Office: Room C4, Building CLV, Clausiusstrasse 47

Office Phone: +41 44 633 84 43

As of September 2014, I am a Junior Fellow at the Institute for Theoretical Studies of the ETH Zurich. I received my Ph.D. in mathematics from the University of Michigan. My advisor was Yongbin Ruan, with whom I studied the Gromov-Witten theory of orbifolds using ideas from algebraic geometry and mathematical physics.

*Mirror Symmetry Constructions*, with Yongbin Ruan.

Expository text comparing the mirror symmetry constructions of Batyrev-Borisov, Hori-Vafa, and Berglund-Hubsch-Krawitz. Available on the arXiv.*Relations on Mbar_{g,n} via the orbifold [C/Z_r]*

Available on the arXiv.*Geometric Quantization with Applications to Gromov-Witten Theory*, with Nathan Priddis and Mark Shoemaker.

Expository text on the techniques of quantization, 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. A more detailed version appears in my Ph.D. Thesis.*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.

At the University of Michigan, I was a Graduate Student Instructor for Math 115 (Fall 2009, Winter 2010, Fall 2010, Fall 2012) and Math 116 (Winter 2011).

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. We re-taught the workshop (in modified form) in May 2014, with a sixth-grade class at Ypsilanti Middle School.

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

- 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.

Last modified: 4 December 2014.