Explicit constructions of quilts with seam condition coming from symplectic reduction

A Calculus of Constructions with Explicit Subtyping

The calculus of constructions can be extended with an infinite hierarchy of universes and cumulative subtyping. Subtyping is usually left implicit in the typing rules. We present an alternative version of the calculus of constructions where subtyping is explicit. We avoid problems related to coercions and dependent types by using the Tarski style of universes and by adding equations to reflect ...

Explicit Constructions of Ramanujan Complexes

In [LSV] we defined and proved the existence of Ramanujan complexes, see also [B1], [CSZ] and [Li]. The goal of this paper is to present an explicit construction of such complexes. Our work is based on the lattice constructed by Cartwright and Steger [CS]. This remarkable discrete subgroup Γ of PGLd(F ), when F is a local field of positive characteristic, acts simply transitively on the vertice...

Quantization of Symplectic Reduction

Symplectic reduction, also known as Marsden-Weinstein reduction, is an important construction in Poisson geometry. Following N.P. Landsman [22], we propose a quantization of this procedure by means of M. Rieffel’s theory of induced representations. Here to an equivariant momentum map there corresponds an operator-valued rigged inner product. We define the operatoralgebraic notions that are invo...

Some New Constructions of Authentication Codes with Arbitration and Multi-Receiver from Singular Symplectic Geometry

Explicit constructions of point sets and sequences with low discrepancy

In this talk we discuss explicit constructions of sequences with optimal $L_2$ discrepancy and explicit constructions of point sets with optimal $L_q$ discrepancy for $1 < q < \infty$. In 1954 Roth proved a lower bound for the $L_2$ discrepancy of finite point sets in the unit cube of arbitrary dimension. Later various authors extended Roth's result to lower bounds also for the $L_q$ discrepanc...