The University of Chicago Mathematics REU 2021

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

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

2021 REU: Announcement and description of the program (pdf)

2021 REU: Application for University of Chicago students (pdf)

Completed U of C applications should be emailed to Prof. May.

2021 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 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 COME DURING THE PROGRAM

• FIRST WEEK SCHEDULE, June 21-25 (pdf)
• FIRST WEEK ABSTRACTS (pdf)
• SECOND WEEK SCHEDULE and ABSTRACTS, June 28-July 2 (pdf)
• THIRD WEEK SCHEDULE and ABSTRACTS, July 5-July 9 (pdf)
• FOURTH WEEK SCHEDULE and ABSTRACTS, July 12-July 16 (pdf)
• FIFTH WEEK SCHEDULE and ABSTRACTS, July 19-July 23 (pdf)
• SIXTH WEEK SCHEDULE and ABSTRACTS, July 26-30 (pdf)
• SEVENTH WEEK SCHEDULE and ABSTRACTS, August 2-6 (pdf)
• EIGHTH WEEK SCHEDULE and ABSTRACTS, August 9-13 (pdf)
• REU: Table of mentorship pairings (pdf)

Notes and readings for talks

• Links for algebraic topology chicken scratch writing
• First two talks: categorical language (pdf)
• Next three talks: a diagram of categories (pdf)

