The University of Chicago Mathematics REU 2020

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

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

2020 REU: Announcement and description of the program (pdf)

2020 REU: Application for University of Chicago students (pdf)

Completed U of C applications should be returned to E314.

2020 REU: Application for non-University of Chicago students (pdf)

To apply, go to MathPrograms: https://www.mathprograms.org/db/login/ja><\H4>

Acceptance forms

2020 REU: Acceptance Form for the Apprentice program (pdf)
2020 REU: Acceptance Form for the Full program (U of C students) (pdf)
2020 REU: Acceptance Form for the Full program (non-U of C students) (pdf)

Links to past REUs

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)
Link to the 2013 REU (Go)
Link to the 2012 REU (Go)
Link to the University of Chicago VIGRE program, 2000-11, and early REUs (Go)

FIRST WEEK SCHEDULE, June 22-26 (pdf)
FIRST WEEK ABSTRACTS (pdf)
SECOND WEEK SCHEDULE, June 29-July 3 (pdf)
SECOND WEEK ABSTRACTS (pdf)
THIRD WEEK SCHEDULE, July 6-July 10 (pdf)
THIRD WEEK ABSTRACTS (pdf)
FOURTH WEEK SCHEDULE, July 13-July 17 (pdf)
FOURTH WEEK ABSTRACTS (pdf)
FIFTH WEEK SCHEDULE, July 20-July 24 (pdf)
FIFTH WEEK ABSTRACTS (pdf)
SIXTH WEEK SCHEDULE, July 27-31 (pdf)
SIXTH WEEK ABSTRACTS (pdf)
SEVENTH WEEK SCHEDULE, August 3-7 (pdf)
SEVENTH WEEK ABSTRACTS (pdf)
EIGHTH WEEK SCHEDULE, August 10-14 (pdf)
REU: Table of mentorship pairings (pdf)

Notes and readings for talks

Links for algebraic topology topics are in the Abstracts
Slides of Agnes Beaudry's talk ``Ants on pants" (pdf)
Notes written during Angelica Osorno's talk (pdf)
Notes from Doug Ravenel's talk ``The coffee cup and best tricks, and their homotopy theoretic explanations" (pdf)
Notes from Inna Zakharevich's first talk ``Scissors congruence" (pdf)
Notes from Matthew Morrow's talk ``Perfectoid spaces" (pdf)
Danny Calegari's notes on fiber bundles (pdf)
Pedro Gaspar Marques Da Silva and Henrik Matthiesen ``Minimal surfaces in 3-space and Bernstein's theorem 1 (pdf)
Pedro Gaspar Marques Da Silva and Henrik Matthiesen ``Minimal surfaces in 3-space and Bernstein's theorem 2 (pdf)
Examples of minimal surfaces (slides) (pdf)
Peter May slide talk ``Finite topological spaces" (pdf)
Peter May slide talk ``Glimpses of equivariant algebraic topology" (pdf)

Miscellaneous program links

Link to Laci Babai's REU web page: (Go)
FINITE SPACES: a book in progress: selected readings to be recommended (pdf)
CHARACTERISTIC CLASSES: a book in progress: selected readings may be recommended (pdf)
LOCALIZATION AND COMPLETION: Simplified excerpts from More concise algebraic topology (slides) (pdf)

The eighth week schedule lists participant talk speakers and titles

2020 REU: PARTICIPANT PAPERS -- FULL PROGRAM

Dead links are to papers under revision

Yiqiao Bao. Primes of the form $x^2+ny^2$. (pdf)

Elle Bower. Impossibility of the classification of finite spaces up to weak homotopy equivalence. (pdf)

Alex Burka. Morley's theorem. (pdf)

Andrew Burke. Hopf algebras and exotic characteristic classes. (pdf)

Yuchen Chen. Fulton's trace formula and elliptic curves over finite fields. (pdf)

Roberto Cohen. A motivated introduction to Gromov's h-principle. (pdf)

Sam Craig. Schram-Loewner evolution as a universal scaling limit. (pdf)

Ari Davidovsky. The number of countable models of a complete theory. (pdf)

Kenneth DeMason. Optimal mass transport and the isoperimetric inequality. (pdf)

Lihuang Ding. A simpler proof of Atiyah-Segal completion theorem. (pdf)

Alex Eastman. Quantum ergodicity on hyperbolic surfaces. (pdf)

