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Category: List of Bases 2011 2011 ICTP Activities in Trieste ICTP Activities in Trieste
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lecture

Start Time:

28 February 2011 at 08:30

Ends On:

18 March 2011

Location:

Trieste - Italy

Venue:

LB (Main Lecture Hall)

Organizer(s):

Directors: Kathrin Bringmann, Lothar Göttsche, Don Zagier

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:

Monday, 28 February 2011

Room: Leonardo da Vinci Building Main Lecture Hall

08:30
10:30
REGISTRATION & ADMINISTRATIVE FORMALITIES
02h00'
Room: Leonardo da Vinci Building, Lobby
10:30
10:45
OPENING
15'
Ramadas Ramakrishnan
ICTP, Trieste, Italy
10:45
12:20
Introduction to modular forms 1
01h35'
M. Vlasenko/A. Mellit
Max-Planck Institute for Mathematics, Bonn, Germany
12:20
14:00
Lunch break
01h40'
Room: Leonardo da Vinci Building Cafeteria
14:00
15:00
Quantum field theory for mathematicians 1
01h00'
I. Runkel
Universität Hamburg, Hamburg, Germany
15:00
15:15
Break
15'
15:15
16:50
Moduli spaces of vector bundles and sheaves 1
01h35'
V.B. Mehta
Tata Institute of Fundamental Research, Mumbai, India
Tuesday, 1 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:45
Introduction to modular forms 2
01h30'
M. Vlasenko/A. Mellit
Max-Planck Institute for Mathematics, Bonn, Germany
10:45
11:15
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
11:15
12:15
Quantum field theory for mathematicians 2
01h00'
I. Runkel
Universität Hamburg, Hamburg, Germany
12:15
14:25
Lunch break
02h10'
Room: Leonardo da Vinci Building Cafeteria
14:25
16:00
Moduli spaces of vector bundles and sheaves 2
01h35'
V.B. Mehta
Tata Institute of Fundamental Research, Mumbai, India
Wednesday, 2 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:50
Introduction to modular forms 3
01h35'
M. Vlasenko/A. Mellit
Max-Planck Institute for Mathematics, Bonn, Germany
10:50
11:20
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
11:20
12:20
Quantum field theory for mathematicians 3
01h00'
I. Runkel
Universität Hamburg, Hamburg, Germany
12:20
14:30
Lunch break
02h10'
Room: Leonardo da Vinci Building Cafeteria
14:30
16:05
Moduli spaces of vector bundles and sheaves 3
01h35'
V.B. Mehta
Tata Institute of Fundamental Research, Mumbai, India
18:30
18:30
RECEPTION
Room: Leonardo da Vinci Building Cafeteria
Thursday, 3 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:50
Introduction to modular forms 4
01h35'
M. Vlasenko/A. Mellit
Max-Planck Institute for Mathematics, Bonn, Germany
10:50
11:20
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
11:20
12:20
Quantum field theory for mathematicians 4
01h00'
I. Runkel
Universität Hamburg, Hamburg, Germany
12:20
14:30
Lunch break
02h10'
Room: Leonardo da Vinci Building Cafeteria
14:30
16:05
Moduli spaces of vector bundles and sheaves 4
01h35'
V.B. Mehta
Tata Institute of Fundamental Research, Mumbai, India
Friday, 4 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:50
Introduction to modular forms 5
01h35'
M. Vlasenko/A. Mellit
Max-Planck Institute for Mathematics, Bonn, Germany
10:50
11:20
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
11:20
12:20
Quantum field theory for mathematicians 5
01h00'
I. Runkel
Universität Hamburg, Hamburg, Germany
12:20
14:30
Lunch break
02h10'
Room: Leonardo da Vinci Building Cafeteria
14:30
16:05
Quantum field theory and modular forms
