Seminar in
MODULI of CURVES, GROMOV-WITTEN INVARIANTS,
QUANTUM COHOMOLOGY and RELATED TOPICS
Seminar outline:
Part I: Moduli spaces of stable curves and stable maps and
their compactifications.
Part II: Gromov-Witten invariants.
Part III: Quantum cohomology.
Part IV: Applications to enumerative geometry.
Part V: Mirror symmetry conjecture.
Part VI: Frobenius manifolds.
Part VII: Non-archimedian amoebas.
Prerequisites:
Basic courses in linear algebra, differential geometry and topology.
Literature:
M. Audin.
Cohomologie quantique, Seminaire Bourbaki, 1995-96, n. 806;
M. Audin.
An introduction to Frobenius manifolds, moduli
spaces of stable maps and
quantum cohomology,
Preprint, IRMA, Universite Louis Pasteur, Strasbourg, 1998;
B. A. Dubrovin.
Geometry of 2D topological field theories,
In: Lect. Notes Math. 1620, Springer, 1996, pp. 120-348;
W. Fulton and R. Pandharipande.
Notes on stable maps and quantum cohomology,
In: Algebraic Geometry, Santa Cruz 1995
(Proc. Symp. Pure Math. vol. 62, part 2), AMS, 1997, pp. 45-96;
A. Givental.
A tutorial on quantum cohomology,
In: Symplectic
geometry and topology (Park City, UT, 1997), 231--264, IAS/Park City
Math. Ser., 7, Amer. Math. Soc., Providence, RI, 1999.
Y. Imayoshi and M. Taniguchi.
An introduction to Teichmuller spaces,
Springer, 1992;
S. M. Natanzon.
Geometry of two-dimensional topological field theories,
Independent Moscow University, 1998;
Quantum fields and strings: A course for mathematicians.
P. Deligne et al., eds.,
AMS, 1999;
Y. Ruan and G. Tian.
A mathematical theory of quantum cohomology;
J. Diff. Geom. 42 (1995), no. 2, pp. 259-367.