Related papers: Polyfold and Fredholm Theory
This is an expository article for the Encyclopedia of Mathematical Physics on the subject in the title.
Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety of geometric elliptic PDEs, in particular moduli spaces of pseudoholomorphic curves. It aims to systematically address…
Computations in the cohomology of finite groups.
This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.
This is a research announcement of the theory of orbifold quantum cohomology.
This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.
We review our construction of the Teichm\"uller TQFT. We recall our volume conjecture for this TQFT and the examples for which this conjecture has been established. We end the paper with a brief review of our new formulation of the…
An observation on Hall-Littlewood polynomials.
This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
We prove a scalar curvature rigidity theorem for convex polytopes. The proof uses the Fredholm theory for Dirac operators on manifolds with boundary. A variant of a theorem of Fefferman and Phong plays a central role in our analysis.
We survey a (nonlinear) Fredholm theory for a new class of ambient spaces called polyfolds, and develop the analytical foundations for some of the applications of the theory. The basic feature of these new spaces, which can be finite and…
This is a survey paper of Shelah's pcf theory. In this part the theory is developed up to the pcf theorem.
Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up to a linear linear degree of freedom. We present new…
This article is a very short introduction to pcf theory for topologists.
This is a review for Elsevier's Encyclopedia of mathematical physics.
See hep-ph/0304045
An overview of the recent developments in plurifine potential theory.
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
This is an expository and introductory note on some results obtained in "Coisotropic embeddings in Poisson manifolds" (ArXiv math/0611480). Some original material is contained in the last two sections, where we consider linear Poisson…