The University of Chicago Mathematics REU 2017

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

An essay about Chicago's REU and DRP programs (Go)

2017 REU: Announcement and description of the program (pdf)

Course offerings, Schedules, Mentorship pairings

Program from Charles Smart

Course notes for algebraic topology

Problem sets for algebraic topology

2017 REU: PARTICIPANT PAPERS -- FULL PROGRAM

Dead links are to papers under revision

  • Esme Bajo. Amalgamated free products, HNN extensions, and decision problems. (pdf)
  • Diego Andres Bejarano Rayo. Saturation by ultrapowers and Keisler's order. (pdf)
  • Amanda Grace Burcroff. Johnson schemes and certain matrices with integral eigenvalues. (pdf)
  • Eric Y. Chen. Crystal combinatorics and geometric Satake. (pdf)
  • Aaron Tsz Kiu Chow. Local existence theory of the vacuum Einstein equations. (pdf)
  • Maeve Coates Welsh. Elliptic curve cryptography. (pdf)
  • Teodoro Fields Collin. The finite element method and curved boundaries. (pdf)
  • Baptiste J. Dejean. Tate's thesis (pdf)
  • Aygul A. Galimova. Glimpses of Bott periodicity. (pdf)
  • William M. Golding. The qualitative local behavior of ordinary differential equations. (pdf)
  • Robert Green. An introduction to homotopy type theory. (pdf)
  • Anh Hoang Trong Nam. Geometry of the Kerr black holes. (pdf)
  • Charles Hudgins. Understanding Noether's theorem with symplectic geometry. (pdf)
  • Viraaj Jayaram. Proving the non-existence of elementary anti-derivatives for certain elementary functions. (pdf)
  • Alexander Johnson. Counting and realizing types: a survey of stability and saturation. (pdf)
  • Alexander S. Kastner. How many countable models can a complete theory have? (pdf)
  • Shin Kim. Basic Morse theory. (pdf)
  • Cameron Alexis Krulewski. K-theory, Bott periodicity, and elliptic operators. (pdf)
  • Arnab Kundu. The \'etale fundamental group of an elliptic curve. (pdf)
  • Noah del Rio Levine. Public key cryptography and elliptic curves (pdf)
  • Siyang Ling. Maxwell equations and Yang-Mills theory. (pdf)
  • Tian Ma. Contemporary cryptosystems. (pdf)
  • Kaitlyn Loyd. Box product of $C_p$ Mackey functors. (pdf)
  • Jacob Manaker. The thermodynamic formalism in dynamical systems. (pdf)
  • Alberto Sam Miguel Malaney. Characteristic classes and cobordism. (pdf)
  • Adel A. Rahman. Chern-Weil theory. (pdf)
  • Charlotte Rieder. Finitely generating the mapping class group with Dehn twists. (pdf)
  • Matthew Scalamandre. Harmonic analysis on LCA groups. (pdf)
  • Jin Woo Sung. Recurrence and convergence in countable state Markov chains. (pdf)
  • Josh Turner. Ultraproducts in algebra. (pdf)
  • Zhengqu Wan. The Boltzmann distribution. (pdf)
  • Yi Wang. Discrete operators in analysis. (pdf)
  • Zijian Wang. Elementary proof of Dirichlet theorem. (pdf)
  • Catherine Wolfram. Persistent homology on phonological data: a preliminary study. (pdf)
  • Molly Wolfson. Weyl curvature as a cross-ratio of points on the celestial sphere. (pdf)
  • Chen Xu. Combinatorics and its connection with representation theory. (pdf)
  • Younggeun Yoo. Stochastic calculus and Black-Scholes model. (pdf)
  • David Yunis. The Birkhoff ergodic theorem with applications. (pdf)
  • Shangxi Zhang. Brownian motion and It\^o's calculus. (pdf)
  • Yujie (Annika) Zhang. Persistent homology and sparse Vietoris-Rips filtration. (pdf)
  • Lingxian (Rose) Zhang. The $L^p$ convergence of Fourier series. (pdf)

