He has held postdoctoral positions at University of Miami, Vienna, and most recently University of Alberta. This theory, of what I call Lagrangian matching invariants, is an example of a much more general formalism in symplectic topology. 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. His research focuses on Lagrangian Floer theory. Dmitry Tonkonog obtained his Ph. The original publication is available at www. 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.

For instance, there are degree 1 pseudo-holomorphic curves of degree 1 from the 2-sphere to a quintic 3-fold Q in complex projective 4-space, and the same is true of any symplectic manifold which is symplectically equivalent to Q. My work has two closely-related aspects; in fact a central theme is the interplay between them. Google Scholar Project Euclid. Mirror symmetry instead refers to the mathematical explanation of an idea from string theory. Lagrangian matching invariants for fibred four-manifolds: Dingxin joined the collaboration in and will spend two years at Brandeis and Harvard.

The projects I proposed were rather sophisticated for undergraduate work. In recent years, symplectic topologists ;erutz increasingly come to appreciate an insight from homological algebra, something that was long understood by algebraic geometers studying coherent sheaves on algebraic varieties.

More like this Lagrangian matching invariants for fibred four-manifolds: Lagrangian matching invariants for fibred four-manifolds: Peng joined the collaboration in and will spend two years at IHES. We have not proved that any large class of geometric mirror pairs obey HMS equivalently, core HMSbut we overcome one major difficulty in doing so, by showing that it suffices to prove core HMS.

You do not have access to this content. That is wholly impractical.

## T I M P E R U T Z

You have access to this content. Two pressing questions about it are to show that it gives invariants of 4-manifolds, independent of the fibrations on them, and to show that it recovers Seiberg-Witten theory. Two contributions to a reading seminar organised by Yann Rollin at Imperial College in Bordered Heegaard Floer homology gives an action of the strongly based mapping class group of an orientable surface on a derived category of modules.

Thurston proved that if K is a hyperbolic knot then the manifolds obtained by increasingly large surgeries on K converge in the Gromov-Hausdorff sense to the complement perktz K. Such counts are called Gromov-Witten invariants. His work in algebraic geometry studies Calabi-Yau varieties, Fano varieties and Landau-Ginzburg models. Keywords four-manifold Lefschetz fibration Seiberg—Witten invariant pseudo-holomorphic curve Lagrangian correspondence.

We prove that under fairly mild assumptions.

Article information Source Geom. Colin Diemer obtained his Ph. This project has grown out of my Ph. Knot Theory Course, Spring I review papers for Mathematical Reviews.

Papers by undergraduate advisees. But symplectic topology refers specifically to the study of global aspects of symplectic manifolds. You have partial access to this content. Her research studies the geometry of SYZ fibrations.

# Collaboration Postdocs – Simons Collaboration on Homological Mirror Symmetry

Both the original content and yhesis writing of papers on this page are entirely due to the authors. Download Email Please enter a valid email address.

Floer homology and cohomology, symplectic aspects 57R Symplectic manifolds can be approached from many angles, and in connection with many mathematical fields integrable systems, representation theory, geometric quantization, Poisson geometry, the algebraic topology of moment maps, …. Mohammad Farajzadeh Tehrani obtained his Ph. Article information Source Geom.

Dingxin joined the collaboration in and will spend two years at Brandeis and Harvard. The original publication is available at www. More like this Lagrangian matching invariants for fibred four-manifolds: 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 perutx broken fibration.