ICTP Mathematics Group: SMR 1137 Final Programme

ICTP - The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

SCHOOL ON DIFFERENTIAL GEOMETRY

(12 - 30 April 1999)

Final Programme (as of 27 April 1999)

ALL LECTURES WERE HELD IN THE MAIN LECTURE HALL, MAIN BUILDING

WEEK 1 (12 - 16 April)

Monday, 12 April
08.30-12.00 Registration and administrative formalities

14.05-14.15 Opening with Professor M.A. Virasoro

14.15-15.15 N. Hitchin (University of Oxford, U.K.)
Lagrangian foliations and mirror symmetry. (1)

15.15-16.45 B.H. Lian (Brandeis University, Waltham, U.S.A.)
Lectures on mirror symmetry. (1)

Tuesday, 13 April
09.30-10/30 A. Bobenko (Technische Universitaet Berlin, Germany)
Exploring surfaces through methods from the theory of integrable systems. Lectures on Bonnet problem. (1)

11.00-12.00 B.H. Lian (Brandeis University, Waltham, U.S.A.)
Lectures on mirror symmetry. (2)

14.30-15.30 N. Hitchin (University of Oxford, U.K.)
Lagrangian foliations and mirror symmetry. (2)

Wednesday, 14 April
09.30:10.30 A. Bobenko (Technische Universitaet Berlin, Germany)
Exploring surfaces through methods from the theory of integrable systems. Lectures on Bonnet problem. (2)

11.00-12.00 B.H. Lian (Brandeis University, Waltham, U.S.A.)
Lectures on mirror symmetry. (3)

14.30-15.30 N. Hitchin (University Oxford, U.K.)
Lagrangian foliations and mirror symmetry. (3)

Thursday, 15 April
09.30-10.30 A. Bobenko (Technische Universitaet Berlin, Germany)
Exploring surfaces through methods from the theory of integrable systems. Lectures on Bonnet problem. (3)

11.00-12.00 B.H. Lian (Brandeis University, Waltham, U.S.A.)
Lectures on mirror symmetry. (4)

14.30-15.30 N. Hitchin (University Oxford, U.K.)
Lagrangian foliations and mirror symmetry. (4)

Friday, 16 April
09.30:10.30 A. Bobenko (Technische Universitaet Berlin, Germany)
Exploring surfaces through methods from the theory of integrable systems. Lectures on Bonnet problem. (4)

11.00-12.00 N. Hitchin (University Oxford, U.K.)
Lagrangian foliations and mirror symmetry. (5)

14.30-15.30 B.H. Lian (Brandeis University, Waltham, U.S.A.)
Lectures on mirror symmetry. (5)

Monday, 12 April
08.30-12.00	Registration and administrative formalities

14.05-14.15	Opening with Professor M.A. Virasoro
14.15-15.15	N. Hitchin (University of Oxford, U.K.) Lagrangian foliations and mirror symmetry. (1)
15.15-16.45	B.H. Lian (Brandeis University, Waltham, U.S.A.) Lectures on mirror symmetry. (1)

Tuesday, 13 April
09.30-10/30	A. Bobenko (Technische Universitaet Berlin, Germany) Exploring surfaces through methods from the theory of integrable systems. Lectures on Bonnet problem. (1)
11.00-12.00	B.H. Lian (Brandeis University, Waltham, U.S.A.) Lectures on mirror symmetry. (2)

14.30-15.30	N. Hitchin (University of Oxford, U.K.) Lagrangian foliations and mirror symmetry. (2)

Wednesday, 14 April
09.30:10.30	A. Bobenko (Technische Universitaet Berlin, Germany) Exploring surfaces through methods from the theory of integrable systems. Lectures on Bonnet problem. (2)
11.00-12.00	B.H. Lian (Brandeis University, Waltham, U.S.A.) Lectures on mirror symmetry. (3)

14.30-15.30	N. Hitchin (University Oxford, U.K.) Lagrangian foliations and mirror symmetry. (3)

Thursday, 15 April
09.30-10.30	A. Bobenko (Technische Universitaet Berlin, Germany) Exploring surfaces through methods from the theory of integrable systems. Lectures on Bonnet problem. (3)
11.00-12.00	B.H. Lian (Brandeis University, Waltham, U.S.A.) Lectures on mirror symmetry. (4)

14.30-15.30	N. Hitchin (University Oxford, U.K.) Lagrangian foliations and mirror symmetry. (4)

Friday, 16 April
09.30:10.30	A. Bobenko (Technische Universitaet Berlin, Germany) Exploring surfaces through methods from the theory of integrable systems. Lectures on Bonnet problem. (4)
11.00-12.00	N. Hitchin (University Oxford, U.K.) Lagrangian foliations and mirror symmetry. (5)

14.30-15.30	B.H. Lian (Brandeis University, Waltham, U.S.A.) Lectures on mirror symmetry. (5)

WEEK 2 (19 - 23 April)

Monday, 19 April
09.30-10.30 J. Wolfson ((Michigan State University, East Lansing, U.S.A.)
The plateau problem for Lagrangian submanifolds. (1)

