University of Chicago REU 2014

• 2014 REU: Announcement and description of the program (pdf)
• 2014 REU: Application (doc)
• 2014 REU: Acceptance Form for the Apprentice program (pdf)
• 2014 REU: Acceptance Form for the Full program (pdf)

  Abstracts and Schedules

  • 2014 REU: Abstracts of the course offerings (pdf)
  • 2014 REU: Schedule for weeks 1 and 2 (pdf)
  • 2014 REU: Schedule for weeks 3 and 4 (pdf)
  • 2014 REU: Schedule for weeks 5 and 6 (pdf)
  • 2014 REU: Schedule for weeks 7 and 8 (pdf)

  • 2014REU: Mentorship pairings (pdf)

  Link to the 2014 CS REU course offerings (Go)

COURSE NOTES (FROM PAST YEARS)

APPRENTICE PROGRAM: Linear Algebra and Combinatorics

• Madhur Tulsiani's 2013 REU web page (Go)
• Laci Babai's 2012 REU web page (Go)

GEOMETRY: Surfaces and comutators

• Link to links on Alden Walker's home page: see the slides! (Go)

ALGEBRA, TOPOLOGY, ETC: Scissors congruence groups

• Link to links on Inna Zakharevich's home page (Go)
• Notes (May): The cohomology of groups 1 (pdf)
• Notes (May): The cohomology of groups 2 (pdf)
• Exercises (May) on the cohomology of groups (pdf)
• (May) Notes on Tor and Ext (pdf)
• Raphael Ho: Classification of group extensions and H^2 (pdf)
• Henry Chan: elementary notes on dual vector spaces (pdf)
• Henry Chan: a primer on homological algebra (pdf)

TOPOLOGY: finite spaces and larger contexts

• Peter May: Updates of a book in progress ($1 for each correction). (Go)
• Past notes and reading materials about finite spaces. (Go)
• Lecture notes for TQFT's. (Go)

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 (with an REU template with more examples) (web page)
• LaTeX -- A document preparation system (web page)

2014 REU: PARTICIPANT PAPERS -- FULL PROGRAM

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)

2014 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

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)