University of Chicago VIGRE REU 2009

• 2009 REU: Announcement and description of the program (pdf) (dvi)
• 2009 REU: Application (doc)
• 2009 REU: Abstracts of the course offerings (pdf)
• 2009 REU: Additional abstracts added May 26 (pdf)
• 2009 REU: Schedule for weeks 1 and 2 (pdf)
• 2009 REU: Schedule for weeks 3 and 4 (pdf)
• 2009 REU: Schedule for weeks 5 and 6 (pdf)
• 2009 REU: Schedule for weeks 7 and 8 (pdf)
• 2009 REU: Acceptance Form for the Apprentice program (pdf) (dvi)
• 2009 REU: Acceptance Form for the YSP/SESAME full program (pdf) (dvi)
• 2009 REU: Undergraduate participants by program, with mentors (pdf)
• 2009 REU: Alphabetical list of undergraduates, with mentors (pdf) 2009 REU: List of courses, with graduate student assistants (pdf)
• 2009 REU: Alphabetical list of graduate mentors, with mentorees (pdf)

  Materials for the Apprentice Program

• Lecture notes for Abert's first three talks, texed by Aaron Marcus (pdf)
• More up to date notes for Abert and Babai's Apprentice talks are on Babai's Apprentice web page (APPweb page)

  Laci Babai's Discrete Mathematics and REU web pages

  (DMweb page) (REUweb page)

  Notes for ABERT's infinite groups course

• Lecture notes, texed by Spencer Dowdall (pdf)

  Notes and references for MAY/ANNO

• Lecture notes, updated July 21, texed by Claire Tomesch and Rolf Hoyer (pdf)
• Preliminary lecture notes (from 2006, with much material not done in 2009) (pdf)
• K-theory and Hopf invariant one notes (pdf)
• A certain Concise book (see Chapter 1 for fundamental groups) (pdf)
• Gorodentsev's Homological Algebra problem sheets (webpage)
• Corrected first problem set (pdf)
• Awodey's book ``Category theory'' (pdf)
• Eugenia Cheng's category theory notes (web page)

  Tex Help

• Template for texing REU papers (use the tex file) (tex) (pdf)
• LaTeX -- A document preparation system (web page)

2009 REU: PARTICIPANT PAPERS -- FULL PROGRAM (some INTERMEDIATE)

• Dylan Allegretti. Differential forms on noncommutative spaces. (pdf)
• John Binder. Tate's thesis on zeta functions on number fields. (pdf)
• Patricia M. Brent. Classification of root systems. (pdf)
• Michael Calderbank. Elliptic curves and cryptography. (pdf)
• Je-ok Choi. Hilbert's Nullstellensatz and its application to graph theory. (pdf)
• Beau Dabbs. Markov chains and mixing times. (pdf)
• Isaac Davis. An introduction to nonstandard analysis. (pdf)
• Marcello Delgado. General abstract nonsense. (pdf)
• Jonathan Emberton. Multidimensional Schr\"odinger operators and spectral theory. (pdf)
• Jonathan James Gleason. The $C^*$-algebraic formalism of quantum mechanics. (pdf)
• Patrick Greene. De Rham cohomology, connections, and characteristic classes. (pdf)
• Namita Gupta. Explaining bifurcations. (pdf)
• Ariel Hafftka. Differential topology and the Poincare-Hopf theorem. (pdf)
• Aaron Halper. Girth and chromatic number of graphs. (pdf)
• Kriz Harper. Explorations of Sperner's lemma and its connections to Brouwer's fixed point theorem. (pdf)
• Justin Hartmann. Brownian motion. (pdf)
• Christopher Henderson. Elementary topoi: sets, generalized. (pdf)
• Ethan Jerzak. Second-order logic, or: how I learned to stop worrying and love the incompleteness theorems. (pdf)
• Adam Kaye. Complex Lie algebras. (pdf)
• Dennis Kriventsov. The restriction problem and the Tomas-Stein theorem. (pdf)
• Satoru Kudose. Equitable partitions and orbit partitions. (pdf)
• Hikaru Kiyo. Poincare duality. (pdf)
• William M. Landau. The fundamental group. (pdf)
• Michelle Lee. Ramsey theory: Van der Waerden's theorem and the Hales-Jewett theorem. (pdf)
• Maxwell Levine. $GL_n(\mathbf{R})$ as a Lie group. (pdf)
• Cong Han Lim. Growth rate of groups. (pdf)
• Melissa Lynn. Galois categories. (pdf)
• Emily Mackevicius. Configuration spaces. (pdf)
• James Murphy. Cardinal and ordinal numbers. (pdf)
• Prerna Nadathur. Arrow's paradox. (pdf)
• Peter Nelson. An introduction to schemes. (pdf)
• Stephen Patrias. Simple closed curves on surfaces with intersection number at most one. (pdf)
• Vladislav Vladilenov Petkov. Modular forms and the Hilbert class field. (pdf)
• Aaron Plavnick. Bezout's theorem on curves. (pdf)
• David Price. Intrinsic volumes and Hadwiger's containment theorem. (pdf)
• Wolfgang Schmaltz. The Jordan-Brouwer separation theorem. (pdf)
• Kathy Snyder. Isometries of the hyperbolic plane. (pdf)
• Shiv Subramaniam. Integration on manifolds. (pdf)
• Valeriya Talovikova. Riemann-Roch theorem. (pdf)
• Caroline Terry. $2$-dimensional topological quantum field theories and Frobenius algebras. (pdf)
• Brooke Ullery. An introduction to affine schemes. (pdf)
• Daping Weng. Invariance of domain and the Jordan curve theorem in R^2. (pdf)
• Isaac Ottoni Wilhelm. Counting self avoiding walks of length $N$. (pdf)
• John Wiltshire-Gordon. Counting perfect matchings. (pdf)
• Matthew Woolf. Connections. (pdf)
• Karen Ye. Temperature theory and the thermostatic strategy. (pdf)
• Tengren Zhang. Freudenthal suspension theorem. (pdf)
• Alex Zorn. Discrete Morse theory on simplicial complexes. (pdf)

