Talks and Write-ups
Things I've written
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Expository article "Connections of K-Theory to Geometry and Topology". Discusses the Hopf invariant one problem, vector fields on spheres, Wall's finiteness obstruction, Whitehead torsion, K-theory of schemes, pseudo-isotopies and higher K-theory, and applications of equivariant K-theory.
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My M.Sc. essay "Riemann Surfaces & Mumford's Conjecture" describes all ingredients in the proof of Mumford's conjecture along the lines of Galatius et al. (2009).
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Lecture Notes from Prof. Reichstein's course on "Geometric Invariant Theory" during Spring 2011 at UBC.
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My B.Sc. Thesis "Introduction to Group Cohomology" presents an introduction to Group Cohomology via derived functors and explains several applications such as the proof of Hilbert's Theorem 90.
Talks I've given
- "Topological Data Analysis", UBC Undergraduate Math Colloquium, September 2012.
- "Whitehead Torsion", UBC Student Topology Seminar, September 2012.
- "Vector Fields on Spheres", UBC Student Topology Seminar, May 2012.
- "Applications of K-Theory: Solution of the Hopf Invariant One Problem", UBC Student Topology Seminar, April 2012.
- "Exotic Spheres", UBC Graduate Student Colloquium, March 2012.
- "Characteristic Classes and the Thom Isomorphism", UBC Student Topology Seminar, March 2012.
- "Mumford's Conjecture", 8th PIMS Young Researchers Conference. UBC, May 2011.
- "Topological Field Theories", Jim Bryan's Algebraic Geometry Reading Course. UBC, Dec 2010.
- "Sheaves of categories and the proof of the main theorem", Working Seminar on Homotopy Theory of Moduli Spaces. UBC, Nov 2010.
- "A sheaf model for Ω∞MTO(d)", Working Seminar on Homotopy Theory of Moduli Spaces. UBC, Nov 2010.
- "Generalized Moduli Problems and Elliptic Cohomology", Jim Bryan's Algebraic Geometry Reading Course. UBC, Nov 2010.
- "Elliptic Cohomology", Jim Bryan's Algebraic Geometry Reading Course. UBC, Oct 2010.
- "Teichmüller Theory and Moduli Spaces", Working Seminar on Homotopy Theory of Moduli Spaces. UBC, Sep 2010.
- "Pontryagin-Thom Theory I", Working Seminar on Homotopy Theory of Moduli Spaces. UBC, Sep 2010.
- "Pontryagin-Thom Theory II", Working Seminar on Homotopy Theory of Moduli Spaces. UBC, Sep 2010.
- "Geodesics and Maximal Tori", Algebraic Groups Reading Course. UBC, Feb 2010.
- "Introduction to Group Cohomology", Presentation of Bachelor Thesis. Monash University, Nov 2008.