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Description
An ICTP Meeting

This winter school is focused on the mathematical aspects of topics in arithmetic geometry, particularly arithmetic aspects of the Langlands program, which have appeared in the context of string theory and quantum field theory. This activity will also focus on developing explicit computational methods via tutorials, and participant led mini-projects. This is the third event in a series meetings on number theory, arithmetic geometry, and connection to physics.

Topics:
  • Hodge theory
  • Arithmetic geometry of periods
  • Harmonic Maass forms
  • K3 surfaces
  • Automorphic representations
  • Hypergeometric functions and local systems

Speakers/Lecturers Include:
C. Alfes, Bielefeld University, Germany
F. Brown, Oxford University, UK
J. Burgos Gil, ICMAT Madrid, Spain
X. de la Ossa Oxford University, UK
S. Friedberg, Boston College, USA
A. Kidambi, MPI-MIS Leipzig, Germany
C. Nazaroglu University of Cologne, Germany
D. Persson Chalmers University of Technology, Sweden
F. Rodriguez Villegas, ICTP, Italy
M. Vlasenko, Kyiv School of Economics, Ukraine
U. Whitcher, Mathematical Reviews (American Mathematical Society), USA
F. Zerbini, UNED Madrid, Spain


Grants: A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee.

Material

Winter School on Number Theory and Physics | (smr 4162)
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  • Monday, 17 November 2025
    • 08:30 - 08:50
      • 08:30 Registration formalities 20' 
        Upon arrival, Visitors not staying in the ICTP Guest Houses, are kindly requested to complete registration formalities at the Adriatico Guest House (Lower level). The Registration Desk will be open in the morning starting from 8:30.
    • 08:50 - 17:30
      • 08:50 Opening Remarks 10'
        Speaker: Abhiram MAMANDUR KIDAMBI (Max Plank Institute for Mathematics in the Sciences, Germany)
        Material: Video
      • 09:00 Arithmetic Geometry of Periods - I 1h15'
        Speaker: Francis BROWN (Oxford University, UK)
        Material: Video
      • 10:15 Tea/Coffee Break 45'
      • 11:00 Harmonic Maass Forms - I 1h15'
        Speaker: Claudia ALFES (Bielefeld University, Germany)
        Material: Video
      • 12:30 Lunch Break 1h30'
      • 14:00 Arithmetic Geometry of Periods - II 1h15'
        Speaker: Francis BROWN (Oxford University, UK)
        Material: Video
      • 15:15 Tea/Coffee Break 45'
      • 16:00 SHCP + Introductions 1h30'
  • Tuesday, 18 November 2025
    • 09:00 - 17:30
      • 09:00 Hypergeometric Functions I 1h15'
        Speaker: Masha VLASENKO (Kyiv School of Economics, Ukraine)
        Material: Video
      • 10:15 Tea/Coffee Break 45'
      • 11:00 Arithmetic Geometry of Periods - III 1h30'
        Speaker: Francis BROWN (Oxford University, UK)
        Material: Video
      • 12:30 Lunch Break 1h30'
      • 14:00 Harmonic Maass Forms - II 1h15'
        Speaker: Claudia ALFES (Bielefeld University, Germany)
        Material: Video
      • 15:15 Tea/Coffee Break 45'
      • 16:00 SHCP 1h30'
  • Wednesday, 19 November 2025
    • 09:00 - 17:30
      • 09:00 Arithmetic Geometry of Periods - IV 1h15'
        Speaker: Federico ZERBINI (UNED Madrid, Spain)
        Material: Video
      • 10:15 Group Photo 5'
      • 10:20 Tea/Coffee Break 45'
      • 11:00 K3 surfaces - I 1h15'
        Speaker: Ursula WHITCHER (University of Michigan, USA)
        Material: Video
      • 12:30 Lunch Break 1h30'
      • 14:00 Harmonic Maass Forms - III 1h15'
        Speaker: Claudia ALFES (Bielefeld University, Germany)
        Material: Video
