Organizational Information

• The Goal: To understand Givental's approach to the mirror conjecture of Candelas, de la Ossa, Green, and Parks which relates the number of rational curves in a generic quintic in CP^4 to a solution of the Picard-Fuchs differential equation.

List of Talks

• First Meeting: Monday July 20, 1998 10am in MCS 153
  • Title: An Overview of the Mirror Conjecture
  • Speaker: Takashi Kimura
• Monday July 27, 1998 at 10am in MCS 153
  • Title: Frobenius Manifolds and Gravitational Descendents I
  • Speaker: Takashi Kimura
• Wednesday July 29, 1998 at 10:30am in MCS 153
  • Title: Frobenius Manifolds and Gravitational Descendents II
  • Speaker: Takashi Kimura
• Monday August 3, 1998 at 12pm in MCS 153
  • Title: Equivariant Cohomology and Equivariant Gromov-Witten Invariants I
  • Speaker: Steve Rosenberg
• Wednesday August 5, 1998 at 12pm in MCS 153
  • Title: Equivariant Cohomology and Equivariant Gromov-Witten Invariants II
  • Speaker: Steve Rosenberg
• Monday October 5, 1998 at 1-2pm in MCS 153
  • Title: Solving the Quantum Differential Equation I
  • Speaker: Kalle Karu
• Friday October 16, 1998 at 2-3pm in MCS 153
  • Title: Solving the Quantum Differential Equation II
  • Speaker: Kalle Karu
• Friday November 6, 1998 at 2-3pm in MCS 153
  • Title: Towards a Solution of the Picard-Fuchs Equation I
  • Speaker: Mihaela Vajiac
• Friday November 13, 1998 at 1:30-3pm in MCS 153
  • Title: Towards a Solution of the Picard-Fuchs Equation II
  • Speaker: Mihaela Vajiac
• Friday November 20, 1998 at 1:30-3pm in MCS B32
  • Title: Towards a Solution of the Picard-Fuchs Equation III
  • Speaker: Mihaela Vajiac
• Friday December 11, 1998 at 1:30-3pm in MCS B32
  • Title: Towards a Solution of the Picard-Fuchs Equation IV
  • Speaker: Kalle Karu
• Friday December 18, 1998 at 1:30-3pm in MCS B32
  • Title: Towards a Solution of the Picard-Fuchs Equation V
  • Speaker: Kalle Karu

References

• Main References
  • G. Bini, C. de Concini, M. Polito, and C. Procesi, On the work of Givental relative to mirror symmetry
    math.AG/9805097
  • A. Givental, Elliptic Gromov-Witten invariants and generalized mirror conjecture
    math.AG/9803053
  • A. Givental, Equivariant Gromov-Witten invariants mirror conjecture
    math.AG/9603021
  • A. Givental, The mirror formula for quintic threefolds
    math.AG/9807070
  • A. Givental, A mirror theorem for toric complete intersections
    math.AG/9701016
  • B. H. Lian, K. Liu, and S. T. Yau, Mirror Principle I
    math.AG/9712011
  • R. Pandharipande, Rational Curves on Hypersurfaces
    math.AG/9806133
• Supplemental References
  • W. Fulton and R. Pandharipande, Notes on Stable Maps and Quantum Cohomology
    math.AG/9608011
  • M. Kontsevich, Enumeration of rational curves via torus actions
    hep-th/9405035
  • M. Kontsevich and Yu. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry
    hep-th/9402147
  • Yu. Manin, Frobenius manifolds, quantum cohomology, and moduli spaces (chapters I, II, III)
    MPI preprint
  • D. Morrison, Mirror symmetry and rational curves on quintic threefolds: A guide for mathematicians
    alg-geom/9202004
  • D. Morrison, Picard-Fuchs equations and mirror maps for hypersurfaces
    alg-geom/9202026

(Return to Takashi's Home Page)