Papers, Preprints, and Notes
 
 
Research:
Expository papers for mathematicians:
Writing for a general audience:



Some less formal notes:

The following are lecture notes from several talks I have given, as well as notes I compiled on a few other topics. Unless otherwise noted, this material is not original. Comments and corrections are welcome; I was often quite inexperienced in these topics at the time the notes were written.
  • Wednesday Lecture Series, ETH:
    • Orbifolds and their cohomology.
      Notes from part one of a three-part lecture series at the ETH in Fall 2014. This lecture covers the basics of orbifolds and Chen-Ruan cohomology, and is based mainly on material from Adem, Leida, and Ruan's book Orbifolds and Stringy Topology.
    • Introduction to the Landau-Ginzburg Model.
      Part two of the series, covering the definition of FJRW theory.
    • The Landau-Ginzburg/Calabi-Yau correspondence.
      Part three of the series, on the idea of the LG/CY correspondence for hypersurfaces (specifically, the quintic threefold) and its generalization to complete intersections.
  • The secondary fan.
    Lecture notes for a guest lecture in Yongbin Ruan's course on Mirror Symmetry in Fall 2011, covering the secondary fan and its relationship to Batyrev-Borisov's toric mirror symmetry. These were also used, in modified form, as lecture notes for part of a "crash course" on toric varieties during the RTG Workshop on Mirror Symmetry at the University of Michigan in February 2012. The main references are Cox, Little, and Schenck's Toric Varieties and Cox and Katz's Mirror Symmetry.
  • Mini-Course on Moduli Spaces.
    Lecture notes for a four-session mini-course for graduate students taught in Summer 2011, based mainly on Kock and Vainsencher's An Invitation to Quantum Cohomology with help from Renzo Cavalieri's notes for his VIGRE mini-course "Introduction to the Moduli Space of Curves".
  • Notes on Localization.
    Notes I wrote for myself in Summer 2011 while studying for my Prelim Exam, based mainly on Graber and Pandharipande's "Localization of virtual cycles", with some help from Hori et al's Mirror Symmetry, Lotte Hollands's master's thesis "Counting curves in topological string theory", and other sources.
  • Notes on Chen-Ruan Cohomology.
    More notes I wrote for myself while studying for my Prelim Exam, based on the material in Adem, Leida, and Ruan's Orbifolds and Stringy Topology.
  • Hilbert polynomials and the degree of a projective variety.
    Final paper for the Algebraic Geometry course taught by Bill Fulton at the University of Michigan in Fall 2010.