### TIM PERUTZ THESIS

The students worked hard on their paper long after the REU ended. His work in algebraic geometry studies Calabi-Yau varieties, Fano varieties and Landau-Ginzburg models. Keywords Four-manifolds Lefschetz fibrations Seibergâ€”Witten invariants pseudo-holomorphic curves Lagrangian submanifolds Hilbert schemes. The other project that summer was advised by Mirela Ciperiani and Kimball Martin. Mauro Porta obtained his Ph. August update ongoing. More by Tim Perutz Search this author in:

This structure is called the Fukaya category and may be denoted by F X. Mirror symmetry instead refers to the mathematical explanation of an idea from string theory. In his thesis, after reviewing the substantail background material, Atanasov begins a program to understand how this kind of convergence interacts with a particular class of modern 3-manifold invariants, Heegaard Floer homology. Mohammad Farajzadeh Tehrani obtained his Ph. I have been impressed at how they have risen to the challenge. Its core questions ask about when a smooth manifold admits a symplectic structure, to what extent that structure is unique, and to what extent its symplectic symmetries coincide with those of the underlying smooth manifold. I was assisted by Thomas Peters; without him, the projects would probably not have been a success.

Dmitry Tonkonog obtained his Ph. A condensed version of this paper is published as: Keywords four-manifold Lefschetz fibration Seibergâ€”Witten invariant pseudo-holomorphic curve Lagrangian correspondence Citation Perutz, Tim.

His research focuses on derived algebraic geometry, rigid analytic geometry, and motivic homotopy theory. Specialized structures on manifolds spin manifolds, framed manifolds, etc.

# Undergraduate student papers

Dmitry spent a year as a postdoc at Uppsala University before joining the collaboration in as a visiting assistant professor at UC Berkeley. I was assisted by Thomas Peters; without him, the projects would probably not have been a success.

In a research itm with S. His research focuses on moduli spaces of pseudoholomorphic curves and Gromov-Witten theory.

The second aspect concerns symplectic geometry, particularly symplectic Floer homology. Neither of these questions is close to being answered, but investigating them has led me to study some new structures in symplectic geometry which hold independent interest. His work in algebraic geometry studies Calabi-Yau varieties, Fano varieties and Landau-Ginzburg perut.

MR Jahrbuch database Zbl: Download Email Please enter a valid email address. That is wholly impractical. The two aspects come together by means of a sort of topological field theory for 3- and 4-manifolds singularly fibred by surfaces, based on the idea that Lagrangian correspondences between symplectic manifolds in this case, symmetric products of Riemann surfaces can serve as boundary conditions for pseudo-holomorphic curves.

McCord showed in that any finite simplicial complex is modeled, up to weak homotopy equivalence, by a space with finitely many points. This is a vector space over a base field kthe cohomology of a cochain complex CF L,L’. In recent years, symplectic topologists have increasingly come to appreciate an insight from homological algebra, something that was long understood by algebraic geometers studying coherent sheaves on algebraic varieties.

## Papers by undergraduate advisees

Edward Trefts’s senior thesis. Its core questions ask about when a smooth manifold admits a symplectic structure, to what extent that tlm is unique, and to what extent its symplectic symmetries coincide with those of the underlying smooth manifold. MR Digital Object Identifier: Both the original content and the writing of papers on this page are entirely due to the authors.

MR Digital Object Identifier: Emily Clader’s senior thesis.

Pseudo-holomorphic curve techniques The tangent spaces of a symplectic manifold can be made into complex vector spaces this involves a choice J for how i will act on tangent vectors, but the choice is in some ways inessential. I have been impressed at how they have risen to the challenge. Yoel Groman obtained his Ph.

## T I M P E R U T Z

Download Email Please enter a valid email address. A lecture given in Harvard in February entitled Fibred 3-manifolds and the Floer homology of fibred Dehn twists.

He joined the collaboration in as a postdoctoral fellow at Brandeis and Harvard. Colin Diemer obtained his Ph. More by Tim Perutz Search this author in: The projects I proposed were rather sophisticated for undergraduate work. Andrew Harder obtained his Ph. Lagrangian matching invariants for fibred four-manifolds: