Symplectic topology Symplectic manifolds arise both from mathematical physics as phase-spaces for hamiltonian systems and from algebraic geometry as smooth quasi-projective varieties over the complex numbers. Hansol Hong obtained his Ph. Justin Hilburn obtained his Ph. You have partial access to this content. The second aspect concerns symplectic geometry, particularly symplectic Floer homology. I was impressed with the results; here’s a sample: Emily Clader, “Inverse limits of finite topological spaces.

The projects I proposed were rather sophisticated for undergraduate work. 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 was impressed with the results; here’s a sample: Dingxin Zhang obtained his Ph. I was assisted by Thomas Peters; without him, the projects would probably not have been a success. Part I—the present paper—is devoted to the symplectic geometry of these Lagrangians. Download Email Please enter a valid email address.

Zack Sylvan obtained his Ph. The second aspect concerns symplectic geometry, particularly symplectic Floer homology. 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.

# PERUTZ, TIMOTHY – Mathematics – CNS Directory

More like tiim Lagrangian matching invariants for fibred four-manifolds: I have given several variants of a talk entitled Broken pencils and four-manifold invariants. Mauro was part of the collaboration as a postdoctoral fellow at the University of Pennsylvania inbefore taking a permanent position in Strasbourg.

The projects I proposed were rather sophisticated for tehsis work. More precisely, we formulate the notion of core homological mirror symmetrywhich asks for an equivalence between some full subcategory A of F X and some full subcategory B of DCoh Ywhere the inclusion of B into DCoh Y is a derived Morita invariance. Floer homology and cohomology, symplectic aspects 57R I hope soon to complement it with a lay-person’s account.

## Papers by undergraduate advisees

More by Tim Perutz Search this author in: You do not have access to this content. Her research studies the geometry of SYZ fibrations.

In the summer ofColumbia ran an internal “research experience for Columbia undergraduates. These results lend support to the conjecture that the invariants coincide with Seiberg—Witten invariants of the underlying four-manifold, and are in particular independent of the broken fibration.

# Perutz : Lagrangian matching invariants for fibred four-manifolds: II

This action was described combinatorially in arXiv: His research concerns partially tom Fukaya categories and their relations to other invariants. Colin Diemer obtained his Ph.

Mirror symmetry instead refers to the mathematical explanation of an idea from string theory. Dingxin Zhang obtained his Ph.

You have partial access to this content. This is a vector space over a base field kthe cohomology of a cochain complex CF L,L’. The REU has continued since Dmitry spent a year as a postdoc at Uppsala University before joining the collaboration in as a visiting assistant professor at UC Berkeley. They fit into a field theory which assigns Floer homology groups to three-manifolds fibred over S 1.

;erutz Zhao obtained her Tij. A lecture given in Harvard in February entitled Fibred 3-manifolds and the Floer homology of fibred Dehn twists. I am interested in the structures in Floer homology arising from Lagrangian correspondences between symplectic manifolds.

Keywords Four-manifolds Lefschetz fibrations Seiberg—Witten invariants pseudo-holomorphic curves Lagrangian submanifolds Hilbert schemes. Her research focuses on equivariant structures in Floer theory.

The students worked hard on their paper long after the REU ended. Mohammad works at the Simons Center for Geometry and Physics in Stony Brook, and has been supported as a fellow of the collaboration in The page showcases the work of a few undergraduate students I have supervised.

MR Jahrbuch database Zbl: Google Scholar Project Euclid.