Yoyo Jiang (Anish Chedalavada, Math)
Chenzhuo Li (Akira Tominaga, Math)
Spencer Huang (Milton Lin, Math)
Dev Lalwani (Milton Lin, Math)
Nick Lu (An Wang, AMS)
Angela Hu (George Kevrekidis, AMS)
Blaise Colberg (George Kevrekidis, AMS)
Zihao Zhao (Abdel Ghani Labassi, AMS)
Tianji Li (Mao Hong, AMS)
Sukriti Gupta (Daniel Lopez, AMS)
Kai Holton (Josiah Lim, AMS)
Will Shiber (Josiah Lim, AMS)
Timothy Ventura (Toan Pham, Math)
Mateusz Ratman (Jon Lin, Math)
Liam Baca (Toan Pham, Math)
Full Project Proposals with detailed abstracts can be found here.
Classical Mathematical Inequalities
Mentor: Jon Lin
Mentee: Mateusz Ratman
Prerequisites: (Required) proof-based course at the level of Honors Linear Algebra (110.212) or Introduction to Proof (110.301). (Recommended) Real Analysis, at the level of (110.405) or more advanced.
Interpretability in Language Models
Mentor: Milton LinΒ
Mentee: Spencer Huang, Dev Lalwani
Prerequisites:Β Introductory knowledge of linear algebra, probability, optimization and neural nets. Familiarity with Python is strongly recommended.
Doing arithmetic using algebraic topology
Mentor: Toan Pham
Mentee: Timothy Ventura, Liam BacaΒ
Prerequisites: Some knowledge of topology and algebra (what is a topological space, a manifold, a group, a ring?) and an extreme curiosity.
(Applied) algebraic topology
Mentor: Akira Tominaga
Mentee: Chenzhuo Li
Prerequisites: Linear algebra. Knowledge of abstract algebra (covered in honors algebra 1, 2) and topological spaces is preferred.
Sheaves and Homological Algebra
Mentor: Anish Chedalavada
Mentee: Yoyo Jiang
Topic self proposed by mentee.
Learning the Energy-based Model and its application in Deep Generative Models
Mentor: An Wang
Mentee: Nick Lu
Prerequisites: Calculus, probability and statistics, basics of optimization, basics of neural network
Spectral Geometry on Triangles
Mentor: Daniel Lopez
Mentee: Sukriti Gupta
Prerequisites: Linear algebra, analysis, Fourier analysis or differential geometry on R^n (just intuition) would be nice, but not necessary.
Exterior Calculus and Clifford Algebra
Mentor: George A. Kevrekidis
Mentee: Angela Hu, Blaise Colberg
Prerequisites: (Required) Calculus (preferably up to calc III), Linear Algebra. Any other knowledge (Analysis, Topology, Algebra, etc.) is welcome.
Gaussian Process Regression for Machine Learning
Mentor: Josiah Lim
Mentees: Kai Holton, Will Shiber
Prerequisites: (Required) Probability with calculus at around EN.553.420 level. (Recommended) Python or some coding skills.
Reinforcement Learning Theory
Mentor: Mao Hong
Mentee: Tianji Li
Prerequisites: Mathematical Analysis, Basic Linear Algebra, Basic Probability, Basic Statistics, Basic Optimization.
Learn to Search in Branch and Bound with Reinforcement Learning
Mentor: Abdel Ghani Labassi
Mentee: Zihao Zhao
Prerequisites: Integer programming, some exposure to machine learning, Python software development.
Organizers: Josiah Lim (Applied Math and Statistics), Milton Lin (Math), Akira Tominaga (Math)