Office: 1852 East Hall

Office Phone: 734-763-2429

I am a fifth-year Ph.D. student in mathematics at the University of Michigan. My advisor is Yongbin Ruan, with whom I study the Gromov-Witten theory of orbifolds using ideas from algebraic geometry and mathematical physics. In September 2014, I will begin a Junior Fellowship at the Institute for Mathematical Research of the ETH Zurich.

*Relations on Mbar_{g,n} via the orbifold [C/Z_r]*

Available on the arXiv.*Geometric Quantization with Applications to Gromov-Witten Theory*

Seventy-three page expository text, available on the arXiv.*Landau-Ginzburg/Calabi-Yau correspondence for the complete intersections X_{3,3} and X_{2,2,2,2}*.

Submitted, arXiv preprint.*Inverse limits of finite topological spaces*.

This was my undergraduate thesis, completed under the guidance of Robert Lipshitz. It was published in Homology, Homotopy, and Applications, 11 (2009), no. 2, 223--227. A longer version is also available on Robert Lipshitz's website.

In the past, I have been a Graduate Student Instructor for Math 115 (Fall 2009, Winter 2010, Fall 2010, Fall 2012) and Math 116 (Winter 2011).

In the summers of 2011 and 2012, I co-taught a two-week course on number theory and related topics for the Michigan Math and Science Scholars, a program for talented high school students. The course was led by Professor Mel Hochster.

In July and August 2012, I co-taught a three-session workshop for middle school students at 826michigan on the interaction between mathematics and creative writing.

In Winter 2012, I was the course co-coordinator for Math 115 (Calculus 1).

- Crash course on toric varieties, part 3: the Kahler cone, the moment map, and the secondary fan.

Lecture notes for part of a "crash course" on toric varieties co-taught with Mark Shoemaker and Nathan Priddis as part of 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*. - The secondary fan.

Lecture notes for a guest lecture in Yongbin Ruan's course on Mirror Symmetry in Fall 2011, on the secondary fan and its relationship to Batyrev-Borisov's toric mirror symmetry. References are the same as above. - Introduction to Gromov-Witten theory.

Lecture notes for an expository talk at the Michigan Student Geometry and Topology Seminar in Fall 2011. This is essentially a revised version of the notes for the talk "Moduli of Curves and Gromov-Witten Theory, Part 1: Kontsevich's Formula" below; as in that case, the main reference is Kock and Vainsencher's*An Invitation to Quantum Cohomology*. - Equivariant localization and Gromov-Witten theory.

Extended version of lectures notes for an expository talk at the student seminar of the Summer School on Moduli of Curves and Gromov-Witten Theory at the Institut Fourier in Summer 2011. - 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 some 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*. - Moduli of Curves and Gromov-Witten Theory, Part 1: Kontsevich's Formula.

Lecture notes for an expository talk at the Michigan Student Geometry and Topology Seminar in Winter 2011. This was the first in a two-part series of talks that closely follows Kock and Vainsencher's*An Invitation to Quantum Cohomology*. - Spectral sequences in topology.

Lecture notes for an expository talk at the Michigan Student Geometry and Topology Seminar in Fall 2010, based on material from Hatcher's book-in-progress and Tim Chow's paper "You Could Have Invented Spectral Sequences", as well as other sources. - Finite topological spaces.

Lecture notes for a talk at the Michigan Undergraduate Math Club in Fall 2010 on the results of my undergraduate thesis (original work). - 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.

Last modified: 21 February 2014.