The University of Chicago Mathematics REU 2018
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Course offerings, Schedules, Mentorship pairings
- 2018 REU: Notes on the 2018 REU program
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- 2018 REU: Schedule for weeks 1 and 2
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- 2018 REU: Schedule for weeks 3 and 4
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- 2018 REU: Schedule for weeks 5 and 6
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- 2018 REU: Schedule for weeks 7 and 8
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- 2018 REU: Mentorship pairings
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Program Notes
- Daniiel Rudenko's Apprentice Program web page
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- Finite spaces and larger contexts (draft)
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- Foling Zou's notes: simplicial sets, nerves of categories, Kan complexes, etc
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- Saad Slaoui Tensor products of functors
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2018 REU: Participant talks Wednesday Aug 8
Leonardo Guilhoto.
Understanding Neural Networks Through Functional Analysis
Xinyu Shi. Cryptography and number theory
Amin Idelhaj. How to multiply complex numbers
Alex Manchester. Geometric group theory
Calder Sheagren. Introduction to Hodge Theory
Marlin Figgins. Classifying Anosov Diffeomorphisms and Manifolds Admitting Them
Matthew Scalamandre. An Introduction to Equivariant Cohomology
Saad Slaoui. Representability in algebraic topology
2018 REU: Participant talks Thursday Aug 9
Cecelia Higgins. An Invitation to Large Cardinals
John Jae Hyung Sim. Introduction to p-adic Numbers and Their Use in Algebraic Number Theory
Gregory Bixler. Introduction to differential forms
Zhiqi (Canvas) Li. An introduction to persistent homology
Douglas Dow. The Plateau Problem of surfaces in R^3
Tejasi Bhatnagar. Modular forms and Modular curves
Douglas Stryker. Eigenvalue Comparison Techniques in Riemannian Geometry
Jacob Keller. Geometric Methods in Representation Theory
2018 REU: Participant talks Friday Aug 10
Rohan Dandavati. Fourier Analysis: an Algorithmic Perspective
James Zhou. A Combinatorial Game and the Method of Conditional Probabilities
Yevgeniya Zhukova. A Look at the Functors Ext and Tor
Eleanor McSpirit. Modeling Homotopy Groups of CW-complexes Using Subdivisions of A-spaces
Colin Ni. Characteristic classes and obstruction theory
Valerie Han. The Graphon as a Limit for Dense Graphs
Esme Bajo. The Erdős-Hajnal Conjecture
2018 REU: PARTICIPANT PAPERS -- FULL PROGRAM
Dead links are to papers under revision
Anand Daniel Abraham. 0-1 laws in logic: an overview.
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Esme Bajo. A study in combinatorics and model theory.
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Esme Bajo. Quillen equivalences of model theories.
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Tejasi Bhatnagar. Modular forms and modular curves.
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Gregory Bixler. Visualizing exterior calculus.
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Andrew Cohen. Modeling tribal populations under multilevel selection.
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Rohan Dandavati. The Fourier transform on finite groups: theory and computation.
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Douglas Dow. The parameterized Plateau problem.
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Marlin Figgins. Anosov diffeomorphisms.
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William J. Garland. An introduction to the Jacobian conjecture.
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Pol Gomez Riguelme. Number fields: an introduction to algebraic number theory.
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Doron Leonardo Grossman-Naples. Finite manifolds and minimal finite models of closed surfaces.
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Leonardo Ferreira Guilhoto. An overview of artificial neural networks for mathematicians.
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Zachary Andrew Halladay. Bott periodicity and K-theory.
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Valerie Han. The graphon as a limit for dense graphs.
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Samuel A. Harder. Gibbs measures and symbolic dynamics.
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Cecilia Higgins. Ultrafilters in logic and set theory.
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Amin Said Idelhaj. Elliptic curves and dreams of youth.
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Kenz Kallal. Ramification in algebraic number theory and dynamics.
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Jacob James Keller. Beilinson-Bernstein localization.
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Chin-Hsun (Paul) Lee. Introduction to topological quantum computation with anyons.
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Che Li. Introduction to Class Field Theory and Primes of the Form $x^2 + ny^2$.
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Xuan Li. The weierstrass preparation theorem and some applications.
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James Alexander Manchester. Geometric group theory.
