Global Arc

Topics in algebra selected from areas such as representation theory of finite groups and the theory of Lie algebras. Prerequisite: MAT 345 or MAT 346.

Introduction to Algebraic Geometry; no previous knowledge of the topic is assumed. Familiarity with commutative algebra is helpful but will cover the necessary background

Elements of smooth manifold theory, tensors, and differential forms, Riemannian metrics, connection and curvature; selected applications to Hodge theory, curvature in topology and general relativity.

Knot theory involves the study of smoothly embedded circles in three-dimensional space. There ar lots of different techniques to study knots: combinatorial invariants, algebraic topology, hyperbolic geometry, Khovanov homology and mathematical gauge theory. This course will cover some of the modern techniques and recent developments in the field.

The course will target the following topics: The definition of knots in the 3-sphere, first invariants; algebraic knots and links in the 3-sphere; classification of algebraic knots, Puiseux pairs, iterated torus knots; fibred links, monodromy, the case of algebraic links; higher dimensional algebraic knots, Milnor theory of complex isolated hypersurface singularities.

Advanced course in Graph Theory. Further study of graph coloring, graph minors, perfect graphs, graph matching theory. Topics covered include: stable matching theorem, list coloring, chi-boundedness, excluded minors and average degree, Hadwiger's conjecture, the weak perfect graph theorem, operations on perfect graphs, and other topics as time permits.

This course will cover topics in Extremal Combinatorics including ones motivated by questions in other areas like Computer Science, Information Theory, Number Theory and Geometry. The subjects that will be covered include Graph powers, the Shannon capacity and the Witsenhausen rate of graphs, Szemeredi's Regularity Lemma and its applications in graph property testing and in the study of sets with no 3 term arithmetic progressions, the Combinatorial Nullstellensatz and its applications, the capset problem, Containers and list coloring, and related topics as time permits.

Wiener measure. Stochastic differential equations. Markov diffusion processes. Linear theory of stationary processes. Ergodicity, mixing, central limit theorem for stationary processes. If time permits, the theory of products of random matrices and PDE with random coefficients will be discussed. Prerequisite: MAT385.

This course gives a mathematical introduction to machine learning. It is not about proving theorems in machine learning, but rather a unified understanding of the models and algorithms used in machine learning. It begins with a simple introduction to supervised and unsupervised learning, including regression, classification, density estimation, clustering, and dimension reduction. Simple models such as linear regression, support vector machines, and k-means will be introduced, followed by focus on deep learning.

Surveying longstanding and emergent themes in the field of Asian American Studies, this course examines how "Asian American" is both a category constructed in service of power and a revolutionary identity formed in rebellion against it. How has US military intervention in Asia shaped shifting ideas about Asian America/the "Asian American"? How might these connections complicate dominant framings of when war begins and ends? In what ways is Asian American racial formation related to settler colonialism, anti-Blackness, and racial capitalism, and what might an Asian American movement that is accountable to these processes look like?