A coding of real null four-momenta into world-sheet coordinates.
A descendent relation in genus 2
Arc operads and arc algebras.
Cosmological symmetry breaking and generation of electromagnetic field.
Dimension vs. genus: A surface realization of the little k-cubes and an operad
We define a new operad based on surfaces with foliations which contains suboperads. We construct CW models for these operads and provide applications of these models by giving actions on Hochschild complexes (thus making contact with string topology), by giving explicit cell representatives for the Dyer-Lashof-Cohen operations for the 2-cubes and by constructing new Ω spectra. The underlying novel principle is that we can trade genus in the surface representation vs. the dimension k of the little...
Dual-null dynamics
Fourier Mukai transforms and applications to string theory.
El artículo es una introducción a la transformación de Fourier-Mukai y sus aplicaciones a varios problemas de móduli, teoría de cuerdas y simetría "mirror". Se desarrollan los fundamentos necesarios para las transformaciones de Fourier-Mukai, entre ellos las categorías derivadas y los functores integrales. Se explican además sus versiones relativas, que se necesitan para precisar la noción de T-dualidad fibrada en variedades de Calabi-Yau elípticas de dimensión tres. Se consideran también varias...
Fuchsian groups and uniformization of Hurwitz spaces.
Ground states of supersymmetric matrix models
We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in . Moreover, it would be unique. Other values of , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation. This seminar...
Multi-instantons in higher dimensions and superstring solitons.
Quantum Cohomology and Crepant Resolutions: A Conjecture
We give an expository account of a conjecture, developed by Coates–Iritani–Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold to the quantum cohomology of a crepant resolution of . We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan–Graber. We also give a ‘quantized’ version of the conjecture, which determines higher-genus...
Quantum gravity: unification of principles and interactions, and promises of spectral geometry.
Twist quantization of string and Hopf algebraic symmetry.