Ludmil Katzarkov

Professor

Phone:
(305) 284-2279
Locator Code:
4250

 
Career

Education

1995Ph.D. University of Pennsylvania

LIST OF SPECIALTIES: Algebraic Geometry, Symplectic Geometry, Mathematics of String Theory

LIST OF SPECIALTIES: Algebraic Geometry, Symplectic Geometry, Mathematics of String Theory

Honors & Acknowledgements

Simons Investigator Award - 2017
Simons Fellowship - 2014
Research

LIST OF SPECIALTIES: 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]

SUMMARY:

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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