11.00-12.00 B. Dubrovin (SISSA, Trieste, Italy)
Frobenius manifolds and differential geometry of integrable hierarchies. (1)

14.30-15.30 G. Tian (M.I.T., Cambridge, U.S.A.)
ymplectic geometry and Gromov-Witten invariants. (1)

Tuesday, 20 April
09.30-10.30 J. Wolfson (Michigan State University, East Lansing, U.S.A.)
The plateau problem for Lagrangian submanifolds. (2)

11.00-12.00 G. Tian (M.I.T., Cambridge, U.S.A.)
Symplectic geometry and Gromov-Witten invariants. (2)

14.30-15.30 G. Tian (M.I.T., Cambridge, U.S.A.)
Symplectic geometry and Gromov-Witten invariants. (3)

16.00-17.00 B. Dubrovin (SISSA, Trieste, Italy)
Frobenius manifolds and differential geometry of integrable hierarchies. (2)

Wednesday, 21 April
09.30-10.30 J. Wolfson (Michigan State University, East Lansing, U.S.A.)
The plateau problem for Lagrangian submanifolds. (2)

11.00-12.00 B. Dubrovin (SISSA, Trieste, Italy)
Frobenius manifolds and differential geometry of integrable hierarchies. (3)

14.30-15.30 G. Tian (M.I.T., Cambridge, U.S.A.)
Symplectic geometry and Gromov-Witten invariants. (4)

16.00-17.00 K. Fukaya (Kyoto University, Japan)
Floer homology (in symplectic geometry). (1)

Thursday, 22 April
09.30-10.30 J. Wolfson (Michigan State University, East Lansing, U.S.A.)
The plateau problem for Lagrangian submanifolds. (3)

11.00-12.00 B. Dubrovin (SISSA, Trieste, Italy)
Frobenius manifolds and differential geometry of integrable hierarchies. (4)

14.30-15.30 K. Fukaya (Kyoto University, Japan)
Floer homology (in symplectic geometry). (2)

Friday, 23 April
09.30-10.30 J. Wolfson (Michigan State University, East Lansing, U.S.A.)
The plateau problem for Lagrangian submanifolds. (4)

11.00-12.00 B. Dubrovin (SISSA, Trieste, Italy)
Frobenius manifolds and differential geometry of integrable hierarchies. (5)

14.30-15.30 K. Fukaya (Kyoto University, Japan)
Floer homology (in symplectic geometry). (3)

Monday, 19 April
09.30-10.30	J. Wolfson ((Michigan State University, East Lansing, U.S.A.) The plateau problem for Lagrangian submanifolds. (1)
11.00-12.00	B. Dubrovin (SISSA, Trieste, Italy) Frobenius manifolds and differential geometry of integrable hierarchies. (1)

14.30-15.30	G. Tian (M.I.T., Cambridge, U.S.A.) ymplectic geometry and Gromov-Witten invariants. (1)

Tuesday, 20 April
09.30-10.30	J. Wolfson (Michigan State University, East Lansing, U.S.A.) The plateau problem for Lagrangian submanifolds. (2)
11.00-12.00	G. Tian (M.I.T., Cambridge, U.S.A.) Symplectic geometry and Gromov-Witten invariants. (2)

14.30-15.30	G. Tian (M.I.T., Cambridge, U.S.A.) Symplectic geometry and Gromov-Witten invariants. (3)
16.00-17.00	B. Dubrovin (SISSA, Trieste, Italy) Frobenius manifolds and differential geometry of integrable hierarchies. (2)

Wednesday, 21 April
09.30-10.30	J. Wolfson (Michigan State University, East Lansing, U.S.A.) The plateau problem for Lagrangian submanifolds. (2)
11.00-12.00	B. Dubrovin (SISSA, Trieste, Italy) Frobenius manifolds and differential geometry of integrable hierarchies. (3)

14.30-15.30	G. Tian (M.I.T., Cambridge, U.S.A.) Symplectic geometry and Gromov-Witten invariants. (4)
16.00-17.00	K. Fukaya (Kyoto University, Japan) Floer homology (in symplectic geometry). (1)

Thursday, 22 April
09.30-10.30	J. Wolfson (Michigan State University, East Lansing, U.S.A.) The plateau problem for Lagrangian submanifolds. (3)
11.00-12.00	B. Dubrovin (SISSA, Trieste, Italy) Frobenius manifolds and differential geometry of integrable hierarchies. (4)

14.30-15.30	K. Fukaya (Kyoto University, Japan) Floer homology (in symplectic geometry). (2)

Friday, 23 April
09.30-10.30	J. Wolfson (Michigan State University, East Lansing, U.S.A.) The plateau problem for Lagrangian submanifolds. (4)
11.00-12.00	B. Dubrovin (SISSA, Trieste, Italy) Frobenius manifolds and differential geometry of integrable hierarchies. (5)

14.30-15.30	K. Fukaya (Kyoto University, Japan) Floer homology (in symplectic geometry). (3)

WEEK 3 (26 - 30 April)

Monday, 26 April
10.00-11.00 F. Aicardi (S.I.S.S.A., Trieste, Italy)
Selflinking number of spatial curves.

