相关论文: Recent Developments in Seiberg-Witten Theory and C…
We formulate and study an extension of gerbe duality to relative Gromov-Witten theory.
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
We construct a Thom class in complex equivariant elliptic cohomology extending the equivariant Witten genus. This gives a new proof of the rigidity of the Witten genus, which exhibits a close relationship to recent work on non-equivariant…
We give a brief survey for the recent development of inverse scattering theory on non-compact Riemannian manifolds. The main theme is the reconstruction of the manifold and the metric from the scattering matrix.
A simplified, user-friendly repackaging of the curvature estimates implied by the Seiberg-Witten equations is formulated in terms of the convex hull of the set of monopole classes. New results are also obtained concerning boundary cases of…
This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.
We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and…
This note gives a brief review of the integrable structures presented in the Seiberg-Witten approach to the N=2 SUSY gauge theories with emphasize on the case of the gauge theories with matter hypermultiplets included (described by spin…
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…
This paper, yet another account of Seiberg-Witten theory and its consequences for algebraic surfaces, is the written version of the author's talk at the Santa Cruz conference.
This is a very brief review of relations between Seiberg-Witten theories and integrable systems with emphasis on the perturbative prepotentials presented at the E.S.Fradkin Memorial Conference.
The talk contains a brief introduction string theory, followed by a discussion of some of the recent developments.
Fix a prime number $p$. We report on some recent developments in algebraic geometry (broadly construed) over $p$-adically complete commutative rings. These developments include foundational advances within the subject as well as external…
These notes provide an introductory exposition of the Seiberg-Witten gauge theory. They collect the material presented in a series of seminars given by the author at the University of Milano.
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
A dual description of 3-dimensional topological Seiberg-Witten theory in terms of the Alexander invariant on manifolds obtained via surgery on a knot is proposed. The description directly follows from a low-energy analysis of the…
We review some recent developments in the theory of $W_\infty$. We comment on its relevance to lower-dimensional string theory.
We survey a number of Weyl type laws that have recently been established in low-dimensional symplectic geometry. These have had a number of applications, which we also introduce. We sketch a number of proofs so that the reader can get a…
This article is an overview of some of the remarkable progress that has been made in Sasaki-Einstein geometry over the last decade, which includes a number of new methods of constructing Sasaki-Einstein manifolds and obstructions.
The formulation of Seiberg-Witten maps from the point of view of consistent deformations of gauge theories in the context of the Batalin-Vilkovisky antifield formalism is reviewed. Some additional remarks on noncommutative Yang-Mills theory…