## About My Research

I am an algebraic geometer whose research involves a combination of homological algebra, category theory, commutative and noncommutative algebra, and symplectic geometry. My primary focus is on derived categories of coherent sheaves on algebraic varieties. The essential direction of my research is to study algebra and geometry by way of gauged Landau-Ginzburg models. Traditionally, algebra and geometry are studied together by thinking of solutions to algebraic equations as shapes. Gauged Landau-Ginzburg models are triples consisting of a geometric shape, an algebraic equation, and a choice of symmetries of this data. The name comes from theoretical physics where Landau-Ginzburg models are used to describe tiny strings propagating through space and time.

**Publications.**

Advances in Mathematics V. 379 I.5, 2021.

Journal de Mathematiques pures et appliquees V. 147 I.9 pgs 29-59, 2021.

Memoirs of the American Mathematical Society, In Press.

Forum of Mathematics, Sigma. Vol. 8. Cambridge University Press, 2020.

Advances in Mathematics V. 352, pgs 943-980, 2019

Journal für die reine und angewandte Mathematik (Crelles Journal) V. 746, pgs 235-303, 2019

Proceedings of the American Mathematical Society V. 146 N. 11 pgs 4633-4647, 2018

Mathematische Annalen V. 371, I. 1-2, pgs 337-370, 2018.

American Journal of Mathematics 139.6, pgs 1493-1520, 2017.

Algebraic Geometry V. 5 I. 5, pgs 596-649, 2018.

Journal of the European Mathematical Society 19.4, pgs 1127-1158, 2017.

Advances in Mathematics, 295, pgs 195-249, 2016.

Trans. Amer. Math. Soc. 36, pgs 8933-8974, 2015.

Pure and Applied Mathematics Quarterly, V. 10 N. 1, pgs 1-55, 2014.

Journal de Mathematiques pures et appliquees V. 102 I. 4, pgs 702-757, 2014.

Lecture Notes of the Unione Matematica Italiana, Vol. 15, pgs 33-42, 2014.

Publications Mathematiques de l'IHES, V. 120 I. 1, pgs 1-111, 2014.

Inventiones Mathematicae, V. 189 I. 2, pages 359-430, 2012.

International Mathematical Research Notices V. 11, pgs 2607-2645, 2012.

Advances in Mathematics, V. 229, I., pgs 1955-1971, 2012.

Journal of Number Theory, 107, pgs 392-405, 2004.

**Preprints.**