The University of Chicago Mathematics REU 2016

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

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

2016 REU: Announcement and description of the program (pdf)

Course offerings, Schedules, Mentorship pairings

Tex Help

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

2016 REU: PARTICIPANT PAPERS -- FULL PROGRAM

Dead links are to papers under revision

  • Fernando Al Assal. Entropy, speed and spectral radius of random walks. (pdf)
  • Frimpong A. Baidoo. L-functions on algebraic number fields. (pdf)
  • Ishan Banerjee. The Hopf invariant one problem. (pdf)
  • Diego Andres Bejarano Rayo. How do ultrafilters act on theories. The cut spectrum and treetops. (pdf)
  • Rush Brown. Irreducible representations of complex semisimple Lie algebras. (pdf)
  • Karen Butt. Elliptic curves and the Mordell-Weil theorem. (pdf)
  • Daniel Chong. Quadratic reciprocity, genus theory, and primes of the form x^2 = ny^2. (pdf)
  • Teodoro Fields Collin. Random matrix theory. (pdf)
  • Paolo Degiorgi. Cellular homology and the cellular boundary formula. (pdf)
  • Rafael Wingester Ribeiro De Oliveira. Excursions in model theory. (pdf)
  • Jacob W. Erickson. Some results for computing automorphism groups of Cartan geometries. (pdf)
  • Robert Green. Alphabet soup. (pdf)
  • Yi Guo. A counterexample to the Lovazc conjecture. (pdf)
  • Araminta Gwynne. The oriented cobordism ring. (pdf)
  • John Halliday. Castelnuovo's criterion and birational geometry of surfaces. (pdf)
  • Hung Ho. Gaussian integers. (pdf)
  • Ryan Hopkins. Nonlinear wave equations. (pdf)
  • Enya Hsiao. Canonical energy and black hole stability. (pdf)
  • Sameer Kailasa. On the Tate-Shafarevich group of a number field. (pdf)
  • Noam Kantor. Model categories: theory and applications. (pdf)
  • Zachary Kirsche Local--global methods in algebraic number theory. (pdf)
  • Daniel Kline. Elliptic curves and cryptography. (pdf)
  • Holly Mandel. What does a Lie algebra know about a Lie group? (pdf)
  • Henry Li. Some properties of integral Apollonian packings. (pdf)
  • Ryan McGaha. (pdf)
  • Alex Mine. Overview of Tate's thesis. (pdf)
  • Daniel Mitsutani. Differential topology: Morse theory and the Euler characteristic. (pdf)
  • Gwyneth Moreland. Class field theory for number fields and complex multiplication. (pdf)
  • Seth Musser. Weyl's law on Riemannian manifolds. (pdf)
  • Adele Padgett. A discussion of Keisler's order. (pdf)
  • Sun Woo Park. Rationality of zeta functions over finite fields. (pdf)
  • Raiann Rahman. Elliptic curves, the group law, and the J invariant. (pdf)
  • David Ran. Birkhoff's ergodic theorem. (pdf)
  • Julian Salazar. The representability hierarchy and Hilbert's 13th problem. (pdf)
  • Julian Salazar and Emma West. Persistent homology and the topology of motor cortical activity. (pdf)
  • Hannah Santa Cruz. A survey on the monodromy groups of algebraic functions. (pdf)
  • Isabella Scott. A conversation between model theory and graph theory. (pdf)
  • Maithreya Sitaraman. Exploring unknown spaces via nerves of coverings. (pdf)
  • Daniel Spiegel. The Hopf-Rinow theorem. (pdf)
  • Sam Spiro. Fourier analysis of Boolean functions. (pdf)
  • Matthew Steed. Development of Morse theory. (pdf)
  • James Stevens. Schur-Weyl duality. (pdf)
  • Sheel Stueber. The word and conjugacy problems. (pdf)
  • Dan Su. The Fourier transform for locally compact Abelian groups. (pdf)
  • Arthur Vale. Barriers in complexity theory. (pdf)
  • Zhengqu Wan. Geometric interpretations of curvature. (pdf)
  • Yi Wang. Using functional analysis and Sobolev spaces to solve Poisson's equation. (pdf)
  • Maeve Coates Welsh. Scissors congruence. (pdf)
  • Emma West and Julian Salazar. Persistent homology and the topology of motor cortical activity. (pdf)
  • Catherine Wolfram. Recursive derivation of 2N gon topologies. (pdf)
  • Dominic L. Wynter. An exposition of the Riemann Roch theorem for curves. (pdf)
  • Peter Xu. Arithmetic incarnations of zeta in Iwasawa theory. (pdf)
  • Arieh Zimmerman. The geometry of elliptic curves over finite fields. (pdf)

