I'm a postdoctoral Research Assistant Professor in the department of mathematics at the University of Miami. I'm part of the Simons Collaboration in Homological Mirror Symmetry.
I'm broadly an algebraic geometer and I've done work on the geometry of Calabi-Yau threefolds, toric geometry, moduli spaces of K3 surfaces and on categorical structures which appear in homological symmetry called perverse sheaves of categories. I'm also interested in Hodge theoretic structures arising from mirror symmetry and category theory. Several of my recent papers deal with the Hodge theory of Landau-Ginzburg models as defined by Katzarkov, Kontsevich and Pantev.
I finished my Ph.D. at the University of Alberta in January 2016 under Chuck Doran.
Publications and preprints
Most of my papers are on the arXiv. Links below either go to the arXiv posting or directly to the paper. There might be some differences between the arXiv versions and published versions.
- On a conjecture of Katzarkov, Kontsevich and Pantev , with Ludmil Katzarkov, Valery Lunts and Victor Przyjalkowski. In preparation.
- Hodge numbers of Landau-Ginzburg models. Submitted, 2017.
- Perverse sheaves of categories and some applications, with Ludmil Katzarkov, 2017.
- Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces, with Charles F. Doran, Andrey Novoseltsev and Alan Thompson. Submitted, 2017.
- Hodge Numbers from Picard-Fuchs Equations, with Charles F. Doran and Alan Thompson. SIGMA 13 (2017) 045.
Perverse sheaves of categories and non rationality , with Ludmil Katzarkov and Yijia Liu. Geometry over nonclosed fields, Springer, (2017).
- Picard-Fuchs uniformization of modular subvarieties, with Brent Doran and Charles F. Doran. To appear in Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds, and Picard-Fuchs Equations, Institut Mittag-Leffler.
- Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds, with Charles F. Doran and Alan Thompson. To appear in String-Math 2015 proceedings.
- Toric Degenerations and the Laurent polynomials related to Givental's Landau-Ginzburg models, with Charles F. Doran. Canad. J. Math. 68(2016), 784-815.
- Calabi-Yau Threefolds Fibred by Kummer Surfaces Associated to Products of Elliptic Curve, with Charles F. Doran, Andrey Novoseltsev and Alan Thompson. String-Math 2014 proceedings.
- Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces, with Charles F. Doran, Andrey Novoseltsev and Alan Thompson. Adv. Math. vol. 298, pp. 369–392.
- The Geometry and Moduli of K3 Surfaces, with Alan Thompson. Fields Institute proceedings.
- Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces, with Charles F. Doran, Andrey Novoseltsev and Alan Thompson. Int. Math. Res. Notices (2015), No. 23, 12265-12318.
Humbert surfaces and the moduli of lattice polarized K3 surfaces, with Chuck Doran, Hossein Movasati and Ursula Whitcher. String-Math 2014 proceedings.
The Geometry of Landau-Ginzburg models. University of Alberta Ph.D. Thesis, January 2016. This contains a bunch of the papers above, along with several new chapters.
Moduli spaces of K3 surfaces with large Picard number. Queen's University M.Sc. Thesis, July 2011.
I've given some talks that were recorded and are now online.
Noncommutative projective spaces and perverse schobers, University of Miami HMS conference, January 2017.
Hodge numbers of hypersurfaces in toric varieties and Landau-Ginzburg models, Algebraic Geometry in Mexico. December 2015.
Here are notes for several talks that I've given recently.
Hodge numbers of Landau-Ginzburg models, Mathematical Congress of the Americas, Special session on Motives and Periods, July 29, 2017.
Perverse schobers and noncommutative deformations. University of Miami, January 26, 2017.
Perverse sheaves of categories and noncommutative deformations. University of Indiana at Bloomington. January 16, 2017.
Picard-Fuchs equations and Shimura subvarieties. Washington University in St. Louis, January 8, 2017.
Hodge structures from differential equations. Washington University in St. Louis, January 4, 2017.
Ph.D. defense presentation. January 19, 2016.
I'm currently teaching Math 162 (Calculus II) and Math 310 (Multivariable Calculus).