The University of Chicago Mathematics REU 2019

PROGRAM, SCHEDULES, and MENTORSHIP PAIRINGS

2019 REU: Participant talks Wednesday Aug 14, 4:30

  • Gabriel Day: Partial Realization of Hilbert's Program: A Conservativity Result in Reverse Mathematics
  • Franklin Mason: Forcing and the Independence of the Continuum Hypothesis
  • Alexander Burka: Higman's Embedding Theorem and Decision Problems
  • Valerie Han: The Ito Integral & Ito's Formula
  • Leonardo Guilhoto: How To Taylor Expand A Nowhere Differentiable Function
  • Spencer Dembner: Torsion on Elliptic Curves
  • Wyatt Reeves: Fantastic Sheaves and Where to Find Them
  • Nathaniel Bannister: An Introduction to Equivariant Homotopy
  • Anubhav Nanavaty: Understanding Wall's Finiteness Obstruction and its Equivariant Analogues
  • Natalie Bohm: Morse Theory and Handle Decompositions

    2019 REU: Participant talks Thursday Aug 15, 4:30

  • Yutong Qing: Introduction to the optimal control theory and some applications
  • Anne Carlstein: Stochastic Differential Equations and Brownian Motion
  • Victor Gardner: An Introduction to Schramm-Loewner Evolutions
  • Alek Skenderi: Marstrand's Theorem and Tangent Measures
  • Yueheng Zhang: On the principal eigenvector of a graph
  • DeMason, Kenneth J: Minimal Surfaces and Min-Max Theory
  • Emma Lennen: Quiver Representations
  • Anshul Adve: CLT and Decay of Correlations in Dynamics
  • Samuel Hsu: Modalities and Axiomatic Cohesion
  • Vinh-Kha Le: An exposition of the Li-Yau Harnack inequality

    2019 REU: Participant talks Friday Aug 16, 10:30

  • Wenminqi (Sophia) Zhang: The Gauss Bonnet Theorem
  • Claire Valva: Ergodicity of Geodesic Flow on Surfaces of Negative Curvature
  • Yuxin Lin: Prime number theorem and zeros of Riemann zeta function
  • Carson Collins: Understanding the Galois Action on Dessins d'Enfant
  • Xingyu Wang: Hasse-Minkowski Theorem and Its Applications
  • Jae Hee Lee: A localization theorem in equivariant cohomology
  • Eleanor McSpirit: Representing Bredon Cohomology and Homology with Naive G-Spectra and Naive G-Cospectra Respectively
  • Colin Ni: The Lazard ring and Quillen's theorem on MU
  • Matthew Lipman: The Thick Subcategory Theorem
  • Sanath Devalapurkar: The Witten genus and topological modular forms

    2019 REU: PARTICIPANT PAPERS -- FULL PROGRAM

    Dead links are to papers under revision, some of which are on advanced research in progress

