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:
Karwasz1Karwasz2
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:
and
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