    2017 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

    Dead links are to papers under revision

  • Benjamin Beach. Fuchsian groups and fundamental regions. (pdf)
  • Tejasi Bhatnagar. Covering spaces. (pdf)
  • Casey Breen-Edelstein. The classification of surfaces. (pdf)
  • Jacob Carbone. Introduction to dynamics on the interval. (pdf)
  • Abhimanyu Choudhary. An elementary proof of the prime number theorem. (pdf)
  • John Churay. Classification of surfaces and characterization of graph imbeddings. (pdf)
  • Dylan Cordaro. Markov chaind and coupling from the past. (pdf)
  • Joshua Cruz. The fundamental theorem of space curves. (pdf)
  • Gabriel Day. The Cayley-Hamilton and Jordan normal form theorems. (pdf)
  • Rose Dong. On the relationship between sets and groups. (pdf)
  • Jackson Dougherty. Some applications of the Borsuk-Ulam Theorem. (pdf)
  • Ari Freedman. Convergence theorem for finite Markov chains. (pdf)
  • Ruth Goldstein-Rose. Introduction to knots and braids using Seifert circles. (pdf)
  • Leonardo Ferreira Guilhoto. Applying Markov chains to Monte Carlo integration. (pdf)
  • Alexander Reed Hummels. Topological equivalence of linear ODEs. (pdf)
  • Varun Iyer. The Google spectrum. (pdf)
  • Eric Karsten. Brouwer's fixed point theorem and the Nash theorem. (pdf)
  • Jasmine Katz. Brouwer's fixed point theorem. (pdf)
  • Natalie Leonard. A local-global principle for sums of two squares. (pdf)
  • Benjamin Levine. Finitely generated modules over a principal ideal domain. (pdf)
  • Declan McNamara. Kolmogorov's zero-one law with applications. (pdf)
  • Trevor Moore. Combinatorial proofs of some theorems in algebraic topology. (pdf)
  • Anubhav Nanavaty. A brief introduction to differential forms in $R^n$ and the Gauss-Bonnet theorem in $R^3$. (pdf)
  • Benjamin Oye. Stable graphs. (pdf)
  • Pooja Patel. Quadratic reciprocity. (pdf)
  • Liam Puknys. The Stone-Weierstrass theorem. (pdf)
  • Saikeerthi Rachavelpula. The category of mereotopology and its ontological consequences. (pdf)
  • Parth Sarin. The cup length in cohomology as a bound on topological complexity (pdf)
  • Meryl Seah. Markov chains and hidden Markov chains. (pdf)
  • Calder Sheagren. Uncertainty principles with Fourier analysis. (pdf)
  • Karolina Grace Simcic. The necklace-splitting problem. (pdf)
  • Ryan Spieler. Group actions. (pdf)
  • Mary Stelow. Hamiltonicity in Cayley graphs and digraphs of finite Abelian groups. (pdf)
  • Mihai Stefan Tesliuc. Random graphs and their applications. (pdf)
  • John Thomas. A brief overview of nonlinear ordinary differential equations. (pdf)
  • Mira Wattal. Motivating smooth manifolds. (pdf)
  • Yifan Xu. Kuratowski's theorem. (pdf)
  • Sophia Xue. Convergence of Fourier series. (pdf)
  • Alicia Xiao. Hilbert spaces in quantum mechanics and the Heisenberg uncertainty principle. (pdf)
  • Allen Yuan. Fixed point theorems and applications to game theory. (pdf)
  • Alec X. Zhang. Polya's enumeration. (pdf)
  • Thomas Zheng. Differential equations: existence and uniqueness of solutions in economic models. (pdf)
  • Guanyu Zhouo. Ultrafilter and Hindman's theorem. (pdf)
  • James Zhou. An introduction to NP-complete problems. (pdf)

    2017 REU: Application for University of Chicago students (pdf)

    Completed U of C applications should be returned to E314.

    2017 REU: Application for non-University of Chicago students (pdf)

    This is a template for your Research Statement to be uploaded to your application.

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

    Acceptance forms

    Miscellaneous program links

  • Link to Laci Babai's REU web page: (Go)
  • Link to Angela Wu's 2016 Apprentice Program web page: (Go)
  • Topology: a book in progress: selected readings to be recommended (pdf)

    • Links to past REUs

    Tex Help

  • Template for texing REU papers: USE THIS TEX FILE (tex)
  • 2017 REU: Mentorship pairings (pdf) (pdf)
  • An excellent latex web page (with an REU template with more examples) (web page)
  • LaTeX -- A document preparation system (web page)

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