    2016 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

    Dead link is to a paper under revision

  • Michael Cronin. Combinatorial games and surreal numbers. (pdf)
  • Elise Darragh-Ford. Minimizing the uncertainty principle in the Weyl-Heisenberg and affine groups. (pdf)
  • Mayanka Dutta. An overview of spectral graph theory with applications. (pdf)
  • Philip Gaddy. The Stone-Weierstrass theorem and its applications to $L^2$ spaces. (pdf)
  • Katharine Gallagher. The fundamental group and Seifert-Van Kampen's theorem. (pdf)
  • Emily Gentles. Simple random walks: improbability of profitable stopping. (pdf)
  • Max Goldberg. Automorphism groups and spectra of circulant graphs. (pdf)
  • Evan Gorstein. Solving and computing the discrete Dirichlet problem. (pdf)
  • Charles Homans. On the group-theoretic properties of the automorphism groups of various graphs. (pdf)
  • Amin Idelhaj. The Sylow theorems and their applications. (pdf)
  • Tali Khain. Fractals and dimension. (pdf)
  • Jordan Laune. Applications of probability theory to graphs. (pdf)
  • Benjamin Ledeaux. Vaught's theorem: the finite spectrum of complete theories in aleph_0. (pdf)
  • Chia-Hsun Lee. Mathematical foundations of topological quantum computation. (pdf)
  • Jingjing (Jenny) Li. Spectral theory and applications. (pdf)
  • Can Liu. Ramsey theory. (pdf)
  • Shirong Liu. Polya's urn and the martingale convergence theorem. (pdf)
  • Phillip Lo. A combinatorial approach to the Brouwer fixed point theorem. (pdf)
  • Mantas Ma\v{z}eika. The singular value decomposition and low rank approximation. (pdf)
  • Katherine Monson. Finite Fourier analysis and Dirichlet's theorem. (pdf)
  • Daniel Morrison. An introduction to percolation theory and its physical applications. (pdf)
  • Joseph Redeker. Lie groups and Lie algebras. (pdf)
  • Jae Hyung Sim. The fundamental group and CW complexes. (pdf)
  • Christopher Stith. The fundamental groups and connections to covering spaces. (pdf)
  • Squid Tamar--Mattis. Planar graphs and Wagner's and Kuratowski's theorems. (pdf)
  • Cheuk To Tsui. Graphs with large girth and large chromatic number. (pdf)
  • Jenny Wang. Geometric constructions and algebraic field extensions. (pdf)
  • Christopher Wilson. A brief introduction to ZFC. (pdf)
  • Younggeun Yoo. Kakutani's fixed point theorem and minimax theorem in game theory. (pdf)
  • Ruby Zhang. Lubotzky--Phillips--Sarnak Ramanujan graphs and collision resistant hashing. (pdf)
  • Yujie (Annika) Zhang. Classification of surfaces. (pdf)

    Miscellaneous program links

  • Link to Angela Wu's 2016 Apprentice Program web page: (Go)
  • First analysis problem set (pdf)
  • Second analysis problem set (pdf)
  • Third analysis problem set (pdf)
  • Topology: a book in progress: selected readings to be recommended (pdf)
  • First topology problem set (pdf)
  • Second topology problem set (pdf)
  • From the web: problem set on normalization (pdf) Solution set in Simplicial Objects book, Section 22
  • Homological algebra primer (pdf)
  • From last year: Notes on homology of posets (pdf)
  • From last year: Notes on Mayer-Vietoris sequences (pdf)
  • Julian Salazars' draft notes on the algebraic topology course (pdf)
  • Links to past REUs

    2016 REU: Application for University of Chicago students (pdf)

    Completed U of C applications should be returned to E314.

    2016 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