The intersection of a complex plane curve with a small three-sphere surrounding one of its
singularities is a nontrivial link. The refined punctual Hilbert schemes of the singularity …

The concept of motivic integration was invented by Kontsevich to show that birationally
equivalent Calabi-Yau manifolds have the same Hodge numbers. He constructed a certain …

Reports on the application of the notion of the integral with respect to the Euler characteristic
over the projectivization of the space of germs of functions, for computing the Poincare …

The Grothendieck semiring S0 (rC) of complex quasi-projective varieties is the semigroup
generated by isomorphism classes [X] of such varieties modulo the relation [X]=[X− Y]+[Y] for …

The notion of integration with respect to the Euler characteristic and its generalizations are
discussed: integration over the infinite-dimensional spaces of arcs and functions, motivic …

We consider knot invariants in the context of large N transitions of topological strings. In
particular we consider aspects of Lagrangian cycles associated to knots in the conifold …

Lectures on knot homology Page 146 Contemporary Mathematics Volume 680 , 2016 http://dx.
doi. org/10.1090/conm/680/13702 Lectures on knot homology Satoshi Nawata and Alexei …

Let C be a locally planar curve. Its versal deformation admits a stratification by the genera of
the fibres. The strata are singular; we show that their multiplicities at the central point are …

Abstract We compute the Heegaard Floer link homology of algebraic links in terms of the
multi-variate Hilbert function of the corresponding plane curve singularities. The main result …

Let $ X\rightarrow\mathrm {spec}(R) $ be a resolution of singularities of a normal surface
singularity $\mathrm {spec}(R) $, with integral exceptional divisors $ E_1,\dotsc, E_r $. We …