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Eleanor Grace McSpirit. Homotopy theory from subdivisions of A-space models.
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Kameron Jordan Mehling. Introduction to ergodic theory with applications to physics.
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Colin Ni. Characteristic classes and obstruction theory.
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Adel Rahman. Quantum fields and knots.
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Matthew Scalamandre. Bredon cohomology and the Conner conjecture.
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Meryl Seah. Bayesian games: games of incomplete information.
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Calder Sheagren. Introduction to Hodge theory.
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Jae Hyung (John) Sim. The $p$-adic numbers and a proof of the Kronecker-Weber theorem.
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Saad Slaoui. Building up to the Pontryagin-Thom theorem and computation of $\pi_*(MO)$.
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Ellis Soodak. New perspectives on the first Rogers-Ramanujan identity: potential steps towards a simple bijective proof.
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Douglas J. Stryker. An Eigenvalue Approach to Sphere Rigidity.
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Squid Tamar-Mattis. Error-correcting codes when error probability varies.
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Indraneel Tambe. Cubical structures of multi-fold internal categories.
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Arthur Oliveira Vale. Efficient proof net verification and sequentialization.
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Zijian Wang. Furstenberg's ergodic theory proof of Szemer\'edi's theorem.
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Yu (Alicia) Xiao. A brief introduction to knot theory.
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Kevin Yan. Global properties of plane and space curves.
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James Zhou. The method of conditional probabilities: derandomizing the probabilistic method.
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Yevgeniya Zhukova. A look at the functors Tor and Ext.
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2018 REU: PARTICIPANT PAPERS -- APPRENTICE PROGRAM
Dead links are to papers under revision
Philip Bell Adams. Undecidability and the structure of the Turing degrees.
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Will Asness. A brief overview of Alexandrov spaces.
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Carlos A. Azpurua. Root systems and a generalization of Catalan numbers.
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Harvey Barnhard. Approximating heavy traffic with Brownian motion.
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Alexander Tomas Burka. Hopf's theorem with elementary homology theory.
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Eli Javier Bussel. Martingale approximations for ergodic systems.
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Sofya Bykova. Chromatic numbers of random graphs.
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Nick Chaiyachakorn. De Rham's ttheorem twice.
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Yuchen Chen. p-Adics, Hensel's lemma and Strassman's theorem.
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Carson Collins. Covering spaces, graphs, and groups.
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Spencer Dembner. Forcing and the continuum hypothesis.
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Shamaul Dilmohamed. Genus theory and convenient numbers.
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Sylvia Durian. Some transfinite induction deductions.
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Alex Eastman. Differential Forms And their application to Maxwell's Equations.
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Suhas Gondi. An elementary proof of Mordell's theorem.
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Skuli Gudmundsson. The fundamentals of complex analysis and its immediate applications.
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Arushi Gupta. The p-adic integers, analytically and algebraically.
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Shaw Hagiwara. Convergence of the Fourier series.
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Max Johnson. ETCS, ordinals, and choice.
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Corry Ke. Introduction to one dimensional dynamics.
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Sang Hoon Kim. Representations of finite groups.
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Myles Alexander Kornfeld. Noether's theorem.
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Xiang (Sherry) Li. Marking a binary tree probabilistic analysis of a randomized algorithm.
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Neha Lingareddy. Calculating persistent homology using discrete Morse theory.
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Connor Lockhart. The continuum hypothesis.
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Jake William Nicoll. Fourier analysis and the wave equation.
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Carlos Olivares. Hyperbolic geometry, Fuchsian groups, and tiling spaces.
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Elizabeth Ombrellaro. Random walks and the probability of returning home.
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Katherine Ottenbreit. Quadratic reciprocity law.
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Mark Schachner. Algebraic and analytic properties of arithmetic functions.
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Eric Shang. Introduction to Markov chains and Markov chain mixing.
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Xinyu Shi. Cryptography and number theory.
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Aleksander Skenderi. Quadratic forms, reciprocity laws, and primes of the form $x^2 + ny^2$.
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Renyi Tang. Counting points on elliptic curves over $F_q$.
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Lia Troy. Simplicial homology and the classification of compact surfaces.
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Kaixin Wang. Fundamental theorem of the local theory of curves.
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Geoffrey West. Measure theory and the central limit theorem.
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