My main interests are in the techniques and tools of the Gross-Siebert program, in particular log geometry and Gromov-Witten invariants. The main applications are to problems in mirror symmetry and degenerations and deformations of varieties.

Research

My CV and research statement may be found below:

My publications and preprints may be found below:

• Tangent curves to degenerating hypersurfaces (joint with N. Nabijou) (https://arxiv.org/abs/2007.05016)

• Logarithmic Chow theory (https://arxiv.org/abs/1810.03746)

• Explicit equations for mirror families to log Calabi-Yau surfaces (https://arxiv.org/abs/1810.08356)

• Convergence of the mirror to a rational elliptic surface (https://arxiv.org/abs/1811.08050)

I have projects on the Doran-Harder-Thompson conjecture, log miracle flatness, the GLSM with tangency conditions and degenerate contributions of maximally tangent curves:

• The Doran-Harder-Thompson conjecture via the Gross Siebert program (joint with C. Doran)

• Logarithmic miracle flatness (joint with D. Holmes)

• GLSM techniques in logarithmic geometry (joint with Q. Chen)

• Degenerate contributions to maximal curve counts (joint with T. Grafnitz and N. Nabijou)

• Functorial derived pushforward in Macaulay2 (joint with Y. Kim and F. Olaf-Schreyer)

If you want to talk about the ideas and ingredients in the above projects, including seeing the current drafts please do contact me.

Teaching

I have taught several courses while in Boston College:

• Maths 1105 Calculus II (2 sections)

• Maths 1103 Calculus II (2 sections)

• Maths 2210 Linear Algebra (1 section)

• An introduction to toric geometry (1 section)

Computer Algebra

I am a proponent of using computer algebra packages to compute in Algebraic Geometry, in particular Sage and Macaulay2. In particular I have code for calculating derived pushforward of morphisms along projective morphisms in M2 and Sage code for calculating scattering diagrams in two dimensions.

Derived Pushforward in Macaulay2

An example of derived pushforward in Macaulay2

The scattering diagram for dP4

In my free time

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