REPORT


The two working days: 18 and 19 November at BC, were mainly devoted to rich mathematics related to singularities of hypersurfaces (mainly isolated but not only).

1. Piotr P. Karwasz (Nancy/ Gdańsk) gave 3 lectures on:


"Higher residue pairings of Kyoji Saito and (a,b)-modules".

The lectures covered: 

- Milnor fibration,
- Brieskorn lattices and M. Saito's theorems,
- K. Saito's higher residues pairings,
- and the theory of (a,b)-modules of Barlet.

The speaker also reported on his recent Doctoral Dissertation (Universit'e Nancy).

For a systematic exposition, see his preprints:

Karwasz1

Karwasz2



Related papers:

E. Brieskorn, Die Monodromie der Isolierten Singularit\"aten von Hyperfl\"achen, Manuscripta Math., 2 (1970), p. 103--161.
link to the French translation by Helene Maynadier-Gervais:
http://math.univ-angers.fr/~hlm/brieskorn.ps.gz

M. Saito, On the structure of Brieskorn lattice, Annales de l'Institut Fourier, 39 No. 1 (1989),
p. 27--72.
link

M. Saito, Period mappings via Brieskorn modules, Bull. Soc. math. France, 119 (1991),
p. 141--171.
link

K. Saito, The higher residue pairings K^{(k)}_F for a family of hypersurface singular points, Proceedings of Symposia in Pure Mathematics, volume 40 (1983), part 2.

See also:

Schulze




The lectures of Karwasz were very related to the talk of Maciej Borodzik (UW).


2. M. Borodzik spoke on:

"Semicontinuity of spectrum. Topological approach".

Abstract. We give a purely knot-theoretical proof of semicontinuity of spectra of
hypersurface singularities in C^2 (i.e. plane curve). We show possible generalisation
to higher dimension. This is joint work with Andras Nemethi and Andrew Ranicki.


For details, consult his preprints:

Borodzik-Nemethi1

and

Borodzik-Nemethi2


3. Halszka Tutaj-Gasinska (UJ) gave a lecture on:


"Symplectic packings, toric packings etc."


A survey, corresponding to this talk, is contained in her preprint:

Seshadri and packing constants



(Last modified on 4.12.2011.)