A general technique is outlined for investigating supersymmetry properties of a charged spin-1 2 quantum particle in time-varying electromagnetic fields. The case of a time-varying uniform magnetic induction is examined and shown to provide a physical realization of a super-symmetric quantum-mechanical system. Group-theoretic methods are used to factorize the relevant Schrödinger equations and ...

These lecture notes cover my talks at the June 2009 “Geometry of Quantum Fields and Strings” summer school at the University of Pennsylvania. I begin by giving a very brief introduction to quantum field theory, quickly moving to nonlinear sigma models and the associated A and B model topological field theories, and the physical realization of derived categories. Later lectures will cover Landau...

Abstract. Our main result offers a new (quite systematic) way of deriving bounds for the cup-length of Poincaré spaces over fields; we outline a general research program based on this result. For the oriented Grassmann manifolds, already a limited realization of the program leads, in many cases, to the exact values of the cup-length and to interesting information on the Lyusternik-Shnirel’man c...

We calculate the symmetry currents for the type IIB superstring on a maximally supersymmetric plane wave background using the N=(2,2) superconformally covariant U(4) formulation developed by Berkovits, Maldacena and Maoz. An explicit realization of the U(4) generators together with 16 fermionic generators is obtained in terms of the N=(2,2) worldsheet fields. Because the action is no longer qua...

We use an extended version of the hadronic SU(3) non-linear realization of the sigma model that also includes quarks to study hybrid stars. Within this approach, the degrees of freedom change naturally as the temperature/density increases. Different prescriptions of charge neutrality, local and global, are tested and the influence of strong magnetic fields and the anomalous magnetic moment on t...

We show that if U∗ is a hypercover of a topological space X then the natural map hocolim U∗→X is a weak equivalence. This fact is used to construct topological realization functors for the A1-homotopy theory of schemes over real and complex fields. In an appendix, we also prove a theorem about computing homotopy colimits of spaces that are not cofibrant. Mathematics Subject Classification (2000...

A residue-theoretic representation is given for massless matter fields in (quotients) of (weighted) Calabi-Yau complete intersection models and the corresponding chiral operators in Landau-Ginzburg orbifolds. The well known polynomial deformations are thus generalized and the universal but somewhat abstract Koszul computations acquire a concrete realization and a general but more heuristic rein...

My research interest lies in the area of arithmetic geometry related to Langlands correspondence, where the theory of automorphic forms and algebraic geometry intersect. It is one of the most interesting and actively studied subject of algebraic number theory, whose origin goes back to the theory of complex multiplication. My research is currently focused on the local aspect of this theory, nam...

The development and use of quantum computers for chemical applications has potentially revolutionary impact opportunities to change the way computing is done in future generations. The workshop brought together leading scientists from the fields of quantum information, quantum computing and quantum chemistry to exchange ideas and discuss ways to develop quantum algorithms and experimental reali...

The long-range fields associated with non-abelian vortices generally obstruct full realization, in the spectrum, of the symmetry of the ground state. In the context of 2+1 dimensional field theories, we show how this effect manifests itself concretely in altered conditions for the angular momentum and in the energy spectrum. A particularly interesting case is supersymmetry, which is obstructed ...