  2008 REU: PARTICIPANT PAPERS -- APPRENTICE and INTERMEDIATE PROGRAM

• Stephanie Avalos-Bock. Fractal geometry: the Mandelbrot and Julia sets. (pdf)
• Samuel Bloom. Fundamental groups and Van Kampen's theorem. (pdf)
• Tracy Boswell. Isometries of the plane. (pdf)
• Ben Chaiken. G\"odel's completeness and incompleteness theorems. (pdf)
• William Chan. Decidability. (pdf)
• Guo Chen. A treatment of the Dirichlet integral via the methods of real analysis. (pdf)
• Jia Lin Chen. Universal coefficient theorem for homology. (pdf)
• James Courtois. Elementary applications of Fourier analysis. (pdf)
• Jasper DeAntonio. Brouwer's fixed point theorem. (pdf)
• Gideon Dresdner. Stoke's theorem on manifolds. (pdf)
• Wenfei Du. Fourier analysis and the uncertainty principle. (pdf)
• Eugenie Fuchs. Behind the intuition of tilings. (pdf)
• Winston Gao. Field extensions and the classical compass and straight-edge constructions. (pdf)
• Jayanth Garlapati. Complexity theory and the RSA cryptosystem. (pdf)
• Graham Casey Gibson. On graph connectivity after path removal. (pdf)
• Julian Hartman. Alternate proof of the spectral theorem. (pdf)
• Riley Heckel. The prime number theorem. (pdf)
• Willy Hu. Dynamical systems. (pdf)
• Adam Koss. A comparison of the graphs of the chromatic and diatonic scale. (pdf)
• Aaron McKnight. Some basic properties of Brownian motion. (pdf)
• Mike Mei. Principal component analysis. (pdf)
• Samuel Moy. An introduction to the theory of field extensions. (pdf)
• Kenneth Oshita. The hexatonic systems under neo-Riemannian theory: an exploration of the mathematical analysis of music. (pdf)
• Neel Patel. Fourier analysis using representation theory. (pdf)
• Alex Poniecki. The Banach contraction principle. (pdf)
• Valer Popa. The index of a vector field as an invariant. (pdf)
• Hannah Provenza. Group theory and the Rubik's cube. (pdf)
• Alexandre R. Puttick. The ising model: phase transition in a square lattice. (pdf)
• Nick Ramsey. Translation equidecomposability. (pdf)
• Mira Scarvalone. RSA encryption and Diffie Hellman key exchange. (pdf)
• Jay Shah. Hausdorff dimension and its applications. (pdf)
• Al Staples-Moore. Network flows and the max-flow min-cut theorem. (pdf)
• Daniel Straus. Electrical network theory and recurrence in discrete random walks. (pdf)
• Joseph Zsolt Terdik. Markov chains. (pdf)
• Alexander Tolish. The Lagrangian and Hamiltonian mechanical systems. (pdf)
• Brad Trotter. Word theory and the musical scale. (pdf)
• Michael Wong. Representing integers as sums of squares. (pdf)
• Christopher Wood. Abstracting tonality: triads and uniform triadic transformations in an atonal context. (pdf)