IST Lecture Series in Algebraic Geometry & Physics
Algebraic Geometry & String Theory
Lisbon, I.S.T., room PA3, 08/02-11/02
by
PROGRAMME
|
13h30-15h00
|
15h30-17h00
|
17h30-19h00
|
08/02
Monday
|
HERNÀNDEZ RUIPÉREZ:
Introduction to Schemes (1) |
BRUZZO:
String Theory & Geometry |
HERNÀNDEZ RUIPÉREZ:
Introduction to Schemes (2) |
09/02
Tuesday |
BRUZZO:
SYZ
and special Lagrangian geometry |
HERNÀNDEZ RUIPÉREZ:
Abelian varieties & K3 surfaces |
|
10/02
Wednesday
|
BRUZZO:
Mirror symmetry for K3 surfaces |
HERNÀNDEZ RUIPÉREZ:
Elliptic surfaces and relative Jacobians |
BRUZZO:
Toplogical mirror symmetry for Calabi-Yau 3-folds |
11/02
Thursday |
HERNÀNDEZ RUIPÉREZ:
Fourier-Mukai Transforms |
BRUZZO:
Mirror symmetry & D-branes.
|
|
REFERENCES
For the course of U. Bruzzo:
- R.C. McLean
Deformations of calibrated submanifolds,
math.duke.edu/preprints/96-01.ps
- I. Dolgachev
Mirror symmetry for lattice polarized K3 surfaces,
alg-geom/9502005
- Andrew Strominger, Shing-Tung Yau, Eric Zaslow
Mirror Symmetry is T-Duality,
hep-th/9606040
- Mark Gross, P. M. H. Wilson
Mirror Symmetry via 3-tori for a class of Calabi-Yau Threefolds,
alg-geom/9608004
- Claudio Bartocci, Ugo Bruzzo, Daniel Hernandez Ruiperez, Jose' M. Mu~noz Porras
Mirror symmetry on K3 surfaces via Fourier-Mukai transform,
alg-geom/9704023
- Nigel Hitchin
The moduli space of special Lagrangian submanifolds
dg-ga/9711002
- Mark Gross
Special Lagrangian Fibrations I: Topology,
alg-geom/9710006
- Mark Gross
Special Lagrangian Fibrations II: Geometry,
math/9809072
- U. Bruzzo, G. Sanguinetti
Mirror symmetry on K3 surfaces as a hyper-Kaehler rotation,
physics/9802044
- C. Bartocci, U. Bruzzo , G. Sanguinetti
Categorial mirror symmetry for K3 surfaces
math-ph/9811004
math-ph/9811004
For the course of D. Hernàndez-Ruipérez:
1) An introduction to sheaf theory and sheaf cohomology, close to the
approach of the course can be found in:
- C. Bartocci, U. Bruzzo, D. Hernández Ruipérez. The Geometry of
Supermanifolds. Kluwer Dordrecht 1991, Chapter 1.
2) For schemes, any text on Algebraic Geometry will be useful. Two
examples are:
- R. Hartshorne. Algebraic Geometry. GTM 52, Springer Verlag 1977
- S. Iitaka. Algebraic Geometry: an introduction to birational geometry of
algebraic varieties. GTM 76, Springer Verlag 1982.
3) For abelian varieties, K3 surfaces and elliptic surfaces:
- D. Mumford. Abelian Varieties. Oxford Univ. Press 1970
- W. Barth, C. Peters, A. Van de Ven. Compact Complex Surfaces,
Ergebnisse...3.Folge-Band 4. Springer verlag 1984.
4) For relative Jacobians:
- A. Altman, S. Kleiman. Compactifying the Picard scheme, Adv. in Math. 35,
(1980) 50-112.
5) For the Fourier-Mukai transform:
- S. Mukai. Duality between D(X) and D(\hat X) with its application to Picard
sheaves. Nagoya Math. J. 81 (1981) 153-175.
- C. Bartocci, U. Bruzzo and D. Hernández Ruipérez, Fourier-Mukai transform
and Index Theory. Manuscripta Math. 85 (1994), 141-163.
- C. Bartocci, U. Bruzzo, D. Hernández Ruipérez. A Fourier-Mukai transform
for stable bundles on K3 surfaces. J. reine angew. Math. 486 (1997) 1-16;
alg-geom/9405006
PREPARATORY LECTURE
A preparatory lecture on sheaves and sheaf cohomology
(some knowledge of these topics will be assumed
in the courses of U. Bruzzo and D. Hernàndez Ruipèrez)
will be given by
Carlos Florentino
as the first session of new Working
Seminar on Algebraic Geometry in mid January.
All are most wellcome!
The VENUE
The lectures will be held at
the Lisbon
Instituto Superior Técnico , Av. Rovisco Pais, Lisboa in room PA3 of Edifício de Pós
Graduação (floor -1 under the Mathematics Department, near the
Bar). The mathematics department is
#5 in the plant of the Institute.
ORGANIZATION
Organization and sponsorship by Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de
Matemática of
Instituto Superior Técnico.
For any questions contact us:
Carlos Florentino
José Mourão
João Pimentel Nunes