Related papers: Quantization of Teichm\"uller spaces and the quant…
Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
We obtain estimates on the character of the cohomology of an $S^1$-equivariant holomorphic vector bundle over a Kaehler manifold $M$ in terms of the cohomology of the Lerman symplectic cuts and the symplectic reduction of $M$. In…
Chekhov, Fock and Kashaev introduced a quantization of the Teichm\"{u}ller space $\mathcal{T}^q(S)$ of a punctured surface $S$, and an exponential version of this construction was developed by Bonahon and Liu. The construction of the…
We prove that the space of convex real projective structures on a surface of genus $g\ge 2$ admits a mapping class group invariant K\"ahler metric where Teichm\"uller space with Weil-Petersson metric is a totally geodesic complex…
We study the Asymptotic Cone of Teichm\"uller space equipped with the Weil-Petersson metric. In particular, we provide a characterization of the canonical finest pieces in the tree-graded structure of the asymptotic cone of Teichm\"uller…
In this paper, we begin a quantization program for nilpotent orbits of a real semisimple Lie group. These orbits and their covers generalize the symplectic vector space. A complex structure polarizing the orbit and invariant under a maximal…
The symplectic reduction of pure spherically symmetric (Schwarzschild) classical gravity in D space-time dimensions yields a 2-dimensional phase space of observables consisting of the Mass M (>0) and a canonically conjugate (Killing) time…
Let M be a compact Kahler manifold equipped with a Hamiltonian action of a compact Lie group G. In this paper, we study the geometric quantization of the symplectic quotient M//G. Guillemin and Sternberg [Invent. Math. 67 (1982), 515--538]…
Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…
We prove a quantitative estimate with a power saving error term for the number of filling closed geodesics of a given topological type and length $\leq L$ on an arbitrary closed, orientable, negatively curved surface. More generally, we…
We consider Thompson's groups from the perspective of mapping class groups of surfaces of infinite type. This point of view leads us to the braided Thompson groups, which are extensions of Thompson's groups by infinite (spherical) braid…
We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove…
The phase space of a compact, irreducible, simply connected, Riemannian symmetric space admits a natural family of K\"ahler polarizations parametrized by the upper half plane $S$. Using this family, geometric quantization, including the…
Hirzebruch surfaces, defined as the projectivization of line bundles over $\C\mathbb{P}^1$, support a toric action and thus represent an infinite class of symplectic toric manifolds of complex dimension 2. In this paper, an infinite class…
Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group $SU_q(2)$ is such…
In the quantum Teichmuller theory, based on Penner coordinates, the mapping class groups of punctured surfaces are represented projectively. The case of a genus three surface with one puncture is worked out explicitly. The projective factor…
In this paper we study the symplectic and Poisson geometry of moduli spaces of flat connections over quilted surfaces. These are surfaces where the structure group varies from region to region in the surface, and where a reduction (or…
Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued distributions. Therefore, one is usually forced to find a…
The space of symplectic connections on a symplectic manifold is a symplectic affine space. M. Cahen and S. Gutt showed that the action of the group of Hamiltonian diffeomorphisms on this space is Hamiltonian and calculated the moment map.…