4 sep 2017 - 9 sep 2017
Trento
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SCHOOL (AND WORKSHOP) ON SYZYGIES
TRENTO, SEPTEMBER 4-9, 2017
First announcement
Lecturers.
M. Chardin (Université Pierre et Marie Curie – Fr)
M.E. Rossi (Università di Genova – It)
Supporting lecturers.
M. Boij (KTH Stockholm – Se)
E. Carlini (Politecnico di Torino – It)
Organizers.
The School/Workshop is organized by G. Casnati, F.
Galluzzi, R. Notari, F. Vaccarino. For contacting the
organizers send a mail to
geometri nospam calvino.polito.it
The School/Workshop is supported by CIRM-Fondazione Bruno
Kessler (formerly CIRM-ITC).
The School and the Workshop will take place at
Fondazione Bruno Kessler-IRST
via Sommarive, 18
38050 Povo (Trento) - Italy
Aim of the School.
The School is mainly aimed to PhD students and young
researchers in Algebraic Geometry, introducing the
participants to research, beginning from a basic level
with a view towards the applications and to the most
recent results. A tentative program is as follows.
M. Chardin.
Notions and tools of homological nature. Complexes,
spectral sequences associated to a double complex. Tor and
Ext modules, local cohomology and local duality.
Castelnuovo-Mumford regularity. Basic properties and
examples from geometry (curves).
Powers of ideals. Asymptotic behavior of regularity, local
cohomology and Betti tables.
Rees algebras and symmetric algebras. Geometric
interpretation of the asymptotic behavior of regularity.
Koszul homology, approximation complexes and applications
to the study of rational maps.
M.E. Rossi.
Hilbert functions and Syzygies. Graded minimal free
resolutions. Resolutions of points in the projective
space and their geometry. Castelnuovo Lemma and
generalizations.
Computational aspects of the free resolutions.
An introduction to Boij-Söderberg theory and the
multiplicity conjecture.
Castelnuovo-Mumford regularity: Kleiman’s result; recent
developments concerning Eisenbud-Goto and Stilmann
conjectures.
Infinite free resolutions and Koszul algebras.
Further announcements.
A more detailed second announcement (containing
information on accommodation, registration, and financial
supports) will follow probably in February 2017.