#### TIM PERUTZ THESIS

I have been impressed at how they have risen to the challenge. Justin Hilburn obtained his Ph. 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. Google Scholar Project Euclid. Kontsevich’s homological mirror symmetry philosophy proposes that, for mirror pairs, there should be a derived Morita equivalence of the Fukaya category F X and the derived category of coherent sheaves DCoh Y.

Both the original content and the writing of papers on this page are entirely due to the authors. He joined the collaboration in as a postdoctoral fellow at Brandeis and Harvard. 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. A lecture given in Harvard in February entitled Fibred 3-manifolds and the Floer homology of fibred Dehn twists. His research interests lie at the interface of geometric representation theory, algebraic and symplectic geometry, and mathematical physics.

Lagrangian matching invariants for fibred four-manifolds: I hope soon to complement it with a lay-person’s account.

# Tim Perutz’s research page

I review papers for Mathematical Reviews. His research focuses on p-adic cohomology, D-modules, and their applications in mirror symmetry. Dmitry Tonkonog obtained his Ph. Zentralblatt MATH identifier Both the original content and the writing of papers on this page are entirely due to the authors.

## T I M P E R U T Z

I am interested particularly in near-symplectic geometry and in maps from 4-manifolds to surfaces Lefschetz fibrations and their generalisations. 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.

We can use pseudo-holomorphic curves in yet another way, studying pseudo-holomorphic polygons with Lagrangian boundary conditions.

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.

# Collaboration Postdocs – Simons Collaboration on Homological Mirror Symmetry

Google Scholar Project Euclid. Roberta joins the collaboration in as a postdoctoral fellow at the University of Pennsylvania.

That is wholly impractical. The PDF is here.

In a little more detail: This action was described combinatorially in arXiv: I was thssis by Thomas Peters; without him, the projects would probably not have been a success.

Floer homology and cohomology, symplectic aspects 57R MR Digital Object Identifier: Instead of a final exam, students in my undergraduate knot theory class in the spring of wrote expository final papers on topics we hadn’t covered.

Roberta Guadagni obtained her Ph. Dingxin Zhang obtained his Ph. Research Papers My papers are available for download via the ArXiv here.

The second aspect concerns symplectic geometry, particularly symplectic Floer homology. His work in algebraic geometry studies Calabi-Yau varieties, Fano varieties and Landau-Ginzburg models.

The REU has continued since The invariants are derived from moduli spaces of pseudo-holomorphic sections of relative Hilbert schemes of points on the fibres, subject to Lagrangian boundary conditions. The derived Morita tm class of F X is, increasingly, a tractable invariant. This project has grown out of my Ph. Peng joined the collaboration in and will spend two years at IHES.

I was impressed with the results; here’s a sample:.

## Papers by undergraduate advisees

The projects I proposed were rather sophisticated for undergraduate work. 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.

Emily Clader’s senior thesis. A lecture given in Harvard in February entitled Fibred 3-manifolds and the Floer homology of fibred Dehn twists.

More like this Lagrangian matching invariants for fibred four-manifolds: