Β (last week of classes)
Viggy Vanchinathan (Milton Lin, Math)
Srisha Nippani (Akira Tominaga, Math)
Talia Hovsepain (Jon Lin/Mitch Majure, Math)
Nicolas Rugo (Mitch Majure, Math)
Erica King (Josiah Lim, AMS)
Alex Ma (Parik Chalise, AMS)
Manuel Panora (George Kevrekidis, AMS)
Jorge Acosta (George Kevrekidis, AMS)
Eric Kim (An Wang, AMS)
Mateusz Ratman (Yuxin Ma, AMS)
Minjae Kim (Daniel Lopez, AMS)
Wynn Zhao (Kailee Lin, AMS)
Yash Permalla (Josiah Lim, AMS)
Chenzhuo Li (Nooria Ahmed, Math)
Yoyo Jiang (Anish Chedalavada, Math)
Radford Green (Mitch Majure, Math)
Moe Frumkin (Toan Pham, Math)
Yixin Zhao (Jon Lin, Math)
Full Project Proposals with detailed abstracts can be found here.
The Historical Development of Galois Theory
Mentor: Mitch Majure
Mentee: Nicolas Rugo, Radford Green, Talia Hovsepain
Prerequisites: High-school algebra with some linear algebra; A proof-based course such as AS.110.212 will suffice to approach this material.
Vector Bundles
Mentor: Nooria Ahmed
Mentee: Chenzhuo Li
Prerequisites: Basic point set topology (e.g., open/closed sets, homeomorphisms), Basic algebra (e.g., vector spaces, groups, rings).
Discrete Differential Geometry
Mentor: Jon Lin
Mentee: Yixin Zhao
Prerequisites: Linear Algebra and Calculus 3 at the level of 110.201 and 110.202. Ideally some familiarity with coding would really enrich the project.
Mechanistic Interpretability for Language Models
Mentor: Milton Lin
Mentee: Viggy Vanchinathan
Prerequisites: Introductory knowledge of linear algebra, probability, and basic machine learning is essential. Familiarity with Python is strongly recommended.
Arithmetic in Elliptic Curves
Mentor: Akira Tominaga
Mentee: Srisha Nippani
Prerequisites: Experience in a proof-based course. Any other projects are welcome.
Surreal Numbers
Mentor: Toan Pham
Mentee: Moe Frumkin
Mathematical Interests: Number theory, representation theory, geometry or topology
Differential forms from a sheaf-theoretic perspective
Mentor: Anish Chedalavada
Mentee: Yoyo Jiang
Self proposed topic by mentee.
Functional Graph Theory
Mentor: Kailee Lin
Mentee: Wynn Zhao
Prerequisites: Basic discrete math and linear algebra required. Graph theory background recommended.
FUNctional Graph Theory
Mentor: Parik Chalise
Mentee: Alex Ma
Prerequisites: Discrete Math (Introductory), Linear algebra (Introductory), Curiosity (Advanced)
Network Partitioning and Clustering
Mentor: Josiah Lim
Mentee: Erica King, Yash Permalla
Prerequisites: (Required) Linear algebra. (Recommended) Graph theory, Python/MATLAB or coding skills.
Algebraic Methods in Deep Learning
Mentor: Yuxin Ma
Mentee: Mateusz Ratman
Prerequisites: Linear algebra and group theory.
Modern Theory of Markov Chain
Mentor: An Wang
Mentee: Eric Kim
Prerequisites: Probability with calculus, such as EN.553.420.
Exterior Calculus and Clifford Algebra
Mentor: George A. Kevrekidis
Mentee: Manuel Panora, Jorge Acosta
Prerequisites: Calculus (preferably up to calc III) and Linear Algebra. Any other knowledge (Analysis, Topology, Algebra, etc.) is welcome.
Symmetries and Representations
Mentor: Daniel Lopez
Mentee: Minjae Kim
Prerequisites: Linear algebra, group theory required. Exposure to differential geometry and Fourier theory is desired but not required.
Organizers: Josiah Lim (AMS), Milton Lin (Math), Akira Tominaga (Math)