The University of Chicago Mathematics REU 2022

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

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

2022 REU: Announcement and description of the program (pdf)

2022 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)

2022 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 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)

LINKS TO COMING DURING THE PROGRAM

• FIRST and SECOND WEEK SCHEDULES, June 13-17 and June 20-24 (pdf)
• FIRST WEEK Abstracts (pdf)
• SECOND WEEK ABSTRACTS (pdf)
• THIRD and FOURTH WEEK SCHEDULES, June 27-July1 and July 5-July9 (pdf)
• THIRD and FOURTH WEEK ABSTRACTS (pdf)
• FIFTH and SIXTH WEEK SCHEDULES, July 11-July 15 and July 18-July 22 (pdf)
• FIFTH and SIXTH WEEK ABSTRACTS (pdf)
• SEVENTH and EIGHTH WEEK SCHEDULES, July 25-July 29 and August 1-August 5 (pdf)
• SEVENTH and EIGHTH WEEK ABSTRACTS (pdf)
• REU: Table of mentorship pairings (pdf)

Notes and readings for talks

• Zhilin Luo's notes ``Sum of two squares" (pdf)
• Links for algebraic topology topics are in the Abstracts

2022 REU: PARTICIPANT PAPERS -- FULL PROGRAM

Dead links are to papers under revision

• Fatima Nasir Abbasi. On the cocompleteness of Cat. (pdf)
• Abdalla Aboarab. Algorithmic unsolvability of manifold and CW-complex simple connectedness. (pdf)
• Gabriel Aguilar. Ricci flow and the geometrization conjecture. (pdf)
• Matthew Akuzawa. Monte Carlo simulations and applications in sports. (pdf)
• Keita Allen. Computing the homology of the $\mathbb{C}$-motivic lambda algebra. (pdf)
• Aiden Bailey. Rat-catching: a pursuit-evasion game on undirected graphs. (pdf)
• Michael Barz. The monodromy of the hypergeometric equation. (pdf)
• Patrick Borse. Floer homologies and the Arnold conjectures. (pdf)
• Finn Braaten. Introduction to the thermodynamic formalism. (pdf)
• Zhaojun (Emma) Chen. Construction and generalization of near-homogeneous tornaments. (pdf)
• Ziyue Chen. Generating Functions and Their Applications. (pdf)
• Benjamin Cooper. Critical orbits and the filled julia set. (pdf)
• Hang Du. A glimpse into Schramm-Lowewner evolution. (pdf)
• Xingzhu Fang. An introduction to geometric Satake equivalence. (pdf)
• Marc de Fontnouvelle. An introduction to the theory of graph limits. (pdf)
• Ben Goldman. Energy methods and the visibility conjecture. (pdf)
• Bryce Goldman. Graded monoidal categories and internalization. (pdf)
• Rebecca Golovanov. Elliptic curves and the Weil conjectures. (pdf)
• William Griffin. Mathematical modeling of derivative pricing. (pdf)
• Henry Herzog. Topological data analysis: an exposition in stability theory. (pdf)
• Lucy Horowitz. Non-associativity of the smash product. (pdf)
• Ruohan Hu. Proof of Riemann-Roch by way of Cech cohomology. (pdf)
• Yuqiao Huang. $KO$-orientability and $w_2$ classes. (pdf)
• Honghao Jing. Groups of exotic spheres. (pdf)
• Yuqin Kewang. Connective periodic spectra revisited. (pdf)
• Dain Kim. Level Set Approach to Mean Curvature Flow. (pdf)
• Muqi (Bill) Lai. Quasirandomness, information, and Szemeredi's regularity lemma. (pdf)
• Hanchen Li. Properties and applications of graph Laplacians. (pdf)
• Wenqi Li. The generic vanishing theorem. (pdf)
• Wenxuan (Wilson) Li. Equidistribution in number theory and Duke's theorem. (pdf)
• Siwei Liang. Teichmuller theory and hyperbolization of three-Manifolds. (pdf)
• Elias Manuelides. Optimal control: large deviations and viscosity solutions. (pdf)
• Zachary Marks. Riemann surfaces, branched coverings, and field extensions. (pdf)
• Andrew (Drew) Melman-Rogers. Hypercohomology and the algebraic de Rham's theorem. (pdf)
• Ethan Naegele. Analyzing random walks with electrical networks: an introduction. (pdf)
• Matthew Niemiro. The Adams Conjecture and the K-theory of finite fields (with Zhong Zhang). (pdf)
• Arjun Nigam. An introduction to stacks. (pdf)
• Jacob Parish. Uncountably-categorical theories. (pdf)
• Helena Perez-Stark. The Furstenberg-Kesten theorem for products of random matrices. (pdf)
• Mariya Pershyna. A brief overview of chaos. (pdf)
• Yaxin (Casey) Qi. A brief introduction to flag algebra. (pdf)
• Luke Schneider. Hausdorff dimension and Falconer's distance conjecture. (pdf)
• Benjamin Scott. Optimal transport applied to geometric and functional inequalities. (pdf)
• Nathaniel Selub. Uniformization of surfaces with Riemannian metrics by extremizing determinants of LaPlacians. (pdf)
• Ray Shang. Relating complex orientation to Chern classes and formal group laws. (pdf)
• Andrey Shapiro. Explainable clustering. (pdf)
• Alex Sheng. Complex multiplication. (pdf)
• Ben Slater. Determinantal point processes and the Eynard-Mehta theorem. (pdf)
• Rohan Soni. Roth's theeorem: a special case of Szemeredi's theorem. (pdf)
• Eha Srivastava. The Adams spectral sequence and the Hopf invariant one problem. (pdf)
• Rachel Struck. Adjunctions and the monadicity theorem. (pdf)
• David Suh. Mean field games (pdf)
• Billion (Bilin) Sun. The genesis of the $p$-adic number fields. (pdf)
• Nick Sweeney. Wigner's semicircle law (with Xinyi Zhang). (pdf)
• Jen Tang. Tangent space properties of manifolds and rectifiable sets. (pdf)
• Ryan Wandsnider. An intuitive introduction to spectral sequences. (pdf)
• Yutong Wu. Rates of convergence and regularity in a homogenization process. (pdf)
• Yannis Wu-Yip. $L$-functions over a number field. (pdf)
• Shuhang Xue. Brown representability and its variants in context. (pdf)
• Dino Zavattini. Tate Cohomology. (pdf)
• Xinyi (Sara) Zhang. Wigner's semicircle law (with Nick Sweeney). (pdf)
• Zhenghui (Sunny) Zhang. Characterization of nerves of posets. (pdf)
• Zhong Zhang. The Adams Conjecture and the K-theory of finite fields (with Matthew Niemiro). (pdf)
• Jingxuan (Alina) Zhu. An introduction fo the theory of oscillatory integrals. (pdf)