  • Anshul Adve. Spectral methods for statistical limit theorems in dynamics. (pdf)
  • Chris Albert. Physical applications of fixed point methods in differential equations. (pdf)
  • Shah Mohammed Areeb. The Freyd-Heller group and the failure of Brown representability. (pdf)
  • Will Asness. A brief survey of inductive descriptive complexity. (pdf)
  • Carlos Azpurua. A comparison of the classification of surfaces. (pdf)
  • Zihni Kaan Baykara. Geometric quantization. (pdf)
  • Nathaniel James Bannister. Coefficient rings of $C_2$-equivariant Eilenberg-MacLane spectra. (pdf)
  • Natalie Bohm. Morse theory and handle decompositions. (pdf)
  • Jordan L. Brown. Scott spaces and the DCPO category. (pdf)
  • Alexander Burka. Higman's embedding theorem and decision problems. (pdf)
  • Anne Carlstein. Stochastic calculus: understanding Brownian motion and quadratic variation. (pdf)
  • Yuchen Chen. Enumerative geometry through intersection theory. (pdf)
  • Carson Collins. The Galois action on dessin d'enfants. (pdf)
  • Dylan Cordaro. The Brownian map. (pdf)
  • Joshua Cruz. Algebraic geometric codes from curves and higher dimensional varieties. (pdf)
  • Gabriel Day. Some conservativity results in reverse mathematics of interest to Hilbert's program. (pdf)
  • Kenneth J. DeMason. Stable minimal surfaces. (pdf)
  • Spencer Dembner. Torsion on elliptic curves and Mazur's theorem. (pdf)
  • Sanath Devalapurkar. An approach to higher chromatic analogues of the Hopkins-Mahowald theorem. (pdf)
  • Sanath Devalapurkar. The Ando-Hopkins-Rezk orientation is surjective. (pdf)
  • Sylvia Durian. Persistent homology analysis of cognitive maps. (pdf)
  • Alex Eastman. Symplectic manifolds. (pdf)
  • Nadia Esquivel M\'arquez. Exploring model structures. (pdf)
  • Jacob Fiedler. Ergodic theory and entropy. (pdf)
  • Victor Bowden Gardner. Introduction to Schramm-Loewner evolution. (pdf)
  • Leonado Ferreira Guilhoto. Numerically solving the Dirichlet problem using stochastic calculus. (pdf)
  • Valerie Han. An introduction to stochastic calculus. (pdf)
  • Xiayimei Han. Introduction to Hodge theory via the example of elliptic curves. (pdf)
  • Ada Sophia Hermelink. Cocompleteness of categories of algebras --- an overview. (pdf)
  • Samuel Hsu. Enriched 2-monads and codescent objects. (pdf)
  • Karhan Kaan Kayan. Orthogonal decomposition of modular forms. (pdf)
  • Sang Hoon Kim. Offline policy evaluation in a contextual bandit problem. (pdf)
  • Tianyu Kong. Ergodic theory, entropy and application to statistical mechanics. (pdf)
  • Jacob Laxer. An introductory overview to characteristic classes. (pdf)
  • Vinh-Kha Le. A concise introduction to the Adams conjecture. (pdf)
  • Jae-Hee Lee. Atiyah-Bott localization in equivariant cohomology. (pdf)
  • Patrick Lei. Plane curves and quantum cohomology. (pdf)
  • Emma O. Lennen. Representations of quivers: Gabriel's theorem and Kac's theorem. (pdf)
  • Zihao Li. Norm of discrete harmonic function. Probability and linear algebra. (pdf)
  • Yuxin Lin. Zeros of Riemann zeta function. (pdf)
  • Matthew Lipman. Unstable chromatic homotopy. (pdf)
  • Shuhong Liu. Stochastic Calculus and Stochastic Differential Equations. (pdf)
  • F. Curtis Mason. Forcing and the independence of the continuum hypothesis. (pdf)
  • Eleanor McSpirit. Bredon homology theories. (pdf)
  • Rushabh Mehta. Galois covers and the fundamental group. (pdf)
  • Ajay Mitra. Morse theory and Bott periodicity. (pdf)
  • Shourya Mukherjee. Classification of finite Coxeter groups. (pdf)
  • Anubhav Nanavaty. Wall's obstruction and its equivariant analogue. (pdf)
  • Sriharin Narayanan. Density under invertible H\"older continuous mappings in $\mathbb{R}^m$. (pdf)
  • Colin Ni. Lubin-Tate and algebraic geometry in chromatic homotopy theory. (pdf)
  • Stephanie Oh. The topology of Cayley graphs. (pdf)
  • Khanh Pham. Classifications simple complex Lie algebras. (pdf)
  • Yutong (Tony) Qing. Introduction to the optimal control theory and some applications. (pdf)
  • Franklin (Fritz) Augustus Reece. Normalized flow and Sperner theory of Coxeter groups. (pdf)
  • Wyatt Richard Reeves. An introduction to algebraic D-modules. (pdf)
  • Rafael M. Saavedra. The Hopf invariant one problem. (pdf)
  • Tomohiro Sawada. Primer to characteristic classes with application to gauge theory. (pdf)
  • Mark Schachner. The game of hex: a study in graph theory and algebraic topology. (pdf)
  • Ethan Schondorf. The Wiener measure and Donsker's invariance principle. (pdf)
  • Meryl Seah. Homological stability and related topics. (pdf)
  • Ryan Patrick Simeon. Introduction to Clifford algebras and uses in representation theory. (pdf)
  • Aleksander Skenderi. Marstrand's theorem and tangent measures. (pdf)
  • Sophia Smith. Harmonic functions with the Dirichlet condition. (pdf)
  • Zoe Smith. Embedding and immersion theorems. (pdf)
  • Claire Valva. On manifolds of negative curvature, geodesic flow, and ergodicity. (pdf)
  • Julia Walchessen. Eigenvalues of the Laplacian on a graph. (pdf)
  • Xingyu Wang. p-Adic numbers, Hasse-Minkowski theorem and its applications. (pdf)
  • Livia Xu. A glimpse of dimension theory. (pdf)
  • Yu (Alicia) Xiao, Yu (Alicia). A proof of the Kronecker-Weber theorem. (pdf)
  • Sarah Zhang. A roundabout introduction to hyperbolic area. (pdf)
  • Ruoqi (Rachel) Zhang. Two-sided bar construction. (pdf)
  • Yueheng Zhang. On the principal eigenvector of a graph. (pdf)

