Brandon Williams
Department of Mathematics
SUNY, Stony Brook

Contact
E-mail: mbw@math.sunysb.edu
Office: 2-105, Math Tower

Advisor: Oleg Viro
Research Interests:

• Low Dimensional Topology (links, 3- and 4-manifolds, Seiberg-Witten invariants, ...)
• Quantum Invariants (Jones Polynomial, Reshetikhin-Turaev invariants, ...)
• Knot homologies (Khovanov homology, Knot Floer homology, ...)
• Floer theories (Heegaard-Floer homology, Monopole homology, ...)
• Higher Categories and Categorification

Teaching

Summer 2009	MAT 203 (Calculus III), Lecture 01
Spring 2009	MAT 125 (Calculus A), Recitation 04
Fall 2008	MAT 132 (Calculus II), Recitation 10
Summer 2008	MAT 125 (Calculus A), Lecture 02
Spring 2008	MAT 131 (Calculus I), Recitation 02
Fall 2007	MAT 171 (Accelerated Calculus), Recitation 02
Summer 2007	MAT 132 (Calculus II), Lecture
Spring 2007	MAT 312 (Applied Algebra), Recitation 02
Fall 2006	MAT 132 (Calculus II), Recitation 03

Notes
These are some notes that I typed up when I was studying for my oral exam, as well as just random topics. Now that orals are over I will not be updating these notes, so the many errors and gaps will stay. I am now creating a more complete set of notes on these topics.

PDF	Oral Exam Syllabus (Last Updated: November 16, 2008)
PDF	Lee's variant of Khovanov Homology (Last Updated: June 04, 2008)
PDF	Computations in Khovanov Homology (Last Updated: June 04, 2008)
PDF	Classifying Spaces and Representability Theorems (Last Updated: June 04, 2008)
PDF	Spectral Sequences (Last Updated: June 04, 2008)
PDF	Homotopy Theory (Last Updated: September 06, 2008)
PDF	Low Dimensional Topology (Last Updated: November 25, 2008)
PDF	Gauge Theory (Last Updated: August 26, 2008)

Personal
Photography
Personal Website
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