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.
With F. Blanchet-Sadri and Gautam Sisodia, Periods in Partial Words: An Algorithm, Journal of Discrete Algorithms, Vol. 16, 2012, pp 113-128.
(From an REU I did in 2007, not related to my current research).
- Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves, with Helge Ruddat
- Donaldson-Thomas invariants from tropical disks, with Man-Wai Cheung
- Notes for my mini-course Log geometry, tropical geometry, and mirror symmetry for cluster varieties, presented at the conference Valuations and birational geometry in Lille, France, May 2019.
- Notes and videos from three lectures I gave at the KIAS scientific workshop Cluster Algebras and Log GW Invariants in GS program in 2017.
- Descendant log GW invariants are tropical curve counts.
- Broken lines and theta functions.
- Theta functions and log GW invariants.
- Slides from my talk Tropical curve counting and canonical bases at the 2015 AMS Summer Institute in Algebraic Geometry.
- Some incomplete notes on Mirror symmetry and cluster algebras from a course I taught at QGM (Fall, 2014).
- Notes from my talk "Gross-Hacking-Keel I" at the MIT-RTG Mirror Symmetry Workshop in 2013, explaining the main construction of the Gross-Hacking-Keel 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.
At University of Utah:
At University of Aarhus (QGM):
At University of Texas at Austin (teaching assistant and grader positions):