UCLA Department of Mathematics


Current projects:


Past projects:

Winter 2019:

Student
Mentor
Project topic
Presentation title
Anish Chedalavada Ian Coley Bott periodicity & topological K-theory Topological K-Theory
Raymond Chu Blaine Talbut Optimal transport Optimal Transportation
Ethan Davis Louis Esser Category theory Quantifiers as Adjoints
Dyusha Gritsevskiy Frederick Vu Finite dimensional representations of semisimple Lie algebras over C Lie Groups in Physics
Bryan Hu Alex Dobner Number theory
Samanda Hu Bar Roytman Algebraic number theory Splitting of Prime Ideals in Quadratic Field Extensions
Saamarth Juneja Clark Lyons
Unchitta Kanjanasaratool Denali Molitor Interpretability of machine learning methods
Rachmiel Klein Clark Lyons The Cycle Space and Simplicial Complexes
William Legg Alex Mennen First-order logic Gödel's Completeness Theorem and applications
Zhengjun Liang Bar Roytman Algebraic topology Applications of Algebraic Topology on Graphs
Nicholas Liskij Gyu Eun Lee Functional analysis & distribution theory Functional Analysis and Distributions
Tyler Lopez Austin Christian Legendrian knots Legendrian Knots
Jackson Morris Abigail Hickok
Jiarui Qu Kevin Carlson Category theory
Vincent Robbins Thomas Gilton Descriptive set theory Axiom of Determinacy & PSP in Polish Spaces
Jas Singh Kevin Carlson Higher category theory
Eric Wang Dohyun Kwon Sets of finite perimeter and geometric variational problems An isoperimetric inequality
Yang Wang Eden Prywes
Sian Wen Riley Thornton
Ruofei Wu Chris Shriver Markov chains and mixing times
Guoran Ye Bar Roytman Algebraic topology Applications of Algebraic Topology on Free Groups
Richard Zhang Robert Housden Higher homotopy group

Fall 2018:

Student
Mentor
Project topic
Presentation title
Urte Adomaityte Frederick Vu Topology, Nielsen-Schreier theorem
Joshua Enwright Mike Miller Differential topology Differential Topology
Bryan Hu Blaine Talbut Harmonic analysis on locally compact abelian groups Fourier Transform on LCA Groups
Samanda Hu Bar Roytman Algebraic number theory Algebraic Integers in Quadratic Fields
Saamarth Juneja Clark Lyons Infinitary Combinatorics
Unchitta Kanjanasaratool Denali Molitor Interpretability in basic machine learning methods Sparse Linear Models and Interpretability
Rachmiel Klein Clark Lyons Knot theory: Reidemeister and invariants
Tyler Lopez Austin Christian Morse theory Morse Theory
Aditya Mallick Mike Miller Differential forms and homological algebra Sheaves and equivalent cohomology theories
Jackson Morris Abigail Hickok Morse Theory
Daniel Ragsdale Bar Roytman Differential topology The Jordan-Brouwer separation theorem
Sam Rhee Gyu Eun Lee Maximal function theory
Vincent Robbins Thomas Gilton Descriptive set theory The Borel Hierarchy
Krysten Schmidt Will Oakley
Nirmay Singaram Riley Thornton Galois theory via model theory Model Theoretic Approach to Galois Theory
Jas Singh Kevin Carlson A Categorical Approach to Universal Algebra
Yang Wang Eden Prywes Stochastic differential equations Ito Calculus
Sian Wen Riley Thornton Model theory Quantifier Elimination
Ken Williard Bon-Soon Lin Spanning trees in complete bipartite graphs
Richard Zhang Robert Housden Brief intro to homology functor
Michael Zshornack David Hemminger Algebraic topology The Brouwer fixed point theorem via homotopy

Summer 2018:

Student
Mentor
Project topic
Presentation title
William Black Gyu Eun Lee Fourier analysis
Juan Carbajal Riley Thornton Graph theory & algebraic combinatorics Stationary Distribution
Manuel Chavez Blaine Talbut Ordinary differential equations Geometric look at ODEs
Collin Cranston David Jekel Free probability & random matrices Free Probability and Free Independence
Joshua Enwright Kevin Carlson Classification of compact surfaces Classification of compact surfaces
Rong Fan Austin Christian Low dimensional geometry Farey Tessellations
Yuan Fang Alex Frederick
Kiyotaka Hachisuka Eli Sadovnik PDE & finite element method Finite Element Method
Yujie He Michelle Feng Fundamental Theorem of Asset Pricing
Arin Khudaverdyan David Jekel Probability & measure theory
Karina Sanchez Thomas Gilton Introduction to mathematical logic Topics of Mathematical Logic
Iris Sun Riley Thornton Model theory 0-1 Law for Random Graphs
Yang Wang Gyu Eun Lee Partial differential equations
Michael Zshornack David Hemminger Representation theory of finite groups Representation Theory of Groups and Its Uses