    2019 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

    Dead links are to papers under revision

  • Jack Barbour. An introduction to the braid groups and their integral cohomology. (pdf)
  • Geoffrey Baring. Counting solutions to diophantine equations using Jacobi sums. (pdf)
  • Anna Bounchaleun. (pdf)
  • Elle Bower. Osaki reduction of finite $T_0$-spaces. (pdf)
  • Dustin Burda. Elementary differential geometry and the Gauss-Bonnet theorem. (pdf)
  • Benjamin Cardinal. The stable manifold theorem and applications. (pdf)
  • Christopher Cebra. Elementary Morse homology. (pdf)
  • Matthew Chen. Paley graphs, quadratic residues, and linear constructions. (pdf)
  • Ariel Davidovsky. Martingales, stopping times, and the optional stopping theorem. (pdf)
  • Palash Goiporia. Subgroups of free groups and free products. (pdf)
  • Alexander Hauser. An introduction to curvature in $\mathbb{R}^3$. (pdf)
  • John Seale Hopper. Riemann mapping theorem and planar models of hyperbolic geometry. (pdf)
  • Joren Husic. The Lickorish-Wallace theorem. (pdf)
  • Stephen Kelly. Introduction to Brownian motion and its fundamental properties. (pdf)
  • George J. Kim. The relationship between the Chomsky hierarchy and automata. (pdf)
  • Benjamin Konstan. Mathematical statistics. (pdf)
  • Judson Kuhrman. A theorem on the classifying space of a group with torsion. (pdf)
  • Mandy La. The Poincar\'e-Hopf theorem. (pdf)
  • Li,Jacky. Introduction of algorithms on network flows. (pdf)
  • Edgar Lin. An overview and proof of the Lefschetz fixed-point theorem. (pdf)
  • Xinyu Liu. Unique factorization of ideals in a Dedekind domain. (pdf)
  • Zhengyang Liu. Fixed point theorems and the existence of a general equilibrium. (pdf)
  • Marc Maliar. Introduction to commutative ring theory and algebraic geometry. (pdf)
  • Elias Manuelides. Morse theory from scratch. (pdf)
  • Oscar Michel. An introduction to the Zariski topology. (pdf)
  • Mishal Mrinal. Galois theory and the Abel-Ruffini theorem. (pdf)
  • Nicholas Purple. Spectral graph theory. (pdf)
  • Samir Rajani. Applications of Chernoff bounds. (pdf)
  • William Phillip Sablan. Equidissections of squares, regular polygons, and hypercubes. (pdf)
  • Mason Shurman. Homotopy types of spaces with 7 or fewer points. (pdf)
  • Edwin Suresh. Stochastic calculus applied to arbitrage-free options pricing. (pdf)
  • George Turer. Dynamical systems on the circle. (pdf)
  • Anna Walker. Finite fields and the first isomorphism theorem: an exploration of $\mathbb{Z}/n\mathbb{Z}$. (pdf)
  • Keegan Yao. Complete manifolds with nonnegative sectional curvature. (pdf)
  • Wenminqi Zhang. The Gauss-Bonnet Theorem. (pdf)
  • Siqi Clover Zheng. Calculus of variations: minimal surface of revolution. (pdf)

    Miscellaneous program links

    Interested in the REU but not at the University of Chicago? (pdf)

    An essay about Chicago's REU and DRP programs (from 2014) (pdf)

    2019 REU: Announcement and description of the program (pdf)

    2019 REU: Application for University of Chicago students (pdf)

    Completed U of C applications should be returned to E314.

    2019 REU: Application for non-University of Chicago students (pdf)

    This is a template for your Research Statement to be uploaded to your application.

    To apply, go to MathPrograms: https://www.mathprograms.org/db/login/ja

    Acceptance forms

    Links to past REUs

    The links below will become operative in due course

  • 2019 REU: Participant talks Wednesday Aug 14 (pdf)
  • 2019 REU: Participant talks Thursday Aug 15 (pdf)
  • 2019 REU: Participant talks Friday Aug 16 (pdf)
  • 2019 REU: Mentorship pairings (pdf)

    2019 REU: PARTICIPANT PAPERS -- FULL PROGRAM

    2019 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM

    Tex Help

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