01h35'
A. Dabholkar
LPTHE, Université Paris VI, Paris, France
Monday, 7 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:15
Mock theta functions, mock modular forms and indefinite theta series 1
01h00'
S.P. Zwegers
Universität zu Köln, Köln, Germany
10:15
10:45
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
10:45
12:20
Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 1
01h35'
L. Goettsche
ICTP, Trieste, Italy
12:20
14:00
Lunch break
01h40'
Room: Leonardo da Vinci Building Cafeteria
14:00
15:00
Mock modular forms and Jacobi forms 1
01h00'
Don B. Zagier
Max-Planck Institute for Mathematics, Bonn, Germany
15:00
15:10
Break
10'
15:10
16:10
Mock modular forms and Jacobi forms 1 (continuation)
01h00'
Don B. Zagier
Max-Planck Institute for Mathematics, Bonn, Germany
Tuesday, 8 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:15
Mock theta functions, mock modular forms and indefinite theta series 2
01h00'
S.P. Zwegers
Universität zu Köln, Köln, Germany
10:15
10:45
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
10:45
12:20
Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 2
01h35'
L. Goettsche
ICTP, Trieste, Italy
12:20
14:00
Lunch break
01h40'
Room: Leonardo da Vinci Building Cafeteria
14:00
15:35
Mock modular forms and Jacobi forms 2
01h35'
Don B. Zagier
Max-Planck Institute for Mathematics, Bonn, Germany
15:35
15:50
Break
15'
15:50
17:25
Quantum black holes and modular forms 1
01h35'
A. Sen/A. Dabholkar
Harish-Chandra Research Institute, Allahabad, India/LPTHE, Paris VI, France
Wednesday, 9 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:15
Mock theta functions, mock modular forms and indefinite theta series 3
01h00'
S.P. Zwegers
Universität zu Köln, Köln, Germany
10:15
10:45
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
10:45
12:20
Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 3
01h35'
L. Goettsche
ICTP, Trieste, Italy
12:20
14:30
Lunch break
02h10'
Room: Leonardo da Vinci Building Cafeteria
14:30
16:05
Quantum black holes and modular forms 2
01h35'
A. Sen/A. Dabholkar
Harish-Chandra Research Institute, Allahabad, India/LPTHE, Paris VI, France
Thursday, 10 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:15
Mock theta functions, mock modular forms and indefinite theta series 4
01h00'
S.P. Zwegers
Universität zu Köln, Köln, Germany
10:15
10:45
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
10:45
12:20
Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 4
01h35'
L. Goettsche
ICTP, Trieste, Italy
12:20
14:30
Lunch break
02h10'
Room: Leonardo da Vinci Building Cafeteria
14:30
16:05
Quantum black holes and modular forms 3
01h35'
A. Sen/A. Dabholkar
Harish-Chandra Research Institute, Allahabad, India/LPTHE, Paris VI, France
Friday, 11 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:15
Mock theta functions, mock modular forms and indefinite theta series 5
01h00'
S.P. Zwegers
Universität zu Köln, Köln, Germany
10:15
10:45
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
10:45
12:20
Wallcrossing for invariants of Moduli spaces of sheaves and Donaldson invariants 5
01h35'
L. Goettsche
ICTP, Trieste, Italy
12:20
14:00
Lunch break
01h40'
Room: Leonardo da Vinci Building Cafeteria
14:00
15:35
Mock modular forms and Jacobi forms 3
01h35'
Don B. Zagier
Max-Planck Institute for Mathematics, Bonn, Germany
Monday, 14 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

