We review the status of duality symmetries in superstring theories. These discrete symmetries mark the striking differences between theories of pointlike objects and theories of extended objects. They prove to be very helpful in understanding non-perturbative effects in string theories. We will also briefly discuss the strange role played by open strings and their solitons in the emerging scena...

We study the Verlinde bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier-Mukai symmetries of the Verlinde bundles are found, consistently with strange duality. Along the way, a transformation formula for the t...

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. With the help of the quantum to classical principle we give presentations of the quantum cohomology algebras. These algebras are semi-simple for adjoint non coadjoint varieties and some properties of th...

This article examines the moral duality presented in Robert Louis Stevenson’s novella The Strange Case of Dr. Jekyll and Mr. Hyde its connection to Christian morals guiding Victorian society. It suggests that undermines a dualistic perception human nature through changes point view by replacing clear with an abject ambiguity. argues abjection part self is portrayed as destructive essentially cr...

The Peterson comparison formula proved by Woodward relates the three-pointed Gromov-Witten invariants for quantum cohomology of partial flag varieties to those complete flag. Another such can be obtained composing a combinatorial version isomorphism with result Lapointe and Morse relating Littlewood-Richardson coefficients Grassmannian k-Schur analogs in homology affine adding rim hooks. We sho...

Global sections of the line bundles on a moduli space of vector bundles (or, more generally, principal G-bundles) are called generalized theta functions. The dimension of the vector spaces of generalized theta functions is given by the celebrated Verlinde formula. If you compute several Verlinde numbers, you will find that some of them coincide unexpectedly. Behind the coincidence, there is oft...