2021 REU: PARTICIPANT PAPERS -- FULL PROGRAM

Dead links are to papers under revision

• Baring, Geoffrey. Representation theory and quantum groups. (pdf)
• Barz, Michael. Counting lattice points with ergodic theory. (pdf)
• Bergen, Sydney. Elliptic curves and modular forms. (pdf)
• Bonciocat, Ciprian. Algebraic cobordism over the complex numbers. (pdf)
• Borges Prado, Lucca. Existence and uniqueness of a classical solution to \ a mean field game system. (pdf)\
• Brous, Philip. Elliptic curves and the Mordell-Weil theorem. (pdf)
• Burke, Andrew. The Grothendieck-Riemann-Roch theorem. (pdf)
• Carney, Julia. SET and finite affine geometry. (pdf)
• Chen, Xiangtao. The generalized Dyer-Lashof operations for $E_{\infty}$ ring spectra. (pdf)
• Chuang, Alexander. Analyzing the Rubik's cube group of various sizes and solution methods. (pdf)
• Cooper, Benjamin. Structural stability of Anosov diffeomorphisms. (pdf)
• Davidovsky, Ari. The classification of vector bundles over $P^1$. (pdf)
• de Fontnouvelle, Marc. A logical insight into the theory of computation. (pdf)
• Donald, Antonio. Shifts and ergodic theory. (pdf)
• Feng, Yuyang. Percolation on uniform infinite triangulations. (pdf)
• Fischer, Noah. Stochastic calculus and the Black-Scholes-Merton model. (pdf)
• Fox, Julian. Besicovitch sets, Kakeya sets, and their properties. (pdf)
• Gao, Xuefei. Stochastic calculus and applications to financial modelling. (pdf)
• Ghorbani, Alexander. The tame geometry of O-minimal structures. (pdf)
• Goldman, Ben. An overview of Lie theory and Peter Weyl theorem. (pdf)
• Hale, Henry. An exposition of a proof of Gabriel's theorem. (pdf)
• Hlavinka, Joseph. Motivic homotopy theory and cellular schemes. (pdf)
• Hopper, John. Ferromagnetic phase transitions in a stacked lattice ising model. (pdf)
• Horowitz, Lucy. The Poincar\'e group. (pdf)
• Huang, Junzhi. On the generators of the real cobordism ring. (pdf)
• Jeon, Hye Woong. Overview of the multifractal model of asset returns. (pdf)
• Jiang, Tianchong. Wigner's semicircle law for Gaussian random matrices. (pdf)
• Kaipa, Rajiv Krishna. Presheaves with four operations. (pdf)
• Kewang, Yuqin. Clifford algebras and Bott periodicity. (pdf)
• Kuhrman, Judson. The disc embedding theorem for $4$-manifolds. (pdf)
• Lehmacher, Connor. Chain theories. (pdf)
• Lei, Heidi. Duality theorems in stable homotopy theory. (pdf)
• Li, Jiatong. A brief overview of graph theory: Erdos-Renyi random graph model and small world phenomenon. (pdf)
• Li, Wenxuan (Wilson). Number rigidity in point processes. (pdf)
• Li, Yangqing (Gabrielle). On the Bockstein and the Adams spectral sequences. (pdf)
• Lin, Chenjia. A roadmap to the Gauss-Bonnet theorem. (pdf)
• Liu, Christian. Brownian motion as the limiting distribution of random walks. (pdf)
• Liu, Huiting. Two-dimensional topological quantum field theories and Frobenius algebras. (pdf)
• Martins, Felipe Teixeira Rodrigues. Introduction to the K-theory in topological matter. (pdf)
• Melman-Rogers, Andrew. Luna's \'etale slice theorem. (pdf)
• Miller, Spencer. An introduction to partitions and their cranks. (pdf)
• Mitra, Ajay. Spin manifolds and positive scalar curvature. (pdf)
• Molnar, Anton. $C^*$-algebras and operator $K$-theory. (pdf)
• Naughton, John. Schubert calculus. (pdf)
• Parish, Jacob. Error-correcting codes and algebraic function fields. (pdf)
• Perez-Stark, Helena. Hyperbolic dynamical systems and the Birkhoff-Smale theorem. (pdf)
• Prodromidis, Jason. The Riemann zeta function and random matrix theory. (pdf)
• Qing, Yutong (Tony). Billiards, hard ball systems, and Boltzmann's ergodic hypothesis. (pdf)
• Shapiro, Andrey. An averaging approach to Frankl's conjecture. (pdf)
• Shastry, Aadeesh. Wishart processes and financial applications. (pdf)
• Sheng, Alex. On realizing rational and polynomial cohomology rings. (pdf)
• Solak, Hakan. Solution to the Plateau problem for maps from the unit disk. (pdf)
• Soliman, Aly. A beginner's guide to modular curves. (pdf)
• Song, Jingxuan (Erin). Hyperbolic 3-manifolds. (pdf)
• Srivastava, Eha. An introduction to the Burau representation of the Artin braid group. (pdf)
• Sun, Minghan. Geodesics and the Hopf-Rinow theorem. (pdf)
• Tamura, Ryan Kenichi. An analysis of elliptic curves via the BSD conjecture. (pdf)
• Thyme, Keyer. Dijkgraaf-Witten theory as a topological quantum field theory. (pdf)
• Turer, George. Arnaud's method in $C^1$ billiards. (pdf)
• Venkatraman, Arjun. Characteristic classes and the Thom isomorphism. (pdf)
• Wandsnider, Ryan. A detailed exposition for the pseudo-arc. (pdf)
• Wang, Cathy. Nonstandard extensions, hyperreals, an application to Szemeredi regularity lemma. (pdf)
• Williams, Ethan. Understanding generalized group sieving through $\lambda$ rings. (pdf)
• Wu, Xinkai. Random matrices and determinantal point process. (pdf)
• Wu, Yinchen. Cut points of Brownian motion on Riemannian manifold. (pdf)
• Wu-Yip, Yannis. Well-behaving dynamics over $Q_p$. (pdf)
• Xu, Ruochuan (Alex). Intersections of Brownian paths. (pdf)
• Yao, Wang. A glimpse into homological mirror symmetry. (pdf)
• Ye, Yiheng. Sheaf cohomology and algebraic de Rham theorem. (pdf)
• Yu, Huishi. A proof of the Mordell-Weil theorem. (pdf)
• Zavattini, Dino. A regularity lemma of Journ\'e. (pdf)
• Zeng, Jiyue, Stochastic calculus and intro to mean field game theory. (pdf)
• Zhang, Suixin (Cindy). $p$-Adic numbers, quadratic forms, and the Hasse-Minkowski theorem. (pdf)
• Zhang, Xinyi (Sara). Inverse Galois problem for $\mathbb{C}(t)$. (pdf)
• Zheng, Yunru. ABP estimate and it applications. (pdf)
• Zhou, Sharon. Galois theory of commutative rings: a historical perspective. (pdf)
• Zweifler, Jake. Algebraic geometry and divisors. (pdf)

