The University of Chicago Mathematics REU 2019

The University of Chicago Mathematics REU 2019


  • 2019 REU: Notes on the 2019 REU program (pdf)
  • 2019 REU: Schedule for weeks 1 and 2 (pdf)
  • 2019 REU: Schedule for weeks 3 and 4 (pdf)
  • 2019 REU: Schedule for weeks 5 and 6 (pdf)
  • 2019 REU: Schedule for weeks 7 and 8 (Revised) (pdf)
  • 2019 REU: Mentorship pairings (pdf)

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


    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 co