Research Interests (Research Statement)
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.
My Teaching Page
Papers
- Descendant log Gromov-Witten invariants for toric varieties and tropical curves, joint with Helge Ruddat.
- Theta bases are atomic, published in Compositio Mathematica (2017)
- 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.
Notes from some talks I've given
Notes and videos from three lectures I gave at the KIAS scientific workshop Cluster Algebras and Log GW Invariants in GS program in 2017.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.