# Research

## Publications

Exceptional Collections for Mirrors of Invertible Polynomials, (with D. Kaplan and T. Kelly)

Math Zeitschrift, 304, 32, 2023.

Windows for CDGAs, (with N. Chidambaram, 25 pages)

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

Kernels for Grassmann Flops, (with M. Ballard, N. Chidambaram, P. McFaddin, and R. Vandermolen)

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

Fundamental Factorization of a GLSM, Part I: Construction,

(with I. Ciocan-Fontanine, J. Guere, B. Kim, and M. Shoemaker, 87 pages)

Memoirs of the American Mathematical Society, 2023.

A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles, (with D. Kaplan and T. Kelly, 8 pages).

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

Derived Categories of BHK Mirrors, (with T. Kelly)

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

Variation of Geometric Invariant Theory Quotients and Derived Categories, (with M. Ballard and L. Katzarkov)

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

Equivalences of Families of Stacky Toric Calabi-Yau Hypersurfaces, (with C. Doran and T. Kelly)

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

Derived Categories of Degree d Hypersurfaces, (with M. Ballard, D. Deliu, U. Isik, and L. Katzarkov)

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

A Proof of a Conjecture of Batyrev and Nill, (with T. Kelly)

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

Fractional Calabi-Yau Categories from Landau-Ginzburg Models, (with T. Kelly)

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

Homological Projective Duality via Variation of Geometric Invariant Theory Quotients,

(with M. Ballard, D. Deliu, U. Isik, and L. Katzarkov)

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

Resolutions in Factorization Categories, (with M. Ballard, D. Deliu, U. Isik, and L. Katzarkov)

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

The Mori Program and Non-Fano Toric Homological Mirror Symmetry,

(with M. Ballard, C. Diemer, L. Katzarkov, and G. Kerr)

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

Griffths Groups for Derived Categories with applications to Fano-Calabi-Yaus, (with A. Iliev and L. Katzarkov)

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

A Category of Kernels for Graded Matrix Factorizations II: Further Implications,

(with M. Ballard and L. Katzarkov)

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

An Orbit Construction of Orlov Spectra, Phantoms, and Knorrer Periodicity, (with F. Haiden and L. Katzarkov)

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

A Category of Kernels for Graded Matrix Factorizations and Its Implications for Hodge Theory,

(with M. Ballard and L. Katzarkov)

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

Orlov Spectra: Gaps and Bounds, (with M. Ballard and L. Katzarkov)

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

Hochschild Dimension of Tilting Objects, (with M. Ballard)

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

Reconstruction and Finiteness Results for Fourier-Mukai Partners,

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

Characters and q-series in the rational numbers adjoin the square root of 2,

(with D. Corson, K. Liesinger, and S. Zubairy)

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

## Preprints

General GLSM Invariants and Their Cohomological Field Theories, (with B. Kim, 80 pages)

Kernels from Compactifications, (with M. Ballard and C. Diemer, 59 pages)

Homotopy Path Algebras, (with J. Huang, 40 pages)

## Research Funding

National Science Foundation

Collaborative Research: Derived Categories in Birational Geometry, Enumerative Geometry, and

Non-commutative Algebra, 2023-2026.

Natural Sciences and Engineering Research Council of Canada

Windows and Mirror Symmetry 2022-2023

Natural Sciences and Engineering Research Council of Canada

Derived Categories and Mirror Symmetry 2015-2022

Natural Sciences and Engineering Research Council of Canada

Factorizations, Projective Duality, and Cycles 2014-2015

Austrian Science Fund

Homological Projective Duality, Gaps, and Phantoms, 2013-2016

Austrian Science Fund

Phase Change and New Hodge-Type Categorical Invariants, 2011-2014

Austrian Science Fund

Homological Mirror Symmetry, Spectral Gaps and Applications 2010-2013