The University of Chicago Mathematics REU 2015

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2015 REU: Mentorship pairings

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APPRENTICE PROGRAM: Linear Algebra and Combinatorics

ALGEBRA, TOPOLOGY, ETC: Scissors congruence groups

TOPOLOGY: finite spaces and TQFTs

Guides to writing papers (Steve Kleiman and Dan Kleitman, MIT)

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Dead links are to papers under revision

  • Will Adkisson. An overview of knot invariants. (pdf)
  • Fernando Al Assal. Entropy, speed and spectral radius of random walks. (pdf)
  • Mario Alegre, Pedro Juarez, and Hani Pajela. Statistics about polynomials over finite fields. (pdf)
  • Qingci An. Hyperbolic plane as a path metric space. (pdf)
  • Eric Antley. Towards the prime number theory. (pdf)
  • Karen Butt. The Gauss-Bonnet theorem. (pdf)
  • Santiago Chaves Aguilar. A survey on Representation Theory. (pdf)
  • Wenyu Chen. The notion of mixing and rank one examples. (pdf)
  • Xi (Cathy) Chen. Cores of Alexandroff spaces. (pdf)
  • Rafael Wingester Ribeiro de Oliveira. The Stone representation theorem for Boolean algebras. (pdf)
  • Effy Fang. An application of probability theory in finance: the Black-Scholes formula. (pdf)
  • Nathan Gill. Deterministic and stochastic models of infectious disease: circular migrations and HIV transmission dynamics. (pdf)
  • Leonid Gladkov. Topics in graph theory. (pdf)
  • Yi Guo. Unique factorization of ideals in O_K. (pdf)
  • Peter J. Haine. Bundles, Stiefel-Whitney classes, and braid groups. (pdf)
  • John Halliday. The Riemann-Roch theorem and Serre duality. (pdf)
  • Pedro Juarez, and Hani Pajela. Statistics about polynomials over finite fields. (See Alegre)
  • Mikayla Kelley. Using ultrapowers to characterize elementary equivalence. (pdf)
  • Zachary Kirsche. Topological K-theory. (pdf)
  • Fizay-Noah Lee. Hopf bifurcation in a low-dimensional subcritical instability model. (pdf)
  • Jackson Macor. A brief introduction to type theory and the univalence axiom. (pdf)
  • Brian McDonald. Applications of prime factorization of ideals in number fields. (pdf)
  • Rachel McEnroe.Milnor's construction of exotic 7-spheres. (pdf)
  • Benjamin McKenna. Random walks and the uniform measure in Gromov-hyperbolic groups. (pdf)
  • Alex Mine. Modulo forms and applications in number theory. (pdf)
  • Seth Musser. From Hamiltonian systems to Poisson geometry. (pdf)
  • Ng Hoi Hei Janson. Line bundles over flag varieties. (pdf)
  • Adele Padgett. An investigation into covers of some finite spaces. (pdf)
  • Hani Pajela. Statistics about polynomials over finite fields. (See Alegre)
  • Sun Woo Park. Existence of Frobenius element and its applications. (pdf)
  • Alex Pieloch. Complexes associated to a surface and the mapping class group. (pdf)
  • Peter Robicheaux. Classifications of the flows of linear ODE. (pdf)
  • Nicolae Sapoval. Higher reciprocity laws. (pdf)
  • Zachary Smith. Compact Riemann surfaces: a threefold categorical equivalence. (pdf)
  • Aaron Geelon So. Quantum computing: efficient prime factorization. (pdf)
  • Jasha Sommer-Simpson. Barycentric subdivision and isomorphisms of groupoids. (pdf)
  • Jonathan Sorce. Transport on smooth manifolds: fiber bundles, connections, and covariant derivatives. (pdf)
  • Daniel Spiegel. Hamiltonian systems and Noether's theorem. (pdf)
  • Ingrid Starkey. Homology theories. (pdf)
  • Matthew Steed. Some theorems and applications of Ramsey theory. (pdf)
  • Danny Stoll. A brief introduction to complex dynamics. (pdf)
  • Eric Thoma. Results on Fourier multipliers. (pdf)
  • Sohini Upadhyay. Gauss-Bonnet for discrete surfaces. (pdf)
  • Randall R. Van Why. Exploring the topology of spaces of polynomials via vector bundle theory. (pdf)
  • Bowen Wang. Introduction to class field theory. (pdf)
  • Weian Wang. Applications of the Birkhoff ergodic theorem. (pdf)
  • Boris Xu. Polynomials with specified root multiplicities. (pdf)
  • Peter Xu. The Grothendieck-Riemann-Roch theorem for varieties. (pdf)
  • Joo Heon Yoo. Lie groups, Lie algebras, and applications in physics. (pdf)
  • Victor Zhang. Model theory for algebraic geometry. (pdf)
  • Yiguang Zhang. Topics on evasiveness of graphs. (pdf)
  • Yuzhou (Joey) Zou. Entropy and kinetic formulations of conservation laws. (pdf)


    Dead links are to papers under revision

  • Megan Adamo. Characterizing the orbits of the rotation map. (pdf)
  • Frimpong Apenteng Baidoo. Uniform convergence of Fourier series. (pdf)
  • Adam Black. The Euler characteristic of finite topological spaces. (pdf)
  • Kasper Borys. Domino tiling. (pdf)
  • Avery Broome. The role of topology in the study of evolution. (pdf)
  • Wei Han Chia. The topological approach to social choice. (pdf)
  • Matthew Correia. A few applications of differential forms. (pdf)
  • Timothy Csernica. Extinction in single and mult-type branching processes. (pdf)
  • Isaac Friend. Finite suspensions and finite $H$-spaces fail to model the topological group $S^1$. (pdf)
  • Robert Green. Vizing's theorem and edge-chromatic graph theory. (pdf)
  • Parker Haviza. Some mathematical foundations of cryptography. (pdf)
  • Daniel Hendrycks. Duality in convex optimization and its application to support vector machines. (pdf)
  • Ryan Hopkins. Finite metric spaces and their embedding into Lebesgue spaces. (pdf)
  • Gregory Howlett-Gomez. Bonnet's theorem and variations of arc length. (pdf)
  • Steven krawcyk. A brief introduction to geometric group theory. (pdf)
  • Jack Kurila. The n-dimensional Stokes' theorem. (pdf)
  • Zixiong Liu and Shayon Sengupta. Representation theory in Fourier analysis and probability. (pdf)
  • Becky Lytle. Introduction to the convergence of sequences. (pdf)
  • Elinore McLain. The Cauchy integral formula: the logic behind it and its applications. (pdf)
  • David Ran. An introduction to the fundamental group. (pdf)
  • Diego Andres Bejarano Rayo. Introduction to non-standard analysis. (pdf)
  • Zixiong Liu and Shayon Sengupta. Representation theory in Fourier analysis and probability. (See Liu).
  • Alejandro Desatnik Sod. Free groups and trees: an introduction to geometric group theory. (pdf)
  • Taylor Sutton. Eilenberg-MacLane spaces as a link between cohomology and homotopy. (pdf)
  • Sagar Tikoo. Introduction to Fourier analysis. (pdf)
  • Joshua Wakefield. Finite spaces and applications to the Euler characteristic. (pdf)
  • Linfeng Xu. Roman domination. (pdf)
  • Jiayang Zhao. Evasiveness of bipartite graph properties. (pdf)
  • Arieh Zimmerman. Representation theory of finite groups and Burnside's theorem. (pdf)

    Address email inquiries to may at math dot uchicago dot edu

    These activities are financed in part by the University of Chicago RTG grant (DMS-1344997)