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Description 
MAIN TOPICS OF THE SCHOOL:
- Review of Modular forms
- Quantum Field Theory for Mathematicians
- Moduli Spaces of Sheaves
- Mock Modular forms
- Siegel Modular forms and Black Hole State counting
- Invariants of Moduli Spaces of Sheaves and Donaldson invariants

The third-week will be an international conference, where leading experts will report on the newest developments in the field of modular forms, mock modular forms and their applications.

Material

School and Conference on Modular Forms and Mock Modular Forms and their Applications in Arithmetic, Geometry and Physics | (smr 2226)
Go to day
  • Monday, 28 February 2011
    • 08:30 - 10:30 REGISTRATION & ADMINISTRATIVE FORMALITIES
      Location: Leonardo da Vinci Building, Lobby
      • 08:30 REGISTRATION & ADMINISTRATIVE FORMALITIES 2h0'
    • 10:30 - 10:45 OPENING
      • 10:30 OPENING 15'
        Speaker: Ramadas Ramakrishnan (ICTP, Trieste, Italy)
    • 10:45 - 12:20 Introduction to modular forms 1
      • 10:45 Introduction to modular forms 1 1h35'
        Speaker: M. Vlasenko/A. Mellit (Max-Planck Institute for Mathematics, Bonn, Germany)
    • 12:20 - 14:00 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:20 Lunch break 1h40'
    • 14:00 - 15:00 Quantum field theory for mathematicians 1
    • 15:00 - 15:15 Break
      • 15:00 Break 15'
    • 15:15 - 16:50 Moduli spaces of vector bundles and sheaves 1
      • 15:15 Moduli spaces of vector bundles and sheaves 1 1h35'
        Speaker: V.B. Mehta (Tata Institute of Fundamental Research, Mumbai, India)
        Material: lecture notes
  • Tuesday, 1 March 2011
    • 09:15 - 10:45 Introduction to modular forms 2
      • 09:15 Introduction to modular forms 2 1h30'
        Speaker: M. Vlasenko/A. Mellit (Max-Planck Institute for Mathematics, Bonn, Germany)
    • 10:45 - 11:15 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:45 Coffee break 30'
    • 11:15 - 12:15 Quantum field theory for mathematicians 2
      • 11:15 Quantum field theory for mathematicians 2 1h0'
        Speaker: I. Runkel (Universität Hamburg, Hamburg, Germany)
        Material: lecture notes
    • 12:15 - 14:25 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:15 Lunch break 2h10'
    • 14:25 - 16:00 Moduli spaces of vector bundles and sheaves 2
      • 14:25 Moduli spaces of vector bundles and sheaves 2 1h35'
        Speaker: V.B. Mehta (Tata Institute of Fundamental Research, Mumbai, India)
        Material: lecture notes
  • Wednesday, 2 March 2011
    • 09:15 - 10:50 Introduction to modular forms 3
      • 09:15 Introduction to modular forms 3 1h35'
        Speaker: M. Vlasenko/A. Mellit (Max-Planck Institute for Mathematics, Bonn, Germany)
    • 10:50 - 11:20 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:50 Coffee break 30'
    • 11:20 - 12:20 Quantum field theory for mathematicians 3
      • 11:20 Quantum field theory for mathematicians 3 1h0'
        Speaker: I. Runkel (Universität Hamburg, Hamburg, Germany)
        Material: lecture notes
    • 12:20 - 14:30 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:20 Lunch break 2h10'
    • 14:30 - 16:05 Moduli spaces of vector bundles and sheaves 3
      • 14:30 Moduli spaces of vector bundles and sheaves 3 1h35'
        Speaker: V.B. Mehta (Tata Institute of Fundamental Research, Mumbai, India)
        Material: lecture notes
    • 18:30 - 18:30 RECEPTION
      Location: Leonardo da Vinci Building Cafeteria
      • 18:30 RECEPTION
  • Thursday, 3 March 2011
    • 09:15 - 10:50 Introduction to modular forms 4
      • 09:15 Introduction to modular forms 4 1h35'
        Speaker: M. Vlasenko/A. Mellit (Max-Planck Institute for Mathematics, Bonn, Germany)
    • 10:50 - 11:20 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:50 Coffee break 30'
    • 11:20 - 12:20 Quantum field theory for mathematicians 4
      • 11:20 Quantum field theory for mathematicians 4 1h0'
        Speaker: I. Runkel (Universität Hamburg, Hamburg, Germany)
        Material: lecture notes
    • 12:20 - 14:30 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:20 Lunch break 2h10'
    • 14:30 - 16:05 Moduli spaces of vector bundles and sheaves 4
