Related papers: Polyfold and Fredholm Theory

An expository survey article on Heegaard splittings

A Short Course on Frame Theory.

An expository hitchhikers guide to some theorems in mathematics.

We present some plausible definitions for the tangent grupoid of a manifold M, as well as some of the known applications of the structure. This is a kind of introductory note.

An erratum to this article is posted at https://gcc.episciences.org/page/errata This paper generalizes results of M. Moon on the fibering of certain compact 3-manifolds over the circle. It also generalizes a theorem of H. B. Griffiths on…

The purpose of this book is to build up the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for the researches of arithmetic geometry in several directions.

Some additional references are included on the last 3 pages.

This note provides a Lefschetz theorem for Minkowski sums of polytopes, and conclude lower bound theorems for Minkowski sums of polytopes. It is written as an appendix to arXiv:1405.7368, so notation and references follow that paper.

This is a pedagogical article cited in the foregoing research note, quant-ph/9911050

We show that layer potential groupoids for conical domains constructed in an earlier paper (Carvalho-Qiao, Central European J. Math., 2013) are Fredholm groupoids, which enables us to deal with many analysis problems on singular spaces in a…

This is a chapter (planned to appear in Wiley's upcoming Encyclopedia of Operations Research and Management Science) describing parts of the theory of convex polyhedra that are particularly important for optimization. The topics include…

This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of polynomial growth and amenability. We discuss the ping-pong…

We show that the open problem presented in "Geometric Folding Algorithms: Linkages, Origami, Polyhedra" [DO07] is solved by a theorem of Burago and Zalgaller [BZ96] from more than a decade earlier.

This article is part introduction and part survey to the mathematical area centered around local cohomology.

The authors show that a wide class of Fredholm determinants arising in the representation theory of "big" groups such as the infinite-dimensional unitary group, solve Painleve equations. Their methods are based on the theory of integrable…

This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4, pp.94--104.

We prove several extensions of the Erdos-Fuchs theorem.

This is the first paper in a series which proposes and develops the polyfold Fredholm structure--Kuranishi structure correspondence, identifying these two abstract perturbative structures which are indispensable for constructing and…

Some geometric structures with associated Riemannian metrics have been considered in the book.

This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier.