University of Chicago REU 2014


APPRENTICE PROGRAM: Linear Algebra and Combinatorics

GEOMETRY: Surfaces and comutators

ALGEBRA, TOPOLOGY, ETC: Scissors congruence groups

TOPOLOGY: finite spaces and larger contexts

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

Tex Help


Dead links are to papers under revision

  • Calista Bernard. Regularity of solutions to the fractional Laplace equation. (pdf)
  • Joshua Biderman, Kevin Cuddy, Ang Li, and Min Jae Song. On sensitivity of $k$-uniform hypergraph properties. (pdf)
  • Ben Call. Introduction to Furstenberg's x2x3 conjecture. (pdf)
  • Zefeng Chen. Quasi-preference: choice on partially ordered sets. (pdf)
  • Sean Colin-Ellerin. Distribution theory and applications to PDE. (pdf)
  • Kevin Cuddy. See Joshua Biderman. (pdf)
  • Kyle Gannon. Introduction to the Keisler order. (pdf)
  • Claudio Gonzales. Polynomials in the Dirichlet problem. (pdf)
  • Justin Guo. Analysis of chaotic systems. (pdf)
  • Jackson Hance. Hodge theory and elliptic regularity. (pdf)
  • Jordan Hisel. Addition law on elliptic curves. (pdf)
  • Yifeng Huang. Characteristic classes, Chern classes and applications to intersection theory. (pdf)
  • Sofi Gjing Jovanovska. Beck's theorem characterizing algebras. (pdf)
  • Sameer Kailasa. Topics in geometric group theory. (pdf)
  • Simon Lazarus. Basic algebraic geometry and the 27 lines on a cubic surface. (pdf)
  • Fizay-Noah Lee. Kummer's theory on ideal numbers and Fermat's last theorem. (pdf)
  • Ang Li. See also Joshua Biderman. The Lefschetz fixed point theorem and solutions to polynomials over finite fields. (pdf)
  • Siwei Li. Strategies in the stochastic iterated prisoner's dilemma. (pdf)
  • Jason Liang. Measure-preserving dynamical systems and approximation techniques. (pdf)
  • Lucas Lingle. Intro to class field theory and the Chebotarev theorem. (pdf)
  • Ben Lowe. The local theory of elliptic operators and the Hodge theorem. (pdf)
  • Benjamin McKenna. The type problem: effective resistance and random walks on graphs. (pdf)
  • Redmond McNamara. Introduction to de Rham cohomology. (pdf)
  • Jing Miao. Convergence of Fourier series in $L^p$ space. (pdf)
  • Victor Moros. The zeta function and the Riemann hypothesis. (pdf)
  • Sun Woo Park. An introduction to dynamical billiards. (pdf)
  • Nicholas Rouse. Compact Lie groups. (pdf)
  • Bryan Rust. A theorem of Hopf in homological algebra. (pdf)
  • Maximilian Schindler. Basic Schubert calculus. (pdf)
  • Noah Schoem. Well-foundedness of countable ordinals and the Hydra game. (pdf)
  • Joel Siegel. Expander graphs. (pdf)
  • Maria Smith. Kolmogorov-Barzdin and spacial realizations of expander graphs. (pdf)
  • Min Jae Song. See Joshua Biderman. (pdf)
  • Blaine Talbut. The uncertainty principle in Fourier analysis. (pdf)
  • Victor Zhang. Incompleteness in ZFC. (pdf)
  • Yuzhou Zou. Modes of convergence for Fourier series. (pdf)


    Dead links are to papers under revision

  • Will Adkisson. Geodesics of hyperbolic space (pdf)
  • Fernando Al Assal. Invitation to Lie algebras and representations. (pdf)
  • John Alhadi. Exploration of various items in linear algebra. (pdf)
  • Kevin Barnum. The axiom of choice and its implications. (pdf)
  • Karen Butt. An introduction to topological entropy. (pdf)
  • Rachel Carandang. Generalization in machine learning: the Vapnik-Chervonenkis inequality. (pdf)
  • David Casey. Galois theory. (pdf)
  • Spencer Chan. Compass and straightedge applications of field theory. (pdf)
  • Cindy Chung. An introduction to computability theory. (pdf)
  • Brenden Collins. An introduction to Lie theory through matrix groups. (pdf)
  • Paul Duncan. The Gamma function and the Zeta function. (pdf)
  • Adam Freymiller. Markov chain tree theorem and Wilson's algorithm. (pdf)
  • Michael Hochman. Chutes and ladders. (pdf)
  • Yunpeng Ji. Discussion of the heat equation. (pdf)
  • Ken Jung. Brouwer's fixed point theorem and price equilibrium. (pdf)
  • Josh Kaplan. Binary quadratic forms, genus theory, and primes of the form p=x^2+ny^2. (pdf)
  • James W. Kiselik. Conic and cubic plane curves. (pdf)
  • Daniel Kline. The structure of unit groups. (pdf)
  • Stefan Lance. A survey of primality tests. (pdf)
  • Scarlett Li. Brouwer's fixed point theorem: the Walrasian auctioneer. (pdf)
  • Jack Liang. Rudimentary Galois theory. (pdf)
  • Larsen Linov. An introduction to knot theory and the knot group. (pdf)
  • David Mendelssohn. Operations and methods in fuzzy logic. (pdf)
  • Matthew Morgado. Modular arithmetic. (pdf)
  • Seth Musser. Weakly nonlinear oscillations with analytic forcing. (pdf)
  • Adele Padgett. Fundamental groups: motivation, computation methods, and applications. (pdf)
  • Daniel Parker. Elliptic curves and Lenstra's factorization algorithm. (pdf)
  • Robert Peng. The Hahn-Banach separation theorem and other separation results. (pdf)
  • Peter Robicheaux. Calculation of fundamental groups of spaces. (pdf)
  • Avery Robinson. The Banach-Tarski paradox. (pdf)
  • Zachary Smith. Fixed point methods in nonlinear analysis. (pdf)
  • Aaron Geelon So. Symbolic dynamics. (pdf)
  • Matthew Steed. Proofs of the fundamental theorem of algebra. (pdf)
  • Ridwan Syed. Approximation resistance and linear threshold functions. (pdf)
  • Shaun Tan. Representation theory for finite groups. (pdf)
  • Zachry Wang. An introduction to stochastic calculus and Black-Scholes option pricing. (pdf)
  • Nolan Winkler. The discrete log problem and elliptic curve cryptography. (pdf)
  • Eric Yao. Plane conics in algebraic geometry. (pdf)
  • Joo Heon Yoo. The Jordan-Chevalley decomposition. (pdf)