      • 14:30 Moduli spaces of vector bundles and sheaves 4 1h35'
        Speaker: V.B. Mehta (Tata Institute of Fundamental Research, Mumbai, India)
        Material: lecture notes
  • Friday, 4 March 2011
    • 09:15 - 10:50 Introduction to modular forms 5
      • 09:15 Introduction to modular forms 5 1h35'
        Speaker: M. Vlasenko/A. Mellit (Max-Planck Institute for Mathematics, Bonn, Germany)
    • 10:50 - 11:20 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:50 Coffee break 30'
    • 11:20 - 12:20 Quantum field theory for mathematicians 5
      • 11:20 Quantum field theory for mathematicians 5 1h0'
        Speaker: I. Runkel (Universität Hamburg, Hamburg, Germany)
        Material: lecture notes
    • 12:20 - 14:30 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:20 Lunch break 2h10'
    • 14:30 - 16:05 Quantum field theory and modular forms
      • 14:30 Quantum field theory and modular forms 1h35'
        Speaker: A. Dabholkar (LPTHE, Université Paris VI, Paris, France)
  • Monday, 7 March 2011
    • 09:15 - 10:15 Mock theta functions, mock modular forms and indefinite theta series 1
      • 09:15 Mock theta functions, mock modular forms and indefinite theta series 1 1h0'
        Speaker: S.P. Zwegers (Universität zu Köln, Köln, Germany)
        Material: lecture notes
    • 10:15 - 10:45 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:15 Coffee break 30'
    • 10:45 - 12:20 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 1
      • 10:45 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 1 1h35'
        Speaker: L. Goettsche (ICTP, Trieste, Italy)
        Material: lecture notes
    • 12:20 - 14:00 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:20 Lunch break 1h40'
    • 14:00 - 15:00 Mock modular forms and Jacobi forms 1
      • 14:00 Mock modular forms and Jacobi forms 1 1h0'
        Speaker: Don B. Zagier (Max-Planck Institute for Mathematics, Bonn, Germany)
        Material: lecture notes
    • 15:00 - 15:10 Break
      • 15:00 Break 10'
    • 15:10 - 16:10 Mock modular forms and Jacobi forms 1 (continuation)
      • 15:10 Mock modular forms and Jacobi forms 1 (continuation) 1h0'
        Speaker: Don B. Zagier (Max-Planck Institute for Mathematics, Bonn, Germany)
        Material: lecture notes
  • Tuesday, 8 March 2011
    • 09:15 - 10:15 Mock theta functions, mock modular forms and indefinite theta series 2
      • 09:15 Mock theta functions, mock modular forms and indefinite theta series 2 1h0'
        Speaker: S.P. Zwegers (Universität zu Köln, Köln, Germany)
        Material: lecture notes
    • 10:15 - 10:45 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:15 Coffee break 30'
    • 10:45 - 12:20 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 2
      • 10:45 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 2 1h35'
        Speaker: L. Goettsche (ICTP, Trieste, Italy)
        Material: lecture notes
    • 12:20 - 14:00 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:20 Lunch break 1h40'
    • 14:00 - 15:35 Mock modular forms and Jacobi forms 2
      • 14:00 Mock modular forms and Jacobi forms 2 1h35'
        Speaker: Don B. Zagier (Max-Planck Institute for Mathematics, Bonn, Germany)
        Material: lecture notes
    • 15:35 - 15:50 Break
      • 15:35 Break 15'
    • 15:50 - 17:25 Quantum black holes and modular forms 1
      • 15:50 Quantum black holes and modular forms 1 1h35'
        Speaker: A. Sen/A. Dabholkar (Harish-Chandra Research Institute, Allahabad, India/LPTHE, Paris VI, France)
  • Wednesday, 9 March 2011
    • 09:15 - 10:15 Mock theta functions, mock modular forms and indefinite theta series 3
      • 09:15 Mock theta functions, mock modular forms and indefinite theta series 3 1h0'
        Speaker: S.P. Zwegers (Universität zu Köln, Köln, Germany)
        Material: lecture notes
    • 10:15 - 10:45 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:15 Coffee break 30'
    • 10:45 - 12:20 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 3
      • 10:45 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 3 1h35'
        Speaker: L. Goettsche (ICTP, Trieste, Italy)
        Material: lecture notes
    • 12:20 - 14:30 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:20 Lunch break 2h10'