2021 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

Dead links are to papers under revision

• Adler, Ben. Hilbert spaces and the Riesz representation theorem (pdf)
• Aguilar Perez, Gabriel. The nonsqueezing theorem. A journey through symplectic geometry. (pdf)
• Baur, Eli. The appeal of nonstandard analysis. (pdf)
• Berkich, Chad. Homology, cohomology, and the de Rham theorem. (pdf)
• Bhardwaj, Aditya. The imaginary-time Feynman path integral. (pdf)
• Bruce, Cade. Topological data analysis for financial time-series. (pdf)
• Chang, Cameron. Quadratic reciprocity, quadratic forms, and primes of the form $x^2 + ny^2$ (pdf)
• Chen, Zhaojun (Emma). On the additivity of trisection genus. (pdf)
• Cravitz, Will. An introduction to the word problem for groups. (pdf)
• Dubey, Kabir. The Fourier uncertainty principles. (pdf)
• Geller, Noah. Dynamics in the plane and the Poincar\'e-Benon theorem. (pdf)
• Gerhard, Nathaniel. Fixed point logics on finite models. (pdf)
• Golovanov, Rebecca. Finite fields and the M\"obius function. (pdf)
• Han, Michael. Three types of dimension and an application. (pdf)
• Jacobs, Jason. Number theory in cryptography. (pdf)
• Jin, Ziqian (Alexa). Cantor sets in topology, analysis, and financial markets. (pdf)
• Labalme, Steven. Basic algebra in inorganic chemistry. (pdf)
• Lai, Bill. Introduction to first order logic and model theory. (pdf)
• Li, Jiatong (Logen). A brief overview of graph theory: Erdos-Renyi random graph model and small world phenomenon. (pdf)
• Mehrotra, Shivesh Ram. Fourier analysis on finite groups and applications to random walks. (pdf)
• Niemiro, Matthew. The derived functor approach to sheaf cohomology. (pdf)
• Petrou-Zeniou, Andreas. Least squares and instrumental variable estimation in econometrics. (pdf)
• Roscoe, Athena. Pappus' theorem and 7 proofs. (pdf)
• Ross, Jason. Stochastic calculus. (pdf)
• Slater, Benjamin. The Frobenius map and Kunz's theorem. (pdf)
• Struck, Tanner. Field theory for compass and straightedge impossibility proofs. (pdf)
• Weinstein, Max. Combinatorial perspectives on Borsuk-Ulam and Brouwer. (pdf)
• Wilson, Ari. Stochastic calculus and arbitrage-free options pricing. (pdf)
• Wu, Carl. Universal approximation theorem. (pdf)
• Wu, Kevin. Riemann-Roch through the dollar game. (pdf)
• Xu, Nancy. Reciprocity Laws. (pdf)
• Xu, Ruize (Richard). A comparison between Diffie-Hellman and RSA. (pdf)
• Yang, Qingchuan (Tony). Construction of the fundamental group in algebraic topology. (pdf)
• Yu, Bradley. Stochastic calculus and numerical methods for stochastic differential equations. (pdf)
• Zhang, Emily. Law of quadratic reciprocity. (pdf)
• Zhang, Jack. Introduction to differential geometry -- a graphics perspective. (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)
• A first guide to mathematical writing, by Chicago's own Philip Lo (overleaf)
• 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)