Outline of talk: My goal is to introduce a few more advanced topics in algebraic geometry but not to go into too much detail. This will be a survey of (1) Elimination Theory and review from last time (BRIEFLY) (a) History and goals (b) Geometric Extension Theorem (2) Invariant Theory (3) Dimension Theory (a) Krull Dimension (b) Hilbert Polynomial (c) Dimension of a variety (4) Syzygies (a) Defi...

Energy-momentum tensor for the toroidal Lie algebras. Abstract. We construct vertex operator representations for the full (N + 1)-toroidal Lie algebra g. We associate with g a toroidal vertex operator algebra, which is a tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine sl N VOA and a twisted Heisenberg-Virasoro VOA. The modules for the toroidal VOA are also modules...

Given a closed convex cone C in a finite dimensional real Hilbert space H, a weakly homogeneous map f : C → H is a sum of two continuous maps h and g, where h is positively homogeneous of degree γ (≥ 0) on C and g(x) = o(||x||) as ||x|| → ∞ in C. Given such a map f , a nonempty closed convex subset K of C, and a q ∈ H, we consider the variational inequality problem, VI(f,K, q), of finding an x∗...

We introduce a class of induced representations of the degenerate double affine Hecke algebra H of glN (C) and analyze their structure mainly by means of intertwiners of H . We also construct them from ŝlm(C)-modules using Knizhnik-Zamolodchikov connections in the conformal field theory. This construction provides a natural quotient of induced modules, which turns out to be the unique irreducib...

The conjugacy classes of the involutive automorphisms of the affine Kac-Moody algebras C (1) ℓ for ℓ ≥ 2 are determined using the matrix formulation of automorphisms of an affine Kac-Moody

This paper addresses the problem of abstracting a set of affine transformers ÝÑv 1 ÝÑv C ÝÑ d , where ÝÑv and ÝÑv 1 represent the prestate and post-state, respectively. We introduce a framework to harness any base abstract domain B in an abstract domain of affine transformations. Abstract domains are usually used to define constraints on the variables of a program. In this paper, however, abstr...

Fish Protein Concentrate (FPC) is a healthy, sustainable and high nutritive product that produced from fish and protein and other nutrients are more concentrated than in the fresh fish. The aim of this research is to study the sustainability of FPC produced from Kilka (combination of three Caspian Sea Kilka species, Clupeonella engrauliformis, C. grimmi and C. cultriventris which were not ident...

Fish Protein Concentrate (FPC) is a healthy, sustainable and high nutritive product that produced from fish and protein and other nutrients are more concentrated than in the fresh fish. The aim of this research is to study the sustainability of FPC produced from Kilka (combination of three Caspian Sea Kilka species, Clupeonella engrauliformis, C. grimmi and C. cultriventris which were ...

We give a type free formula for the expansion of k-Schur functions indexed by fundamental coweights within the affine nilCoxeter algebra. Explicit combinatorics are developed in affine type C.