Research & Publications


Papers under review (arXiv, GoogleScholar)
Publications 
Theses
  1. Skeletons, degenerations, & Gromov-Witten theory. 2016 Doctoral thesis, Yale University. 
  2. Gromov-Witten theory of blowups of toric threefolds 2012 Undergraduate thesis, Harvey Mudd College. 

In Preparation 

    My ongoing projects include the following. In a project with Markwig, I am working towards a determination of the logarithmic Gromov-Witten theory of toric varieties in genus 0, including descendant insertions. Our methods combine enhancements of well-known tropical computational tools known as floor diagrams, with structural results about the space of logarithmic stable maps in genus 0, proved in my thesis. Our long term target is an all genus recursive determination of the descendant theory of toric varieties using a generalization of double ramification cycle. I am also completing work on a tropical degeneration formula for the genus 1 enumerative invariants of toric varieties, building on earlier work with Santos-Parker and Wise. I am also trying to find alternate approaches in simpler situations to the logarithmic decomposition formula of Abramovich-Chen-Gross-Siebert. A longer term project, still in its infancy, is an alternative method towards the full degeneration and localization formulas in logarithmic Gromov-Witten theory, by "sheaffification in the topology of toroidal modifications". If you'd like to know more about any of these ideas, email me!

Unpublished Notes
  1. Analytification and tropicalization over Z. I establish Sam's inverse limit over the integers. I never found an application.
  2. Toric Severi degrees are logarithmic Gromov-Witten invariants. Sam asked if the logarithmic GW invariants of toric surfaces were enumerative.