University of Chicago VIGRE REU 2008

• 2008 REU: Announcement and description of the program (pdf) (dvi)
• 2008 REU: Application (doc)
• 2008 REU: Acceptance Form for the Apprentice program (pdf) (dvi)
• 2008 REU: Acceptance Form for the YSP/SESAME full program (pdf) (dvi)
• 2008 REU: Abstracts of the course offerings (pdf) (dvi)
• 2008 REU: Undergraduate student lists and job assignments (pdf) (dvi)
• 2008 REU: Preference form for the June 5 meeting (pdf) (dvi)
• 2008 REU: Mentoring pairings and graduate student course assignments (pdf)
• 2008 REU: Schedule for week 1 (pdf) (dvi)
• 2008 REU: Schedule for weeks 2 and 3 (pdf) (dvi)
• 2008 REU: Schedule for weeks 4 and 5 (pdf) (dvi)
• 2008 REU: Schedule for weeks 6 and 7 (pdf) (dvi)
• 2008 REU: NEW Schedule for week 8
• 2008 REU: YSP Room Schedule, July 1 -- July 25 (doc)
• 2008REU: McReynolds and Schmidt Geometry REU course description (pdf)

2008 REU: Links to Miklos Abert's problem sheets

• Weekly problem sheets (here)

2008 REU: Links for Peter May's Finite Spaces talks

• Finite topological spaces (pdf) (dvi)
• Low dimensional examples (pdf) (dvi)
• Basic point set topology (pdf) (dvi)
• Finite spaces and simplicial complexes (pdf) (dvi)
• Finite groups and finite spaces (pdf) (dvi)
• Exercises and problems on finite spaces (pdf)
• Subdivisions of small categories (pdf) (dvi)

  2008 REU: PARTICIPANT PAPERS -- FULL PROGRAM

• William Abram. The dynamical system generated by the 2D Navier-Stokes equations. (pdf)
• Dylan G. L. Allegretti. Simplicial sets and Van Kampen's theorem. (pdf)
• Elan Bechor. Statistical group theory. (pdf)
• Sarah Bennett. Applications of Grobner bases. (pdf)
• Ioana Bercea. Perspectives on an open question about SET. (pdf)
• Jahnavi Bhaskar. Sum of two squares. (pdf)
• John Binder. Analytic number theory and Dirichlet's theorem. (pdf)
• Patricia Brent. Representations of GL_2(F_q). (pdf)
• Eleanor Brush. Three theorems in knot theory. (pdf)
• Michael Calderbank. An introduction to linear and cyclic codes. (pdf)
• Corrin Clarkson. Cohomology and vector bundles. (pdf)
• Lauren Cote. Free groups and graphs: the Hanna Neumann theorem. (pdf)
• Beau Dabbs. Brownian motion. (pdf)
• Joseph Doliner. A more stable approach to LISP tree GP. (pdf)
• John Dyer. The shrinking wedge of circles. (pdf)
• Jonathan Emberton. An elucidation of vector calculus through differential forms. (pdf)
• Daniel Feltey. Matrix groups. (pdf)
• Alex Fix (joint with Stephen Patrias). Enumeration of homotopy classes of finite T_0 topological spaces. (pdf)
• Nicholas Ford. The mordell-Weil theorem for Q. (pdf)
• Patrick Greene. Magical triangles. (pdf)
• Ariel Hafftka. The regularity lemma and graph theory. (pdf)
• Aaron Halper. A proof of the Gauss--Bonnet theorem. (pdf)
• Dustin Hedmark. An exploration of the metrizability of topological spaces. (pdf)
• Chris Henderson. Generalized abstract nonsense: category theory and adjunctions. (pdf)
• Justin Huang. Classification of surfaces. (pdf)
• Ethan Jerzak. Fundamental groups and covering spaces. (pdf)
• Hikaru Kiyo. A combinatorial approach to Stallings' algorithm. (pdf)
• Dennis Kriventsov. CW complexes of the form $K(G,n)$. (pdf)
• Carmel Levy. Stallings' folding process in (almost) linear time. (pdf)
• Brian Libgober. The Borsuk--Ulam and ham sandwich theorems. (pdf)
• Alice Mark. The algebraic geometry dictionary for beginners. (pdf)
• Ellen McCullagh. SET and affine caps. (pdf)
• Tom Milnor. Maximum knotted switching sequences. (pdf)
• Alexander J. Munk. Representation theory of SL_2 over a p-adic field: the principal series. (pdf)
• Prerna Nadathur. To infinity and beyond: some notes on set theory and transfinite numbers. (pdf)
• Peter Nelson. Free product factorization. (pdf)
• Matt Olson. An introduction to the stochastic integral. (pdf)
• Guillaume Pouliot. The spectral theorem and beyond. (pdf)
• Alex Rosenfeld. Understanding irreducible representations. (pdf)
• James Salvatore. The weak homotopy equivalence of S^n and a space with 2n+2 points. (pdf)
• Noah Schweber. Brauer algebras and the Brauer group. (pdf)
• Michael Travis. Elliptic curves over C. (pdf)
• Brooke Ullery. Minkowski theory and the class number. (pdf)
• Katie Waddle. The Grigorchuk group. (pdf)
• Matthew Woolf. An exploration of complex Jacobian varieties. (pdf)
• Seung-Hyun Yang. Continued fractions and Pell's equation. (pdf)
• Tengren Zhang. Triangle free graphs and their chromatic numbers. (pdf)