2022 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

Dead links are to papers under revision

• Raman Aliakseyeu. Bernstein's theorem and other basics of minimal surface theory. (pdf)
• Jiahong Cai. Markov chains and applications in options markets (pdf)
• Jessica Cao. Erd\"os distance problems. (pdf)
• Guanyu (James) Chen. Introduction to basic properties of Markov chain and its application in simple random walk. (pdf)
• Ethan Dintzner. Proving the Napoleon-Barlotti theorem with affine geometry. (pdf)
• Josh Edington. Lebesgue integrals and the Basel problem. (pdf)
• Austin Feng. Introduction t Lie algebras, Engel's theorem, and Lie's theorem. (pdf)
• Ishaan Goel. Introduction to Martingales with an application in finance. (pdf)
• Robert Hale. The Gauss-Bonnet theorem. (pdf)
• David Hu. Markov chains in finite state spaces. (pdf)
• Ruopu (Harley) Huang. An introduction to algebraic coding theory. (pdf)
• Dhruv Kohli. An introduction to Galois theory and the Abel-Ruffini theorem. (pdf)
• Charles Dow LaFevers. A combinatorial identity involving roots of unity. (pdf)
• Rachel Lee. Shifts and their classification. (pdf)
• Daniel Li. Stochastic calculus for arbitrage free pricing with stochastic volatility. (pdf)
• Elena Li. The Fermat-Euler theorem and its application to public key cryptography. (pdf)
• Angela Liu. Introduction to topological data analysis. (pdf)
• Hangyu (Jerry) Liu. A brief introduction to knot theory and the Jones polynomial. (pdf)
• Roy Long. An introduction to Martingales with applications to betting games. (pdf)
• Zane Maggio. Cell structures on Grassmannians. (pdf)
• Ian Magnell. Linear representations of finite groups. (pdf)
• Joseph (Nico) Marin Gamboa. Morse theory for partially ordered sets in context. (pdf)
• Shreya Mukherjee. Ergodic properties of the L\"uroth and Gauss maps. (pdf)
• Jian Park. On the cardinalities and isomorphisms of finite fields. (pdf)
• Mahnav Ethan Petersen. An introduction to Fourier series and their applications. (pdf)
• Aditya Raman. Discrete time Martingales and applications to random walks. (pdf)
• Jay Sagrolikar. Random motion and random trees. (pdf)
• Tianqi (Charene) Shen. An introduction to non-synchronous trading. (pdf) (pdf)
• Alex Stern. Introduction to category theory and the Yoneda lemma. (pdf)
• Samanthak Thiagarajan. Theory of Laplace transforms and their applications. (pdf)
• Berkin Ucar. Introduction to Lie algebras and superalgebras with applications in physics. (pdf)
• Haoshu Wang. Advantages and applications of quantum game theory. (pdf)
• Yuzhou Wang. Markov chain and Markov decision process. (pdf)
• Zongjin (Tracy) Wu. Brownian motion and random triangulations of the circle. (pdf)
• Haolin (Tony) Zhong. Introduction to the chip-firing game. (pdf)
• Haokai (Kevin) Zhou. Homogeneous Markov chains in discrete time. (pdf)
• Jake Zummo. An introduction to geometric group theory. (pdf)

Tex Help

• Template for texing REU papers: 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)