University of Chicago REU 2013

• 2013 REU: Announcement and description of the program (pdf)
• 2013 REU: Application (doc)
• 2013 REU: Acceptance Form for the Apprentice program (pdf)
• 2013 REU: Acceptance Form for the Full program (pdf)

  Abstracts and Schedules

  • 2013 REU: Abstracts of the course offerings (pdf)
  • 2013 REU: Schedule for weeks 1 and 2 (pdf)
  • 2013 REU: Schedule for weeks 3 and 4 (pdf)
  • 2013 REU: Schedule for weeks 5 and 6 (pdf)
  • 2013 REU: Schedule for week 7 (pdf)
  • 2013 REU: Schedule for week 8 (pdf)
  • Abstract of Rediet Abebe's talk:Laplacian eigenvalues of simplicial complexes (pdf)
  • Abstracts for Thursday's participant talks (tex)
  • Abstracts for Friday's participant talks (tex)

  • 2013REU: Mentorship pairings (pdf)

  COURSE NOTES (The notes included from past years may still be of interest)

  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)
  • Henry Chan's notes on hyperbolic geometry (pdf)
  • Henry Chan's notes on ``Measure Zero" (pdf)
  • Elden Elmanto and Henry Chan lecture notes: Scissors congruence (pdf)
  • 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)

  Matthew Morrow's notes ``Number theory: Reciprocity and polynomials'' (Go)

  Maryanthe Malliaris's pointers to REU paper topics (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)

  2013 REU: PARTICIPANT PAPERS -- FULL PROGRAM

• Matthew Actipes: On the fundamental group of surfaces (pdf)
• Tsvi Benson-Tilsen: Isometry groups of compact Riemann surfaces (pdf)
• Calista Bernard: Interpolation theorems and applications (pdf)
• Brian Chen: Stochastic calculus and an application to the Black-Scholes model (pdf)
• Yo Joong Choe: The Bhattacharyya kernel between sets of vectors (pdf)
• Adrindrima Datta: Introduction to Markov decision theory (pdf)
• Andrew Ding: The p-adic numbers and basic theory of valuations (pdf)
• Jun Hou Fung: Serre duality and applications (pdf)
• Yiding Hao: The dimension and entropy of omega-languages (pdf)
• Mitch Hill: The uncertainty principle for Fourier transforms on the real line (pdf)
• George Hyun: Hyperbolicity and the word problem (pdf)
• Jiaqi Jiang: Representations of Lie groups and Lie algebras (pdf)
• Sofi gjing Jovanovska: The Freudenthal-Hopf theorem (pdf)
• Hyung Kyu Jun: The density of primes of the form a+km (pdf)
• Charles Koenig: An elementary proof of the prime number theorem (pdf)
• Simon Lazarus: On the recurrence of random walks (pdf)
• Ang Li: Fundamental groups and Van Kampen's theorem (pdf)
• Lucas Lingle: Galois theory and Hilbert's theorem 90 (pdf)
• Conor Mahany: Algorithmic probability in hypothesis selection (pdf)
• Jake Marcinek: Elliptic cures and the Mordell-Weil theorem (pdf)
• Alexander Bertoloni Meli: Cyclotomic extensions and quadradic reciprocity (pdf)
• Jing Miao: Dirichlet prime number theorem (pdf)
• Luke Multanen: Probability and Dirichlet's theorem (pdf)
• Ruth Ii-Yung Ng: A probabilistic analysis of binary and cascade (pdf)
• Teddy Niemiec: The Black-Scholes-Merton equations in practice (pdf)
• Dan Older: Mathematics of the big bang (pdf)
• Brian Reszutek. Commutator length of $[x,y]^{n}$: algebraic and geometric approaches (pdf)
• James Robertson. The topology of complex hypersurfaces (pdf)
• Bryan Rust. Convergence of Fourier series (pdf)
• Jack Sempliner. A primer on de Rham cohomology and spectral sequences (pdf)
• Salman Siddiqi. 2-Sylow theory for groups of finite Morley rank (pdf)
• Jasha Sommer-Simpson. Automorphism groups for semidirect products of cyclic groups (pdf)
• Min Jae Song. An introduction to the PCP theorem (pdf)
• Henry Steinitz. Kolmogorov complexity and algorithmic randomness (pdf)
• Blaine Talbut. A short tour of harmonic analysis (pdf)
• George Torres. Spectral and chromatic properties in vertex removal (pdf)
• Abigail Ward. Semi-simple Lie algebras and their representations (pdf)
• Botao Wu. A survey of properties of finite horizon differential games under Isaacs' condition (pdf)
• Wayne Yang. Markov chains and ant colony optimization (pdf)
• Thomas Yu. The sphere theorem in Riemannian geometry (pdf)

  2013 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

• Nikolas Anderson: Computation of stable commutator length in free groups (pdf)
• Elizabeth Black: Mathematical models of membranes (pdf)
• Freddy Boulton: A sampling of numerical techniques (pdf)
• Benjamin Call: The compactness theorem and applications (pdf)
• Rachel Carandang: Introduction to the homology groups of complexes (pdf)
• Patrick Chen: Quadratic reciprocity (pdf)
• Zefeng Chen: Rudiments of ergodic theory (pdf)
• James Clarke: The intersection of topological and metric spaces (pdf)
• Michael Fosco: LaPlace's equation from two perspectives (pdf)
• Michael Galperin: Torsion points of elliptic curves (pdf)
• Kira Ghandhi: Khovanov homology as an invariant (pdf)
• Nathan Gill: The fundamental group and the Brouwer fixed point theorem (pdf)
• Justin Guo: Card shuffling (pdf)
• Nora Helfand: Polya's urn and the beta-Bernoulli process (pdf)
• Yong Jae Kim: The automorphism group on the Riemann sphere (pdf)
• Philip Liang: Finite Markov chains and the top-to-bottom shuffle (pdf)
• Julian Manasse-Boetani: An introduction to Galois theory (pdf)
• David Mao: Building the compound Poisson process (pdf)
• Julian Marohnic: The p-adics, Hensel's lemma, and Newton polygons (pdf)
• Anne Marsden: Eigenvalues of the Laplacian and their relationship to the connectedness of a graph. (pdf)
• Sarah McConnell: The Riemann mapping theorem. (pdf)
• Redmond McNamara: Irreducible representations of the symmetric group (pdf)
• Yujia Pan: The Erd\"os-Szekeres theorem: a geometric application of Ramsey's theorem (pdf)
• Nicholas Rouse: Vinogradov's three prime theorem (pdf)
• Nathaniel Sauder: Notes on introductory algebraic number theory (pdf)
• Mishel Skenderi: A primer of Lebesgue integration with a view to the Lebesgue-Radon-Nikodym theorem (pdf)
• Frederick Vu: Central limit theorem. (pdf)
• Liyu Xia: Strong approximation of Brownian motion (pdf)