  2008 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

• Robert E. Bishop. On Fermat's little theorem. (pdf)
• Siddhartha Biswas. Introduction to Coding theory: basic codes and Shannon's theorem. (pdf)
• Isaac M. Davis. Understanding ruler and compass constructions with field theory. (pdf)
• Kristin Dean. Projective geometry. (pdf)
• Marcello Delgado. Shannon information and the mutual information of two random variables. (pdf)
• Wai Lee Chin Feman. Surprisingly difficult lattice problems. (pdf)
• Namita Gupta. Symmetries in R^3. (pdf)
• Hong Gyun Kim. Algebraically trivial, but topologically non-trivial map. (pdf)
• Korei Klein. Dependance rank. (pdf)
• Maxwell Levine. Plane symmetry groups. (pdf)
• James Murphy. Topological proofs of the extreme and intermediate value theorems. (pdf)
• Jia Hong Ray Ng. Quaternions and the four square theorem. (pdf)
• Ben Nordstrom. Finite Markov chains. (pdf)
• Stephen Patrias (joint with Alex Fix; see above). (pdf)
• Aaron Plavnick. The fundamental theorem of Markov chains. (pdf)
• Mira Scarvalone. Game theory and the minimax theorem. (pdf)
• Nathan Schulz. The roommates problem discussed. (pdf)
• Jeremy Schwartz. The law of large numbers. (pdf)
• Joohyun Shon. More is better: an investigation of monotonicity assumption in economics. (pdf)
• Alexander Staples--Moore. Equitable partitions in graph theory. (pdf)
• Matthew Steffen. Even walks on vertex--transitive graphs. (pdf)
• Kegon Teng Kok Tan. The first fundamental theorem of welfare economics. (pdf)
• Caroline Terry. What the functor?: category theory and the concept of adjointness. (pdf)
• Justin Walker. A brief introduction to Ramsey theory of graphs. (pdf)
• Isaac Ottoni Wilhelm. Packing triangles on a sphere. (pdf)
• John Wiltshire--Gordon. Rectilinear embeddings of K_n in the plane. (pdf)
• Angelica Wong. Primes and quadratic reciprocity. (pdf)
• Allison Wu. The Banach--Tarski paradox. (pdf)
• Karen Ye. NIM. (pdf)
• Richard Yeung. Optimal bluffing frequencies. (pdf)

  2008 REU: Links to Past Course Materials

• Laci Babai: Summer 2007 REU -- Discrete Mathematics
• Peter May: TQFT
• Mitya Boyarchenko: Topics in algebra
• Mitya Boyarchenko: Naturality in category theory (pdf)
• Tom Fiore: Music
• Vigleik Angeltveit: Products on spaces
• Uri Bader: Groups of two by two matrices

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