10.15-11.15 M. Herman (Université de Paris VII, France)
Introduction to Hamiltonian dynamics and invariant curves of twist maps (KAM) (5)

11.30-12.30 K. Fukaya (Kyoto University, Japan)
Homological algebra, deformation theory and Q-correction to the moduli spaces (1).

14.30-15.30 L. Goettsche (I.C.T.P., Trieste, Italy)
On the cobordism class of the Hilbert scheme.

Tuesday, 27 April
09.30-10.30 A. Kovalev (University of Edinburgh, U.K.)
Moduli space for Hitchin's self-duality equations on a non-compact Riemann surface.

11.00-12.00 U. Bruzzo (SISSA, Trieste, Italy)
Complex Lagrangian embeddings of moduli spaces of vector bundles.

14.30-15.30 X. Ma (Humboldt Universitaet Berlin, Germany)
Family rigidity theorem for elliptic genera.

16.00-17.00 J. Li (Stanford University, U.S.A.)
Virtual moduli cycle and related topics.

Wednesday, 28 April
09.30-10.30 R. Kaufmann (I.H.E.S., Bures sur Yvette, France)
Products of Frobenius manifolds.

11.00-12.00 B. Siebert (Ruhr-Universitaet-Bochum, Germany)
Hyperelliptic symplectic Lefschetz fibrations and symplectic submanifolds in ruled surfaces.

14.30-15.30 K. Fukaya (Kyoto University, Japan)
Homological algebra, deformation theory and Q-correction to the moduli spaces (2).

16.00-17.00 A. Matsev (S.I.S.S.A., Trieste, Italy)
Dubrovin-Novikov brackets in Whitham averaging method.

Thursday, 29 April
09.30-10.30 V. Matveev (Chelyabinsk State University, Russia)
Geodesic equivalence as integrability.

11.00-12.00 W. Minicozzi (Johns Hopkins University, Baltimore, U.S.A.)
Minimal surfaces without area bounds.

14.30.-15.30 G. Valli (Universita' di Pavia, Italy)
Bi-invariant grassmannians and Atiyah-Jones theorems.

Friday, 30 April
09.30-10.30 I. Taimanov (Academy of Sciences, Novosibirsk, Russia)
On nonformal symplectic manyfolds.

11.00-12.00 S.P. Tsarev (Krasnoyarsk State Pedagogical University, Russia)
Integrable equations in differential geometry: from 19th to the end of 20th century.

Monday, 26 April
10.00-11.00	F. Aicardi (S.I.S.S.A., Trieste, Italy) Selflinking number of spatial curves.
10.15-11.15	M. Herman (Université de Paris VII, France) Introduction to Hamiltonian dynamics and invariant curves of twist maps (KAM) (5)
11.30-12.30	K. Fukaya (Kyoto University, Japan) Homological algebra, deformation theory and Q-correction to the moduli spaces (1).

14.30-15.30	L. Goettsche (I.C.T.P., Trieste, Italy) On the cobordism class of the Hilbert scheme.

Tuesday, 27 April
09.30-10.30	A. Kovalev (University of Edinburgh, U.K.) Moduli space for Hitchin's self-duality equations on a non-compact Riemann surface.
11.00-12.00	U. Bruzzo (SISSA, Trieste, Italy) Complex Lagrangian embeddings of moduli spaces of vector bundles.

14.30-15.30	X. Ma (Humboldt Universitaet Berlin, Germany) Family rigidity theorem for elliptic genera.
16.00-17.00	J. Li (Stanford University, U.S.A.) Virtual moduli cycle and related topics.

Wednesday, 28 April
09.30-10.30	R. Kaufmann (I.H.E.S., Bures sur Yvette, France) Products of Frobenius manifolds.
11.00-12.00	B. Siebert (Ruhr-Universitaet-Bochum, Germany) Hyperelliptic symplectic Lefschetz fibrations and symplectic submanifolds in ruled surfaces.

14.30-15.30	K. Fukaya (Kyoto University, Japan) Homological algebra, deformation theory and Q-correction to the moduli spaces (2).
16.00-17.00	A. Matsev (S.I.S.S.A., Trieste, Italy) Dubrovin-Novikov brackets in Whitham averaging method.

Thursday, 29 April
09.30-10.30	V. Matveev (Chelyabinsk State University, Russia) Geodesic equivalence as integrability.
11.00-12.00	W. Minicozzi (Johns Hopkins University, Baltimore, U.S.A.) Minimal surfaces without area bounds.

14.30.-15.30	G. Valli (Universita' di Pavia, Italy) Bi-invariant grassmannians and Atiyah-Jones theorems.

Friday, 30 April
09.30-10.30	I. Taimanov (Academy of Sciences, Novosibirsk, Russia) On nonformal symplectic manyfolds.
11.00-12.00	S.P. Tsarev (Krasnoyarsk State Pedagogical University, Russia) Integrable equations in differential geometry: from 19th to the end of 20th century.

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