavattini. Structural stability of Anosov diffeomorphisms. (pdf)
• Zhenghui (Sunny) Zhang. An equivariant generalization of McDuff's theorem. (pdf)
• Zhuo Zhang. A geometric view of bordism homology. (pdf)
• John Xiaoshu Zhou. Galois representations from elliptic curves. (pdf)
• Kevin Zhou. The connective constant of hexagonal lattice is $\sqrt{2+\sqrt 2}$ (pdf)
• Peter Zhou. Modular curve and modularity theorem. (pdf)
• Jingxuan (Alina) Zhu. Lyapunov exponents and the multiplicative ergodic theorem. (pdf)

2023 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

Dead links are to papers under revision

• Jun An. (pdf)
• Oliver Bock. (pdf)
• Rohan Buluswar. Generating functions and subsets of $\mathbf{N} with constrained spacing. (pdf)
• Wei Cai. Powerful bijections for planar maps and lattice walks. (pdf)
• Dadu Chen. An introduction to Markov chain Monte Carlo method. (pdf)
• Richard Chen. Imaginary quadratic Euclidean domains. (pdf)
• Maryam Contractor. The Pesin entropy formula. (pdf)
• Sacha de Poyen-Brown. Fermat's Christmas theorem. (pdf)
• AJ DeRosa. Bell's theorem in categorical quantum mechanics. (pdf)
• Lucio Figueiredo Filho. An introduction to the fundamental group. (pdf)
• Riley Fisher. (pdf)
• Jeremi Forman-Duranona. A Trojan horse for logic. (pdf)
• Gebeyehu. (pdf)
• Joseph Gorman. Ergodic Markov chains and end behavior. (pdf)
• Arush Guliani. Theoretical models of computations. (pdf)
• Emet Hirsch, A point to set principle from a computational cold start. (pdf)
• Aaron Ho. The Stone-\u{C}ech compactification. (pdf)
• Julian Hovanec. A brief discussion of the dimension drop conjecture. (pdf)
• Jiaqi Hu. (pdf)
• Ray Huang. Bezout and Group Laws on Cubics. (pdf)
• Karlvin Jeanty. (pdf)
• Inanna Khansa. Stochastic differential equations and financial applications. (pdf) Hung Le Tran. Harmony in randomness: the LaPlacian and the heat equation. (pdf)
• Michael Lee. Leray-Hopf weak solutions to the Navier-Stokes equations. (pdf)
• Johnston Liu. Symmetric monoidal preorders and applications to finite spaces. (pdf)
• Neel Maheshwari. Exposition of geometric measure theory and rectifiable sets. (pdf)
• Zane Miller. Existence and uniqueness of stochastic optimal controls. (pdf)
• Will Moller. (pdf)
• Jonathan Norber. Construction of smooth manifolds and tangent spaces. (pdf)
• Mark O'Shea. Lebesgue spaces and the Riesz-Fischer theorem. (pdf)
• Juliet Oliver. Factorization. (pdf)
• Pranav Padmanabhan. (pdf)
• Minh Pham. Weyl integration formula. (pdf)
• Jingwei (Ariana) Qin. Fractal intersections and products via traditional and algorithmic methods. (pdf)
• Nathan Quiroa. Introduction to projective spaces and basic moduli space constructions. (pdf)
• Andrew Razborov. Scaled oscillations and Lipschitz continuity in one dimension. (pdf)
• Otto Reed. Recursive estimation in hidden Markov models. (pdf)
• Tomi Rossini. An exploration of Hausdorff and box counting dimension. (pdf)
• Ezra Santos. Persistent homologies of simple homeomorphic point clouds. (pdf)
• Prakhar Saxena. Martingales in gambling and finance. (pdf)
• Aidan Schmitt. (pdf)
• Simon Seignourel. The Farey tessellation. (pdf)
• Samuel Shen. Topologies of random geometric complexes. (pdf)
• Everett Smith. Lie groups and Ratner's orbit closure theorem. (pdf)
• Adam Strupp. (pdf)
• Jacob Stump. Introduction to the Lebesgue integral. (pdf)
• Junfei Sun. Persistent homology with application in connectivity-loss function for autoencoders. (pdf)
• Justin Tarquino. An introduction to Fourier series and transforms. (pdf)
• Kara Taylor. (pdf)
• Aman Wadhwa. (pdf)
• Zhiren (Su) Wang. Two models of hyperbolic geometry. (pdf)
• Parth Wokhlu. Markov chains and musical composition. (pdf)
• Sally Yang (pdf)
• Ruizhe Ye. (pdf)
• William Zhu. Democratizing the Black-Scholes-Merton model. (pdf)

Tex Help

• Template for texing REU papers: \underline{YOU MUST USE THIS TEX FILE} (tex) (pdf)
• An excellent latex web page (with an REU template with more examples) (web page)
• LaTeX -- A document preparation system (web page)
(web page)
• LaTeX -- A document preparation system (web page)

Guides to writing papers (Steve Kleiman and Dan Kleitman, MIT)

• Writing a math paper (two formats): READ THIS CAREFULLY (pdf) (pdf)
• Another useful guide: READ THIS TOO (pdf)