    • 14:30 - 16:05 Quantum black holes and modular forms 2
      • 14:30 Quantum black holes and modular forms 2 1h35'
        Speaker: A. Sen/A. Dabholkar (Harish-Chandra Research Institute, Allahabad, India/LPTHE, Paris VI, France)
  • Thursday, 10 March 2011
    • 09:15 - 10:15 Mock theta functions, mock modular forms and indefinite theta series 4
      • 09:15 Mock theta functions, mock modular forms and indefinite theta series 4 1h0'
        Speaker: S.P. Zwegers (Universität zu Köln, Köln, Germany)
        Material: lecture notes
    • 10:15 - 10:45 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:15 Coffee break 30'
    • 10:45 - 12:20 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 4
      • 10:45 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 4 1h35'
        Speaker: L. Goettsche (ICTP, Trieste, Italy)
        Material: lecture notes
    • 12:20 - 14:30 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:20 Lunch break 2h10'
    • 14:30 - 16:05 Quantum black holes and modular forms 3
      • 14:30 Quantum black holes and modular forms 3 1h35'
        Speaker: A. Sen/A. Dabholkar (Harish-Chandra Research Institute, Allahabad, India/LPTHE, Paris VI, France)
  • Friday, 11 March 2011
    • 09:15 - 10:15 Mock theta functions, mock modular forms and indefinite theta series 5
      • 09:15 Mock theta functions, mock modular forms and indefinite theta series 5 1h0'
        Speaker: S.P. Zwegers (Universität zu Köln, Köln, Germany)
        Material: lecture notes
    • 10:15 - 10:45 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:15 Coffee break 30'
    • 10:45 - 12:20 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 5
      • 10:45 Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 5 1h35'
        Speaker: L. Goettsche (ICTP, Trieste, Italy)
        Material: lecture notes
    • 12:20 - 14:00 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:20 Lunch break 1h40'
    • 14:00 - 15:35 Mock modular forms and Jacobi forms 3
      • 14:00 Mock modular forms and Jacobi forms 3 1h35'
        Speaker: Don B. Zagier (Max-Planck Institute for Mathematics, Bonn, Germany)
        Material: lecture notes
  • Monday, 14 March 2011
    • 08:45 - 09:45 Theta liftings, cycles, and harmonic weak Maass forms
      • 08:45 Theta liftings, cycles, and harmonic weak Maass forms 1h0'
        Speaker: J. Funke (University of Durham, Durham, UK)
    • 09:45 - 10:00 Break
      • 09:45 Break 15'
    • 10:00 - 11:00 Weak Harmonic Maass forms of weight zero: algebraicity and congruences
      • 10:00 Weak Harmonic Maass forms of weight zero: algebraicity and congruences 1h0'
        Speaker: P. Guerzhoy (University of Hawaii, Honolulu, USA)
    • 11:00 - 11:30 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 11:00 Coffee break 30'
    • 11:30 - 12:30 Harmonic Siegel-Maass forms and their Fourier-Jacobi expansions
      • 11:30 Harmonic Siegel-Maass forms and their Fourier-Jacobi expansions 1h0'
        Speaker: M. Raum (Max-Planck Institute for Mathematics, Bonn, Germany)
    • 12:30 - 14:30 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:30 Lunch break 2h0'
    • 14:30 - 15:30 Mock Jacobi forms and moment asymptotics
      • 14:30 Mock Jacobi forms and moment asymptotics 1h0'
        Speaker: K. Mahlburg (Princeton University, Princeton NJ, USA)
    • 15:30 - 15:45 Break
      • 15:30 Break 15'
    • 15:45 - 16:45 Faber polynomials and Poincaré series
      • 15:45 Faber polynomials and Poincaré series 1h0'
        Speaker: Ben Kane (University of Cologne, Cologne, Germany)
  • Tuesday, 15 March 2011
    • 08:45 - 09:45 The simplest reflective modular forms
      • 08:45 The simplest reflective modular forms 1h0'
        Speaker: V. Gritsenko (Université Lille 1, Villeneuve d'Ascq, France)
    • 09:45 - 10:00 Break
      • 09:45 Break 15'
    • 10:00 - 11:00 Generalised Kac-Moody Algebra, Automorphic Forms, and the sporadic group M24
      • 10:00 Generalised Kac-Moody Algebra, Automorphic Forms, and the sporadic group M24 1h0'
        Speaker: M. Cheng (Harvard University, Cambridge MA, USA)
    • 11:00 - 11:30 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 11:00 Coffee break 30'
