Ludmil Katzarkov
Professor
Executive Director of the Institute of Mathematical Sciences of the Americas
Education
| 1995 | Ph.D. , University of Pennsylvania |
Algebraic Geometry, Symplectic Geometry, Mathematics of String Theory
Honors & Acknowledgements
Simons Investigator Award - 2017
Simons Fellowship - 2014
Algebraic Geometry, Symplectic Geometry, Mathematics of String Theory
Publications
Ballard, M., Deliu, D., Favero, D., Isik, M. U. & Katzarkov, L. "On the derived categories of degree d hypersurface fibrations" Mathematische Annalen 1-34 (Feb 1 2018). [Link]
We provide descriptions of the derived categories of degree d hypersurface fibrations which generalize a result of Kuznetsov for quadric fibrations and give a relative version of a well-known theorem of Orlov. Using a local generator and Morita theory, we re-interpret the resulting matrix factorization category as a derived-equivalent sheaf of dg-algebras on the base. Then, applying homological perturbation methods, we obtain a sheaf of (Formula presented.)-algebras which gives a new description of homological projective duals for (relative) d-Veronese embeddings, recovering the sheaf of Clifford algebras obtained by Kuznetsov in the case when (Formula presented.).
Ilia Itenberg, Ludmil Katzarkov, Grigory Mikhalkin, Ilia Zharkov "Tropical Homology" Mathematische Annalen 1-44 (May 26 2018). [Link]
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