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QUANTUM COHOMOLOGY OF ORTHOGONAL GRASSMANNIANS
ORTHOGONAL GRASSMANNIANS QUANTUM COHOMOLOGY
2015/12/17
Let V be a vector space with a nondegenerate symmetric form and
OG be the orthogonal Grassmannian which parametrizes maximal isotropic
subspaces in V . We give a presentation for the (small) quantum...
Let G be a classical Lie group and P a maximal parabolic subgroup. We describe a quantum Pieri rule which holds in the small quantum
cohomology ring of G=P. We also give a presentation of this ring i...
Let G be a semisimple complex algebraic group and P a parabolic subgroup of G.
The homogeneous space X = G=P is a projective complex manifold. My aim in
this lecture is to survey what is known about...
We study the three point genus zero Gromov-Witten invariants
on the Grassmannians which parametrize non-maximal isotropic subspaces in
a vector space equipped with a nondegenerate symmetric or skew-...
A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere
Gluing Dirac Type Operators Mirror Quantum Two-Sphere
2014/12/12
The goal of this paper is to introduce a class of operators, which we call quantum Dirac type operators on a noncommutative sphere, by a gluing construction from copies of noncommutative disks, subjec...
Information geometry and the hydrodynamical formulation of quantum mechanics
Information geometry the hydrodynamical formulation quantum mechanics Differential Geometry
2012/4/18
Let (M,g) be a compact, connected and oriented Riemannian manifold. We denote D the space of smooth probability density functions on M.
Abstract: We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-tim...
Integrable defects in affine Toda field theory and infinite dimensional representations of quantum groups
Integrable defects affine Toda field theory infinite dimensional representations quantum groups
2011/3/3
Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations.
Riemann hypothesis and Quantum Mechanics
Bost-Connes model Riemann Hypothesis Primorial numbers
2011/2/24
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
Riemann hypothesis and Quantum Mechanics
Bost-Connes model Riemann Hypothesis Primorial numbers
2011/3/4
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
Quantum Gravity coupled to Matter via Noncommutative Geometry
Quantum Gravity Matter Noncommutative Geometry
2011/3/2
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construc-tion which encodes the kinematics of quantum gravity.
Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction
Quantum Geometric Tensor Simple Quantum System pedagogical Introduction
2011/3/2
Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that
our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (o...
Quantum Isometries of the finite noncommutative geometry of the Standard Model
Quantum Isometries finite noncommutative geometry Standard Model
2010/12/6
We compute the quantum isometry group of the finite noncommutative geometry F describing
the internal degrees of freedom in the Standard Model of particle physics. We show that this
provides genuine...
Three realizations of quantum affine algebra $U_q(A_2^{(2)})$
Three realizations quantum affine algebra $U_q(A_2^{(2)})$
2010/12/3
We establish explicit isomorphisms between three realizations of the quantum twisted affine algebra Uq(A(2)2 ): the Drinfeld (“current”) realization, the Chevalley realization, and
the so-called RLL ...
On the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$
Skew Brownian motion advection-diffusion local time
2010/12/14
Advective skew dispersion is a natural Markov process defined by a diffusion with drift across an interface of jump discontinuity in a piecewise constant diffusion coefficient.