Joshua Enwright. Some norms for Mackey functors. (pdf)

Jacob B. Fiedler (with Schondorf). On the existence and dimension of Besicovitch sets. (pdf)

Nitya Gadhiwala. Intersections and collisions of simple random walks in $\mathbb{Z}^d$. (pdf)

Rohin Gilman. An overview of bond percolation. (pdf)

Ben Goldman. Progress on the invariant subspace problem. (pdf)

Sayali Gove. The basics of the probabilistic method. (pdf)

Letong (Carina) Hong. Model categories and cofibrant posets. (pdf)

John Hopper. Basic Schubert calculus without cohomology. (pdf)

Samanda (Yuting) Hu. Modular forms and Hecke operators. (pdf)

Chuhao Huang. Mirror symmetry of elliptic curves. (pdf)

Max Johnson. (Pro-$G$)-spectra and pro-($G$)-spectra. (pdf)

Kenz Kallal. Representation theory at infinity: automorphic forms and the Selberg trace formula. (pdf)

Nathan Kapsin. A brief overview of introductory topics in Lee's ``Introduction to smooth manifolds" (pdf)

Judson Kuhrman. Characteristic classes. (pdf)

Zhuoming Lan. Floer cohomology and Fukaya category. (pdf)

Ethan Lewis. Brownian motion and Ito's formula. (pdf)

Gabrielle Yanqing Li. Classification of bundles and orientation. (pdf)

Wenxuan Li. Sobolev spaces and Calderon's inverse problem. (pdf)

Yuanpu Liang. Mean curvature of Riemannian hypersurface under the exponential map. (pdf)

Connor Lockhart. The Baldwin-Lachlan proof of Morley's theorem. (pdf)

Elias Manuelides. What are spectra? (pdf)

Isaac Martin. Algebraic de Rham cohomology and the Hodge spectral sequence. (pdf)

F. Curtis Mason. A survey in model-theoretical forcing. (pdf)

Jessica Metzger. Phase transitions in lattice systems. (pdf)

Sabrina Mi. Algebraic statistics. (pdf)

Jinghong Miao. Viscosity solutions of the Eikonal equations. (pdf)

Ajay Mitra. The image of the $J$ homomorphism (pdf)

Shourya Mohaniya. Fractal geometry and its application to continued fractions. (pdf)

Mishal Mrinal. The Gaussian free field and SLE coupling. (pdf)

Anushka Murthy. Representations of matroids and the excluded minor theorems. (pdf)

Anushka Murthy. On the combinatorial parameters of highly symmetric graphs. (pdf)

Beckham Myers. The homotopy type of the cobordism category. (pdf)

Srihari Narayanan. Applications of the braid group and wider knot theory to Chern-Simons theory. (pdf)

Stephanie Youngmi Oh. Inner product spaces and Fourier series. (pdf)

Vedant Pathak. An introduction to stochastic calculus. (pdf)

Lucca Borges Prado. Differntial games and viscosity solutions. (pdf)

Qing Qi. Symmetry group of a tessellation in the hyperbolic plane. (pdf)

Benjamin Rapport. Applications of stochastic calculus to financial modeling. (pdf)

Qiuyu Ren. Quantization commutes with reduction. (pdf)

Sivakorn Sanguanmoo. Optimal stopping time and its applications to economic models. (pdf)

Tomohiro Sawada. Classification of exotic spheres: an exposition. (pdf)

Mark Schachner. Enlargements and the non-standard perspective. (pdf)

Ethan Schondorf (with Fiedler). On the existence and dimension of Besicovitch sets. (pdf)

Ryan Simeon. An operadic description of algebraic quantum field theories. (pdf)

Aleksander Skenderi. Related interpretations of elliptic curves. (pdf)

Jennifer Sun. Changing ground category in operad theory. (pdf)

Arjun Venkatraman. Heights and the Mordell-Weil theorem. (pdf)

Xiaomeng Wang. Stochastic calculus and volatility models. (pdf)

Ethan Williams. The Rota-Welsh conjecture for representable matroids. (pdf)

Yinchen Wu. Construction of small $(n,k)$ cylinders and $n$-rectifiable sets for Nikodym sets. (pdf)

Wenxi Yao. Koszul duality of quadratic operads. (pdf)

Naimeng Ye. Equivariant $K$-theory and the Atiyah-Segal completion theorem. (pdf)

