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We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
A fundamental problem from computational learning theory is to well-reconstruct an unknown function on the discrete hypercubes. One classical result of this problem for the random query model is the l...
Nonlinear partial differential equations (PDEs) are crucial to modelling important problems in science but they are computationally expensive and suffer from the curse of dimensionality. Since quantum...
Topology and entanglement are two powerful principles for characterizing the structure of complex quantum states. In a new paper in the journal Physical Review X, researchers from the University of Pe...
It is a great pleasure to announce the 7th Workshop on Quantum Many-Body Computation, which will be held in Beijing from May 5 to 7, 2017. This workshop is organized by the University of Chinese Acade...
Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V . We give a presentation for the (small) quantum cohomology ring QH¤(LG) ...
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...
This is the written version of my ˉve lectures at the Banach Center mini-school on `Schubert Varieties', in Warsaw, Poland, May 18{22, 2003.
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-...
Let X be a symplectic or odd orthogonal Grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas ...
Models of quantum computing rely on transformations of the states of a quantum memory. We study mathematical aspects of a model proposed by Wu in which the memory state is changed via the scattering o...
We consider the problem of detecting the true quantum state among r possible ones, based onmeasurements performed on n of copies of a finite dimensional quantum system. It is known that the exponent f...
We consider the problem of detecting the true quantum state among r possible ones, based of measurements performed on n copies of a finitedimensional quantum system. A special case is the problem of d...

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