Notes
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Topics in Differential Topology - lecture notes from a course by Prof. Blaine Lawson. 

Topological Quantum Field Theory - lecture notes from a course by Prof. Alexander Kirillov, Jr. 

Space Curves as Complete Intersections - expository notes, written during a summer project at TIFR. 

Topics in Loop Groups and Vertex Algebras - expository notes, written in preparation for my oral examination. 

Floer Homology in Gauge Theory - expository notes based on a paper by Prof. Kenji Fukaya. 

What is an Infinity Algebra? - expository notes for self-edification. 

The Whitehead Product on Homotopy Groups - expository notes for self-edification. 

A Comparison Between Two Four Manifolds - mostly expository article; contains a result about higher homotopy groups. 

An Introduction to Equivariant Homology - an expository article giving an axiomatic characterization and a few examples. 



Talks
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The Maximal Tori Theorem of E'. Cartan - talk given at the graduate student seminar (fall '06) 

An Introduction to Chern-Simons Theory - talk given at the graduate student seminar (spring '07). 

The Growth and End of Groups - talk given at the graduate student seminar (fall '07). 

What is an Eilenberg-MacLane space? - talk given at the graduate student seminar (spring '09). 

Homotopy Groups of Lie groups - talk given at the graduate student seminar (spring '09). 

Games on Graphs - talk given at CTY (Stony Brook) for high school students (fall '09). 

Cohomology of Lie Groups - talk given at the graduate student seminar (fall '09). 



Miscellaneous
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Batalin Vilkovisky Algebra - on the equivalence of the various definitions. 

Intermediate Algebraic Topology II (Final Exam) - solutions to the final exam.