Xifan Yu. A survey of the Neggers-Stanley conjecture. (pdf)

Shangjie Zhang. Multiplicative structures induced by $N_{\infty}$ operads. (pdf)

Yueheng Zhang. Approximating graph conductance: from global to local. (pdf)

Siqi Clover Zheng. Frobenius algebra structure in Hopf algebra and cohomology ring with Poincar\'e duality. (pdf)

Sharon Zhou. Types of homotopy in simplicial complexes and finite spaces. (pdf)

Stanley Zhu. An introduction to the Loewner differential equation. (pdf)

2020 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

Dead links are to papers under revision

Hong Thien An Bui. Classifying the finite subgroups of $SO_3$. (pdf)

Don Assamongkol. Cubic graph symmetries. (pdf)

Ribhav Bose. The elliptic curve factorization method. (pdf)

Shu-Nan Justin Chang. An introduction to category theory and the Yoneda lemma. (pdf)

Andrew Chen. Baire categories, continuous functions, and approximations. (pdf)

Benjamin Cooper. The Schwarzian derivative in one-dimensional dynamics. (pdf)

John M. Dewhurst. Hilbert's theorem on immersion of the hyperbolic plane. (pdf)

Runtong Ding. Fourier series and its applications to geometry an equidistribution theorem. (pdf)

Antonio Donald. Dynamics of maps of the circle. (pdf)

Marc de Fontnouvelle. Three sideways reflections on Ramsey theory. (pdf)

Alexander Ghorbani. Applications of representation theory to combinatorics. (pdf)

Grayson Montgomevy Graham. The ring of symmetric polynomials. (pdf)

Jordan Matthew Hebert. Completeness in modal logic. (pdf)

Ling Hu. Law of quadratic reciprocity. (pdf)

Hye Woong Jeon. Equivalent notions of entropy under ergodicity. (pdf)

Raunak Kundagrami. Hopf fibrations. (pdf)

Astrid (Anran) Li. Four types of cryptosystems and related algorithms. (pdf)

Chenjia Lin. Introductory differential topology and an application to the Hopf fibration. (pdf)

Tarika Mane. Galois actions on torsions of elliptic curves. (pdf)

Spencer C. Miller. $MMH^*_{32}$ from scratch: an introduction to hash functions. (pdf)

Karol Mukhamediyeva. Graph theory, cohomology, and paradoxes in social choice and logic. (pdf)

Ethan Naegele. Random walk meeting times on graphs. (pdf)

Jinseo Park. Representation of semisimple Lie algebras. (pdf)

Helena Perez-Stark. Elliptic curves and Mordell's theorem. (pdf)

Alexa Pomerantz. An introduction to the $p$-adic numbers. (pdf)

Logan James Quick. $p$-adic absolute values. (pdf)

Irene Ryu. Introduction to number theory and cryptography. (pdf)

Vivek Anthonv Sasse. Classification of the 17 wallpaper groups. (pdf)

Andrey Shapiro. Billiard dynamics and Masur's criterion. (pdf)

Olga Shevchuk. Introduction to elliptic curve cryptography. (pdf)

Aly Soliman. Laws of large numbers and Khinchin's constant. (pdf)

Keyer Thyme. Priority methods in computability theory. (pdf)

Ryan Wandsnider. The fundamental theorem of algebra over the tropical semiring. (pdf)

Cathy Wang. The Lovasz local lemma, $K$-coloring, and applications in graph theory. (pdf)

David Wang. Measure theory and central limit theorem. (pdf)

David Wu. Applications of M\"obius inversion on partially ordered sets. (pdf)

Xinkai (Kai) Wu. Finite projective planes an quadratic forms with applications. (pdf)

Yannis Wu-Yip. Classification of finite groups. (pdf)

Ruochuan Xu. Permutation representations. (pdf)

Jialin Yang. Super five of Ramsey theory. (pdf)

Lingyue Yu. Stochastic calculus on Brownian motion and stochastic integration. (pdf)

Tianyi Zhang. A game theoretic discussion of a repeated game model inspired by shoot 'em up video games. (pdf)

Yiduan Zheng. $p$-Adic numbers, $\mathbb{Q}_p$, and Hensel's lemma. (pdf)

Yuerong Zhuang. Random walks on finite groups. (pdf)

Jake Zweifler. Elliptic curves and complex multiplication. (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\ )