    • 11:30 - 12:30 Symmetries of K3 in M_{24}: I Geometry
      • 11:30 Symmetries of K3 in M_{24}: I Geometry 1h0'
        Speaker: A. Taormina (University of Durham, Durham, UK)
    • 12:30 - 14:30 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:30 Lunch break 2h0'
    • 14:30 - 15:30 Symmetries of K3 in M_{24}: II Group Theory
      • 14:30 Symmetries of K3 in M_{24}: II Group Theory 1h0'
        Speaker: K. Wendland (University of Augsburg, Augsburg, Germany)
    • 15:30 - 15:45 Break
      • 15:30 Break 15'
    • 15:45 - 16:45 Rigid semistable objects and kinds of modular forms
      • 15:45 Rigid semistable objects and kinds of modular forms 1h0'
        Speaker: So Okada (Kyoto University, Kyoto, Japan)
  • Wednesday, 16 March 2011
    • 08:45 - 09:45 Harmonic Maass forms and periods
      • 08:45 Harmonic Maass forms and periods 1h0'
        Speaker: H. Bruinier (Technical University of Darmstadt, Darmstadt, Germany)
    • 09:45 - 10:00 Break
      • 09:45 Break 15'
    • 10:00 - 11:00 Harmonic Weak Maass Forms and CM values of automorphic green functions
      • 10:00 Harmonic Weak Maass Forms and CM values of automorphic green functions 1h0'
        Speaker: T. Yang (University of Wisconsin, Madison WI, USA)
    • 11:00 - 11:30 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 11:00 Coffee break 30'
    • 11:30 - 12:30 Generalized Mathieu Moonshine
      • 11:30 Generalized Mathieu Moonshine 1h0'
        Speaker: S. Govindarajan (Indian Institute of Technology Madras, Chennai, India)
    • 12:30 - 14:30 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:30 Lunch break 2h0'
  • Thursday, 17 March 2011
    • 09:15 - 10:15 Modularity in Chern-Simons theory
      • 09:15 Modularity in Chern-Simons theory 1h0'
        Speaker: T. Dimofte (Institute for Advanced Study, Princeton NJ, USA)
    • 10:15 - 10:45 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:15 Coffee break 30'
    • 10:45 - 11:45 Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes
      • 10:45 Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes 1h0'
        Speaker: A. Klemm (Humboldt University of Berlin, Berlin, Germany)
    • 11:45 - 12:00 Break
      • 11:45 Break 15'
    • 12:00 - 12:30 Kac-Wakimoto characters, asymptotics and mock modular forms
      • 12:00 Kac-Wakimoto characters, asymptotics and mock modular forms 30'
        Speaker: A. Folsom (Yale University, New Haven CT, USA)
    • 12:30 - 14:30 Lunch break
      Location: Leonardo da Vinci Building Cafeteria
      • 12:30 Lunch break 2h0'
    • 14:30 - 15:30 The Betti numbers of the moduli space of sheaves of rank 3 on the projective plane
      • 14:30 The Betti numbers of the moduli space of sheaves of rank 3 on the projective plane 1h0'
        Speaker: J. Manschot (IPhT, Gif-sur-Yvette, France)
    • 15:30 - 15:45 Break
      • 15:30 Break 15'
    • 15:45 - 16:45 Quantum black holes, wall crossing and mock modular forms
      • 15:45 Quantum black holes, wall crossing and mock modular forms 1h0'
        Speaker: S. Murthy (TIFR, Mumbai, India)
  • Friday, 18 March 2011
    • 09:15 - 10:15 Congruences for smallest parts functions
      • 09:15 Congruences for smallest parts functions 1h0'
        Speaker: J. Lovejoy (Université Denis Diderot Paris 7, Paris, France)
    • 10:15 - 10:45 Coffee break
      Location: Leonardo da Vinci Building, Lobby
      • 10:15 Coffee break 30'
    • 10:45 - 11:45 p-adic properties of the partition function
      • 10:45 p-adic properties of the partition function 1h0'
        Speaker: Z. Kent (Emory University, Atlanta GA, USA)
    • 11:45 - 12:00 Break
      • 11:45 Break 15'
    • 12:00 - 12:30 Bounds for coefficients of cusp forms and extremal lattices
      • 12:00 Bounds for coefficients of cusp forms and extremal lattices 30'
        Speaker: P. Jenkins (Brigham Young University, Provo UT, USA)
    • 12:30 - 14:30 Lunch break
      • 12:30 Lunch break 2h0'
    • 16:00 - 18:00 ICTP Colloquium "Quantum Modular Forms"
      • 16:00 ICTP Colloquium "Quantum Modular Forms" 2h0'
        Speaker: Professor Don Zagier (Max Planck Institute for Mathematics (Bonn) and Collège de France)
        Material: lecture notes
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