Teichmüller Theory

This is a report on the workshop on Teichmüller theory held in Oberwolfach, from November 28 to December 4, 2010. The workshop brought together people working in various aspects of the field, with a focus on recent developments. The topics discussed included higher Teichmüller theory, moduli spaces of flat connections, cluster algebras, quantization of Teichmüller spaces, the dynamical aspects of the Teichmüller and Weil-Petersson geodesic flows, the metric and the boundary theory of Teichmüller space including the new developments on Thurston’s asymmetric metric, string topology, geometric analysis on moduli spaces, and relations with three-manifold topology and with minimal surface theory were also highlighted. The mapping class group was also discussed in detail, from various points of view, including its actions on simplicial complexes and on infinite-dimensional Teichmüller spaces, its asymptotic dimension, the relation with the arc operad, the generalizations of the Johnson homomorphisms to the monoid of homology cylinders, making contact with knot theory and with the Casson invariant and other 3-manifolds invariants. There was an open problem session, which is also reported on here

This Week's Finds in Mathematical Physics (1-50)

These are the first 50 issues of This Week's Finds of Mathematical Physics, from January 19, 1993 to March 12, 1995. These issues focus on quantum gravity, topological quantum field theory, knot theory, and applications of $n$-categories to these subjects. However, there are also digressions into Lie algebras, elliptic curves, linear logic and other subjects. They were typeset in 2020 by Tim Hosgood. If you see typos or other problems please report them. (I already know the cover page looks weird).Comment: 242 page

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition