Global Arc

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?

This course is an introductory survey of the major works and debates in Asian American literature and culture. We will study a variety of genres--novels, short stories, comics, memoirs, films, and science fiction--to examine how writers treat issues of racial and ethnic identity, gender, queerness, history, memory, colonialism, immigration, technology, and war. By placing Asian American subject formation in relationship to social, economic, and intellectual developments, we will explore the potential of Asian American literary texts to deepen our global and historical understanding of Asians in the U.S. and the U.S. in Asia.

What does a minor and shallow category like "cuteness" have to do with the abject histories of race and gender? This course offers an introduction to key terms in Asian American Studies through the lens of the seemingly insatiable American appetite for "Asian cuteness." How do we reconcile this desire with the long history of anti-Asian sentiments in this country? Why aren't other races "cute"? We will explore cuteness as racial and gendered embodiment, commodity, globalization, aesthetics, affect, and politics. Above all, we explore the implications of understanding race as a style.

This course will analyze and evaluate through a psychological lens the psychosocial causes and consequences of significant current events that impact different Asian groups in the U.S., such as pandemic-spurred anti-Asian sentiment and educational policy (e.g., the debate over magnet schools moving to lottery systems rather than test based), as well as long-standing "everyday" experiences common to Asian Americans (e.g., navigating biculturalism, microaggressions and model minority stereotypes) that may impact identity and mental health.