University of Chicago REU 2012

Abstracts of the final week talks

COURSE NOTES (The notes below from past years are also relevant)

APPRENTICE PROGRAM: Linear Algebra and Combinatorics




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)

    Tex Help

  • Template for texing REU papers: USE THIS TEX FILE (tex) (pdf)
  • An excellent latex web page (web page)
  • LaTeX -- A document preparation system (web page)

  • Joshua Bosshardt: The classification of simple complex Lie algebras (pdf)
  • Kerisha Burke: Exploring graphs of triangulated $n$-gons (pdf)
  • Hunter Chase: Fundamental forms of surfaces and the Gauss-Bonnet theorem (pdf)
  • Chaofan Chen: Rings of integers, Gauss-Jacobi sums, and their applications (pdf)
  • Daniel Comeaux: An exploration of Minkowski theory and its applications (pdf)
  • Max Cytrynbaum: $\hat{\text{I}}$to calculus and derivative pricing with risk-neutral measure (pdf)
  • Genevieve Denoeux: Stability in mathematical game theory (pdf)
  • Andrew Ding: Plane algebraic curves (pdf)
  • Alexander J. Dunlap: Topics in percolation (pdf)
  • Erika Dunn-Weiss: Introduction to geometry (pdf)
  • Jun Hou Fung: The cohomology of Lie groups (pdf)
  • Alexander Grant: Preissman's theorem (pdf)
  • Mitchell Hill: Convergence of random Fourier series (pdf)
  • Zihao Jiang: Application of manifold theory to Hamiltonian mechanics (pdf)
  • Matthew Joseph: Markov chain Monte Carlo (pdf)
  • Young Kun Ko: Probabilistic checking of proofs and hardness of approximation (pdf)
  • Aaron Krahn: Quantum computation and quantum algorithms (pdf)
  • Nina Kuklisova: Introduction to Markov chains (pdf)
  • James Leiner: Brownian motion and the strong Markov property (pdf)
  • Haoru Liu: Error-correcting codes and finite fields (pdf)
  • Shankara Pailoor: Meromorphic forms on Riemann surface structures (pdf)
  • Anirudh Sankar: Monads and algebraic structures (pdf)
  • Miranda Grace Seitz-McLeese: Classifying the representations of sl_2(C) (pdf)
  • Abhinav Shrestha: An introduction to the fusion systems of blocks (pdf)
  • Salman Siddiqi: An introduction to geometric stability theory (pdf)
  • Yan Shuo Tan: A skeleton in the category: the secret theory of covering spaces (pdf)
  • Chen Hui George Teo: Brownian motion and Liouville's theorem (pdf)
  • Kairui Glen Wang: The basic theory of persistent homology. (pdf)


  • Matthew Actipes: A probabilistic view on the economics of gambling (pdf)
  • Daniele Caratelli: Brouwer fixed point theorem (pdf)
  • Brian Chen: The heat equation and harmonic functions over graphs (pdf)
  • Yo Joong Choe: Increasing chromatic number and girth (pdf)
  • Kevin Cuddy: Convergence of Fourier series (pdf)
  • Jiaqi Jiang: An introduction to spectral graph theory (pdf)
  • Daniel Kassler: Nonlinear equations: contractions and chaos (pdf)
  • Ilyas Khan: Hyperbolic geometry: isometry groups of hyperbolic space (pdf)
  • Simon Lazarus: Internal set theory and an intuitive development of the calculus (pdf)
  • Do Q Lee: Numerically efficient methods for solving least squares problems (pdf)
  • Ang Li: Dirichlet's theorem about primes in arithmetic progressions (pdf)
  • Lucas Lingle: Lie theory, universal enveloping algebras, and the Poincar\'e-Birkhoff-Witt theorem (pdf)
  • Ryan Liu: Prime number theorem (pdf)
  • Conor L. Mahany: Elementary topos theory and intuitionistic logic (pdf)
  • Christopher Natoli: Fractals as fixed points of iterated function systems (pdf)
  • Teddy Niemiec: The discrete-time binomial asset-pricing model (pdf)
  • Daniel Older: Applications of variational principles to dynamics and conservation laws in physics (pdf)
  • Rick Presman: The generalized Stokes' theorem (pdf)
  • Kevin Qian: Applications of Fourier analysis to non-analytic fields (pdf)
  • Turner Smith: Martingales and a basic application (pdf)
  • Min Jae Song: Euler's formula and the five color theorem (pdf)
  • Anagha Sundararajan: Shifting and moving: an introduction to dynamical systems (pdf)
  • George Robert Woodbury: The representation of a number by two or four squares (pdf)
  • Alejandro Younger: An exploration of Khinchin's constant (pdf)
  • Thomas Yu: Lagrangian formulation of the electromagnetic field (pdf)