This is a link to my papers on the arXiv and here are three publications that illustrate my research interests:
- Local Gromov-Witten Invariants are Log Invariants, joint with T. Graber and H. Ruddat, arXiv:1712.05210.
- A constructive approach to a conjecture by Voskresenskii, joint with M. Florence, appeared in Selecta Mathematica, vol. 23, no. 4, 2017.
- Integrality of relative BPS state counts of toric del Pezzo surfaces, joint with T. Wong and G. Zaimi, Communications in Number Theory and Physics, vol. 7, no. 4, 2013.
- One direction of my research is concerned with rationality properties of varieties. Whether a variety is rational or not is a fundamental and important yet difficult question that currently is approached on a case by case basis. In my ongoing collaboration with M. Florence, we aim to systematically determine rationality for a large class of varieties given as certain (easy to describe) birational quotients.
- Parallel to that, I’m interested in relations between curve counting theories such as (log) Gromov-Witten and stable pair invariants. I have mainly worked in the log Calabi-Yau and log K3 settings and my research has brought me closer to the …
- … Gross-Siebert program, which gives an algebra-geometric realization of the (symplecto-geometric/string theoretic) SYZ conjecture in mirror symmetry. The Gross-Siebert program is a powerful and versatile construction that geometrically explains mirror symmetry.
While at the Fields institute, I gave a series of introductory lectures, which were filmed. One concerned Donaldson-Thomas and Pandharipande-Thomas invariants and is found at DT/PT. In the lecture log geom, I introduced logarithmic geometry and log stable maps, and logarithmic Gromov-Witten invariants in log GW.
At KIAS, I have helped organize a number of workshops. The first one virtual was about virtual enumerative geometry, the second one wall-crossing about derived categories, wall-crossing and Donaldson-Thomas theory. The third was about the Gross-Siebert program. Then we organized a workshop that served as an introduction to both BCOV and tropical geometry and another workshop about matrix factorizations. Then came one on moduli and mirror symmetry, followed by the most recent one on the Gross-Siebert program again. As a finale, we are organizing a third workshop on the Gross-Siebert program, this time with both Mark Gross and Bernd Siebert.
For the first workshop on the Gross-Siebert program, I gave a lecture series on that program in relation to log geometry. The video notes can be found here. I also gave a lecture series on the Gross-Siebert program at Warwick University in January 2017, it was however not filmed.