title>VIGRE REU 2011

University of Chicago VIGRE REU 2011

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

(Morrow notes)

Lecture notes for TQFT's (Updated and collated))

(May notes)

Maryanthe Malliaris's pointers to REU paper topics

(Malliaris topics)

Laszlo Babai's summer 2011 REU page

(Babai's REU web page)

Past notes and reading materials about finite spaces

(May notes)

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)

    • 2011 REU: PARTICIPANT PAPERS -- FULL PROGRAM

  • Carsen Berger. On some aspects of the theory of monads (pdf)
  • Joshua Bosshardt. The Hopf degreee theorem (pdf)
  • Benjamin Boyajian. Dedekind domains and the ideal class group (pdf)
  • James Buchanan. Poincar\'e's theorem for Fuchsian groups (pdf)
  • William Chan. Reverse mathematics of topology (pdf)
  • Je-ok Choi. The method of stationary phase (pdf)
  • Jahan Aden Claes. Spectral rigidity on $\mathbb{T}^n$ (pdf)
  • Hannah Constantin. Markov chains and queueing theory (pdf)
  • Joseph DiCapua. On the Chebyshev polynomials (pdf)
  • Elden Elmanto. $2$-Dimensional lattice topological field theories (pdf)
  • Jonathan Gleason. From Classical to Quantum: the $F^*$-algebraic Approach (pdf)
  • Rebecca Hoberg. Knots and braids (pdf)
  • Rowan Jacobs. Forcing (pdf)
  • Watson Ladd. The use of Martingales (pdf)
  • Andrew Mackie-Mason. The $h$-cobordism theorem (pdf)
  • Andrei Markov. Regular polytopes in $\mathbb{Z}^n$ (pdf)
  • David McDiarmid. Binary tree-structured partition and classification schemes (pdf)
  • Jeremy McKey. Homotopy groups of spheres (pdf)
  • Dileep Menon. B\'ezout's Theorem for Curves (pdf)
  • Paige North. Some degenerate weak categories (pdf)
  • David Ramsey. The sensitivity conjecture and the complexity of Boolean functions (pdf)
  • Nick Ramsey. Many generic automorphisms (pdf)
  • Jay Shah. Vector fields on spheres (pdf)
  • Ben A. Sherwood. Frobenius' theorem (pdf)
  • Abhinav Shrestha. Representations of semisimple Lie algebras (pdf)
  • Bradly Stadie. Tools from harmonic analysis (pdf)
  • Maxwell Stolarski. Brownian motion (pdf)
  • Yan Shuo Tan. On the diameter of Cayley graphs of finite groups (pdf)
  • Alex Tolish. The effect of gravitational radiation on the observational period of pulsars. (pdf)
  • Evan Turner. The $p$-adic numbers and finite field extensions of $\mathbf{Q}_p$ (pdf)
  • Weston Ungemach. Sobolev spaces with applicaion to second--order elliptic PDE (pdf)
  • Andrew Villadsen. The Galois anti-isomorphism (pdf)
  • Daping Weng. A categorical introduction to sheaves (pdf)
  • Michael Wong. An analytic approach to the theorems of Riemann-Roch and Abel (pdf)
  • Alec Zimmer. Stochastic calculus (pdf)

    2011 REU: PARTICIPANT PAPERS -- INTERMEDIATE PROGRAM

  • Peter Brown. Measure theory and the central limit theorem (pdf)
  • Peter Giles Hansen. Brownian motion and Hausdorff dimension (pdf)
  • Naftali Harris. Stochastic control (pdf)
  • Raphael Ho. Classification of group extensions and $H^2$ (pdf)
  • John Kopper. The theory of numbers in Dedekind rings (pdf)
  • Miranda Seitz-McLeese. Theorem number prime the: a backwards proof (pdf)
  • Salman Siddiqi. Lindstr\"om's theorem (pdf)
  • Peter Yanakiev. The uniformization theorem and universal covers (pdf)

    2011 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

  • Di Ai. Martingales and the abracadabra problem (pdf)
  • Ian Alevy. Expander graphs and property (T) (pdf)
  • Samuel Bryant. Differential topology and the Jordan Brouwer separation property (pdf)
  • Clive Chang. The continuum hypothesis and its relation to the Lusin set (pdf)
  • Bradley Cohn.The evolution of diversity in two-level selection (pdf)
  • Cassie Deskus. An introduction to the regularity lemma (pdf)
  • Matthew Dirks. The Stone representation theorem for Boolean algebras (pdf)
  • Samantha Dixon. Composite knot determinants (pdf)
  • Sam Dooley. Basic algebraic topology: the fundamental group of a circle (pdf)
  • Joshua Gensler. An application of the van Kampen theorem (pdf)
  • Thomas George. The classification of surfaces with boundary (pdf)
  • Eric Guan. Random walks in $\mathbb{Z}^n$ and the Dirichlet problem (pdf)
  • Nathan Hatch. Group theory: an introduction and an application (pdf)
  • Qizhen (Sally) He. Lie algebras and Lie brackets of Lie groups -- matrix groups (pdf)
  • Theodor Herwig. The $p$-adic completion of $\mathbb{Q}$ and Hensel's lemma (pdf)
  • Mitchell Hill. Approximating the random walk using the central limit theorem (pdf)
  • Sean Hogan. A gentle introduction to computational complexity theory, and a little bit more (pdf)
  • Zihao Jiang. Applications of number theory in cryptography (pdf)
  • Derek Johnston. An introduction to random walks (pdf)
  • David Kang. Group representations and character theory (pdf)
  • Zi Chong Kao. Classical mechanics: the three-body problem (pdf)
  • Edward Karabinus. Basic functional analysis with applications (pdf)
  • Ezra Karger. A $2$-adic extension of the Collatz function (pdf)
  • Vladislav A. Krokhmal. Introductory probability and the central limit theorem (pdf)
  • Geon Lee. Proving Szemer\"edi's regularity lemma (pdf)
  • Wesley Lee. Convergence of random series and Martingales (pdf)
  • Tony Lian. Fundamentals of Zermelo-Fraenkel set theory (pdf)
  • Joshua Lieber. Introduction to braid groups (pdf)
  • Haoru Liu. Elliptic curves and integer factorization (pdf)
  • Hannah Mark. Classifying subgroups of $SO_3$ (pdf)
  • Alexander Bertoloni Meli. Spectral equivalence classes of tori are finite (pdf)
  • Jennifer Momkus. Introductory group theory and Fermat's little theorem (pdf)
  • Peter J. Nebres. Renewal theory and its applications (pdf)
  • Shankara Pailoor. On the additive structure of $\mathbb{Q}_p$ and the nature of $P$-adic power series (pdf)
  • Luke Peeler. Metric spaces and the contraction mapping principle (pdf)
  • Ben Riffer-Reinert. The zeta function and its relation to the prime number theorem (pdf)
  • James Robertson. Waring's problem for $n=2$ (pdf)
  • Zachariah Sachs. Classification of the isometries of the upper half-plane (pdf) Chen Hui George Teo. Classification of surfaces (pdf)
  • Vrushank Vora. An introduction to underlying computational problems of public key cryptosystems (pdf)
  • Annie Wang. Lebesque measure and $L^2$ space (pdf)
  • Kairui Wang. Limits, colimits and how to calculate them in the category of modules over a P.I.D. (pdf)
  • Philip Wertheimer. How $n$ people can simulate a fair coin flip (pdf)
  • Botao Wu. Invariant probability distributions (pdf)