We recall our construction of fundamental classes in the algebraic cobordism of smooth quasi-projective varieties, and show by examples that it is not possible to extend this to fundamental classes, functorial for local complete intersection morphisms, for Cohen-Macaulay varieties.

Given a smooth projective toric variety X, we construct an A∞ category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line bundles on X.

Interpolation by translates of \radial" basis functions is optimal in the sense that it minimizes the pointwise error functional among all comparable quasi{interpolants on a certain \native" space of functions F . Since these spaces are rather small for cases where is smooth, we study the behavior of interpolants on larger spaces of the form F 0 for less smooth functions 0. It turns out that in...

In this note we define the Chern-Simons classes of a flat superconnection, D + L, on a complex Z/2Z-graded vector bundle E on a manifold such that D preserves the grading and L is an odd endomorphism of E. As an application, we obtain a definition of Chern-Simons classes of a (not necessarily flat) morphism between flat vector bundles on a smooth manifold. An application of Reznikov’s theorem s...

This paper describes an approved algorithm for the problems of unequal circle packing – the quasi-physical quasihuman algorithm. First, the quasi-physical approach for the general packing problems is described in solving the pure problems of unequal circle packing. The method is an analogy to the physical model in which a number of smooth cylinders are packed inside a container. A quasi-human s...

In this note, we will show that the fundamental group of any negatively δ-pinched (δ > 14) manifold can’t be the fundamental group of a quasi-compact Kähler manifold. As a consequence of our proof, we also show that any nonuniform lattice in F4(−20) cannot be the fundamental group of a quasi-compact Kähler manifold. The corresponding result for uniform lattices was proved by Carlson and Hernánd...