08:45
09:45
Theta liftings, cycles, and harmonic weak Maass forms
01h00'
J. Funke
University of Durham, Durham, UK
09:45
10:00
Break
15'
10:00
11:00
Weak Harmonic Maass forms of weight zero: algebraicity and congruences
01h00'
P. Guerzhoy
University of Hawaii, Honolulu, USA
11:00
11:30
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
11:30
12:30
Harmonic Siegel-Maass forms and their Fourier-Jacobi expansions
01h00'
M. Raum
Max-Planck Institute for Mathematics, Bonn, Germany
12:30
14:30
Lunch break
02h00'
Room: Leonardo da Vinci Building Cafeteria
14:30
15:30
Mock Jacobi forms and moment asymptotics
01h00'
K. Mahlburg
Princeton University, Princeton NJ, USA
15:30
15:45
Break
15'
15:45
16:45
Faber polynomials and Poincaré series
01h00'
Ben Kane
University of Cologne, Cologne, Germany
Tuesday, 15 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

08:45
09:45
The simplest reflective modular forms
01h00'
V. Gritsenko
Université Lille 1, Villeneuve d'Ascq, France
09:45
10:00
Break
15'
10:00
11:00
Generalised Kac-Moody Algebra, Automorphic Forms, and the sporadic group M24
01h00'
M. Cheng
Harvard University, Cambridge MA, USA
11:00
11:30
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
11:30
12:30
Symmetries of K3 in M_{24}: I Geometry
01h00'
A. Taormina
University of Durham, Durham, UK
12:30
14:30
Lunch break
02h00'
Room: Leonardo da Vinci Building Cafeteria
14:30
15:30
Symmetries of K3 in M_{24}: II Group Theory
01h00'
K. Wendland
University of Augsburg, Augsburg, Germany
15:30
15:45
Break
15'
15:45
16:45
Rigid semistable objects and kinds of modular forms
01h00'
So Okada
Kyoto University, Kyoto, Japan
Wednesday, 16 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

08:45
09:45
Harmonic Maass forms and periods
01h00'
H. Bruinier
Technical University of Darmstadt, Darmstadt, Germany
09:45
10:00
Break
15'
10:00
11:00
Harmonic Weak Maass Forms and CM values of automorphic green functions
01h00'
T. Yang
University of Wisconsin, Madison WI, USA
11:00
11:30
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
11:30
12:30
Generalized Mathieu Moonshine
01h00'
S. Govindarajan
Indian Institute of Technology Madras, Chennai, India
12:30
14:30
Lunch break
02h00'
Room: Leonardo da Vinci Building Cafeteria
Thursday, 17 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:15
Modularity in Chern-Simons theory
01h00'
T. Dimofte
Institute for Advanced Study, Princeton NJ, USA
10:15
10:45
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
10:45
11:45
Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes
01h00'
A. Klemm
Humboldt University of Berlin, Berlin, Germany
11:45
12:00
Break
15'
12:00
12:30
Kac-Wakimoto characters, asymptotics and mock modular forms
30'
A. Folsom
Yale University, New Haven CT, USA
12:30
14:30
Lunch break
02h00'
Room: Leonardo da Vinci Building Cafeteria
14:30
15:30
The Betti numbers of the moduli space of sheaves of rank 3 on the projective plane
01h00'
J. Manschot
IPhT, Gif-sur-Yvette, France
15:30
15:45
Break
15'
15:45
16:45
Quantum black holes, wall crossing and mock modular forms
01h00'
S. Murthy
TIFR, Mumbai, India
Friday, 18 March 2011

Room: Leonardo da Vinci Building Main Lecture Hall

09:15
10:15
Congruences for smallest parts functions
01h00'
J. Lovejoy
Université Denis Diderot Paris 7, Paris, France
10:15
10:45
Coffee break
30'
Room: Leonardo da Vinci Building, Lobby
10:45
11:45
p-adic properties of the partition function
01h00'
Z. Kent
Emory University, Atlanta GA, USA
11:45
12:00
Break
15'
12:00
12:30
Bounds for coefficients of cusp forms and extremal lattices
30'
P. Jenkins
Brigham Young University, Provo UT, USA
12:30
14:30
Lunch break
02h00'
16:00
18:00
ICTP Colloquium "Quantum Modular Forms"
02h00'
Professor Don Zagier
Max Planck Institute for Mathematics (Bonn) and Collège de France
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