7 research outputs found
Instantons, Topological Strings and Enumerative Geometry
We review and elaborate on certain aspects of the connections between
instanton counting in maximally supersymmetric gauge theories and the
computation of enumerative invariants of smooth varieties. We study in detail
three instances of gauge theories in six, four and two dimensions which
naturally arise in the context of topological string theory on certain
non-compact threefolds. We describe how the instanton counting in these gauge
theories are related to the computation of the entropy of supersymmetric black
holes, and how these results are related to wall-crossing properties of
enumerative invariants such as Donaldson-Thomas and Gromov-Witten invariants.
Some features of moduli spaces of torsion-free sheaves and the computation of
their Euler characteristics are also elucidated.Comment: 61 pages; v2: Typos corrected, reference added; v3: References added
and updated; Invited article for the special issue "Nonlinear and
Noncommutative Mathematics: New Developments and Applications in Quantum
Physics" of Advances in Mathematical Physic
Signed countings of types B and D permutations and t,q-Euler numbers
[[abstract]]It is a classical result that the parity-balance of the number of weak excedances of all permutations (derangements, respectively) of length n is the Euler number , alternating in sign, if n is odd (even, respectively). Josuat-Vergès obtained a q-analog of the results respecting the number of crossings of a permutation. One of the goals in this paper is to extend the results to the permutations (derangements, respectively) of types B and D, on the basis of the joint distribution in statistics excedances, crossings and the number of negative entries obtained by Corteel, Josuat-Vergès and Kim.
Springer numbers are analogous Euler numbers that count the alternating permutations of type B, called snakes. Josuat-Vergès derived bivariate polynomials and as generalized Euler numbers via successive q-derivatives and multiplications by t on polynomials in t. The other goal in this paper is to give a combinatorial interpretation of and as the enumerators of the snakes with restrictions.[[notice]]補正完
Approximate Methods for the Real-Time Evolution of Quantum Systems and Fields
Tesis doctoral inédita leida en la Universidad Autónoma de Madrid. Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura:26-10-201
Heavy Quarkonium Physics
This report is the result of the collaboration and research effort of the
Quarkonium Working Group over the last three years. It provides a comprehensive
overview of the state of the art in heavy-quarkonium theory and experiment,
covering quarkonium spectroscopy, decay, and production, the determination of
QCD parameters from quarkonium observables, quarkonia in media, and the effects
on quarkonia of physics beyond the Standard Model. An introduction to common
theoretical and experimental tools is included. Future opportunities for
research in quarkonium physics are also discussed.Comment: xviii + 487 pages, 260 figures. The full text is also available at
the Quarkonium Working Group web page: http://www.qwg.to.infn.i
Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education
International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland