If you have taken Calc I & II...

• Topics: Measure theory (just intro), ODE, PDE, differential geometry, or advanced calculus.

• References: Folland (Measure theory), Perko (ODE), Strauss (PDE), Pressley (Differential Geometry), or Rudin (Advanced Calculus)

• Additional prerequisites: Basic understanding of set theory

If you have taken Calc III & Linear Algebra...

• Topics: geometric group theory, algebraic geometry, cryptography

• References: clay/margalit, cox/little/o'shea , fulton (algebraic curves), katz

• Additional prerequisites: abstract algebra knowledge for geometric group theory or algebraic geometry topics

• Topics: 1) An introduction to A_infinity algebras/categories,  2) An introduction to Morse and Floer theory, 3) An introduction to Fukaya categories

• References: 1) The book ''Fukaya categories and Picard Lefschetz Theory'' by Paul Seidel, 2) The book ''Morse Theory and Floer Homology'' by Michèle Audin and Mihai Damian, 3) An expository paper ''A beginner's introduction to Fukaya categories'' by Denis Auroux

• Topics: limit theorems in Probability / Fourier Analysis / Convex Analysis

• References: Probability: Theory and Examples (Rick Durrett) / Classical Fourier Analysis (Loukas Grafakos) / Convex Analysis An Introductory Text by Jan van Triel

If you have taken Real Analysis & Abstract Algebra...

• Topics: Algebraic topology, Riemann surfaces

• References: Algebraic topology: Hatcher’s book on algebraic topology, Atiyah’s book on topological K-theory; Riemann surfaces: Narasimhan, Forster

• Topics: Parking function/ probabilistic methods

• References: Handbook of Enumerative Combinatorics /Probabilistic Methods in Combinatorics

• Topics: Logic, Category Theory, Computer Science (any related topic depending on the student's interests)

• Topics: Optimal Transport

• References: Optimal Transport for Applied Mathematicians by Filippo Santambrogio

Current Organizers

Zijian Rong (zijianro@usc.edu)