My interests include:
- Tropical, log, and real Gromov-Witten theory
- Algebro-geometric aspects of mirror symmetry (e.g., theta functions, coherent sheaves, polyvector fields)
- Cluster varieties
- Quantization and Hall algebras
- The interplay of everything listed above.
For more details, see my research statement.
- Descendant log Gromov-Witten invariants for toric varieties and tropical curves, joint with Helge Ruddat.
- Some incomplete notes on Mirror symmetry and cluster algebras from a course I taught at QGM (Fall, 2014).
From an REU I did in 2007 (not related to my current research): Periods in Partial Words: An Algorithm, with F. Blanchet-Sadri and Gautam Sisodia, Journal of Discrete Algorithms, Vol. 16, 2012, pp 113-128.
Slides from my talk Tropical curve counting and canonical bases at the 2015 AMS Summer Institute in Algebraic Geometry.
Notes from my talk "Gross-Hacking-Keel I" at the MIT-RTG Mirror Symmetry Workshop in 2013, explaining the main construction of the GHK paper Mirror symmetry for log Calabi-Yau surfaces I.
Some very short introductory notes on GIT from a talk I gave at UT Austin's student geometry seminary in 2013.
Worksheet from a talk I gave on compass and straightedge constructions for Saturday Morning Math Group (SMMG), a UT Austin program where graduate students and faculty memebers give lectures to elementary, middle, and high-school students.