      • 15:15 Tea/Coffee Break 45'
      • 16:00 Social Activity / Free evening 1h30'
  • Thursday, 20 November 2025
    • 09:00 - 17:30
      • 09:00 SHCP 1h15'
      • 10:15 Tea/Coffee Break 45'
      • 11:00 K3 surfaces - II 1h15'
        Speaker: Ursula WHITCHER (University of Michigan, USA)
        Material: Video
      • 12:30 Lunch Break 1h30'
      • 14:00 Hypergeometric Functions II 1h15'
        Speaker: Masha VLASENKO (Kyiv School of Economics, Ukraine)
        Material: Video
      • 15:15 Tea/Coffee Break 45'
      • 16:00 SHCP 1h30'
  • Friday, 21 November 2025
    • 09:00 - 17:30
      • 09:00 K3 surfaces - III 1h15'
        Speaker: Ursula WHITCHER (University of Michigan, USA)
        Material: Video
      • 10:15 Tea/Coffee Break 45'
      • 11:00 Hypergeometric Functions III 1h15'
        Speaker: Masha VLASENKO (Kyiv School of Economics, Ukraine)
        Material: Video
      • 12:30 Lunch Break 1h30'
      • 14:00 K3 surfaces - IV 1h15'
        Speaker: Abhiram MAMANDUR KIDAMBI (Max Plank Institute for Mathematics in the Sciences, Germany)
        Material: Video
      • 15:15 Tea/Coffee Break 45'
      • 16:00 SHCP 1h30'
  • Monday, 24 November 2025
    • 08:50 - 17:30
      • 08:50 Opening Remarks 10'
        Speaker: Abhiram MAMANDUR KIDAMBI (Max Plank Institute for Mathematics in the Sciences, Germany)
      • 09:00 Harmonic Maass Forms - IV 1h15'
        Speaker: Caner NAZAROGLU (University of Cologne, Germany)
        Material: Video
      • 10:15 Tea/Coffee Break 45'
      • 11:00 Automorphic Representations - I 1h15'
        Speaker: Solomon FRIEDBERG (Boston College, USA)
        Material: Video
      • 12:30 Lunch Break 1h30'
      • 14:00 Hypergeometric Local Systems - I 1h15'
        Speaker: Fernando VILLEGAS (ICTP, Italy)
        Material: Video
      • 15:15 Tea/Coffee Break 45'
      • 16:00 SHCP 1h30'
  • Tuesday, 25 November 2025
    • 09:00 - 17:30
      • 09:00 Hodge Theory - I 1h15'
        Speaker: Jose Ignacio BURGOS GIL (ICMAT, Spain)
        Material: Video
      • 10:15 Tea/Coffee Break 45'
      • 11:00 Automorphic Representations - II 1h15'
        Speaker: Solomon FRIEDBERG (Boston College, USA)
        Material: Video
      • 12:30 Lunch Break 1h30'
      • 14:00 Hypergeometric Local Systems - II 1h15'
        Speaker: Fernando VILLEGAS (ICTP, Italy)
        Material: Video
      • 15:15 Tea/Coffee Break 45'
      • 16:00 SHCP 1h30'
  • Wednesday, 26 November 2025
    • 09:00 - 17:30
      • 09:00 Automorphic Representations - III 1h15'
        Speaker: Solomon FRIEDBERG (Boston College, USA)
      • 10:15 Group Photo 5'
      • 10:20 Tea/Coffee Break 40'
      • 11:00 Hodge Theory - II 1h15'
        Speaker: Jose Ignacio BURGOS GIL (ICMAT, Spain)
      • 12:30 Lunch Break 1h30'
      • 14:00 Free Afternoon/Social Activity 3h30'
  • Thursday, 27 November 2025
    • 09:00 - 17:30
      • 09:00 Hypergeometric Local Systems - III 1h15'
        Speaker: Fernando VILLEGAS (ICTP, Italy)
      • 10:15 Tea/Coffee Break 45'
      • 11:00 Hodge Theory - III 1h15'
        Speaker: Jose Ignacio BURGOS GIL (ICMAT, Spain)
      • 12:30 Lunch Break 1h30'
      • 14:00 Automorphic Representations - IV 1h15'
        Speaker: Daniel PERSSON (Chalmers University, Sweden)
      • 15:15 Tea/Coffee Break 45'
      • 16:00 SHCP 1h30'
  • Friday, 28 November 2025
    • 09:00 - 17:30
      • 09:00 Hodge Theory - IV 1h15'
        Speaker: Xenia DE LA OSSA OSEGUEDA (University of Oxford, UK)
      • 10:15 Tea/Coffee Break 45'
      • 11:00 SHCP 1h15'
      • 12:30 Lunch Break 1h30'
      • 14:00 Departures 3h30'
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