Semester 1

Banach spaces

Portal & Ware

Category Theory

Morrison

Prerequisites: algebraic topology or algebraic geometry

Commutative Algebra

Neeman

Geometric PDE with rough data

Portal

Prerequisites: Analysis 3 + Theory of PDE + Differential Geometry or a demonstrated ability to read this: https://projecteuclid.org/euclid.ajm/1333976883

(e.g., confidence in using the material of Stein-Shakarchi's Functional Analysis Chapter 3, and basic knowledge of Riemannian geometry)

Introduction to Ergodic Theory and Dynamical Systems

Schindler

Three-Manifolds

J Licata

Vector Bundles and K-Theorey

Angeltveit

Semester 2

Infinity Categories

Angeltveit

Commutative Algebra

Neeman

Text - "A course in commutative algebra" by Kemper

Applied Topology

Turner/Robins

Numerical Polynomial Algebra

Hegland/Deopurkar

Dirac Operators and Applications 

Prerequisite:  MATH2320, MATH2322

Guage Theories and Gravitation

Prerequisite:  MATH3342

String Theory

Peter Bouwknegt