Home /  Holomorphic Differentials in Mathematics and Physics

Workshop

Holomorphic Differentials in Mathematics and Physics November 18, 2019 - November 22, 2019
Registration Deadline: November 22, 2019 over 4 years ago
To apply for Funding you must register by: August 18, 2019 almost 5 years ago
Parent Program:
Location: SLMath: Eisenbud Auditorium
Organizers LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at Urbana-Champaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (Yale University), Laura Schaposnik (University of Illinois at Chicago), Gabriela Weitze-Schmithuesen (Universität des Saarlandes), Anton Zorich (Institut de Mathematiques de Jussieu)
Speaker(s)

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Description
Sn image
An example of a spectral network associated to the group SL(4).
Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special - Hitchin or higher Teichmuller - components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry). It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our workshop will be of interest to those working in many different fields, including low-dimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Meromorphic Differentials

  • spectral networks

  • stability conditions

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Nov 18, 2019
Monday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:30 AM
  Arakelov-Milnor inequalities and maximal variations of Hodge structure
Oscar Garcia-Prada (Consejo Superior de Investigaciones Científicas (CSIC))
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Novikov’s problem: from physics of metals to modern dynamical systems
Alexandra Skripchenko (Higher School of Economics)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Geometric Recursion
Jorgen Ellegaard Andersen (Syddansk Universitet (University of Southern Denmark))
03:00 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  The saddle connection complex
Anja Randecker (University of Toronto)
05:15 PM - 06:15 PM
  Screening of Secrets of the Surface: The Mathematical Vision of Maryam Mirzakhani
Nov 19, 2019
Tuesday
09:30 AM - 10:30 AM
  The Euler characteristic of moduli spaces of meromorphic differentials
Martin Moeller (Johann Wolfgang Goethe-Universität Frankfurt)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Spectral networks and stability conditions
Fabian Haiden (University of Oxford)
12:00 PM - 01:15 PM
  Lunch
01:15 PM - 02:15 PM
  K3 surfaces: dynamics and moduli spaces
Simion Filip (University of Chicago)
02:30 PM - 03:30 PM
  The realization problem for twisted quadratic differentials (dilation surfaces)
Jane Wang (Indiana University)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Cyclic harmonic bundles on noncompact surfaces
Qiongling Li (Chern Institute of Mathematics)
05:00 PM - 07:00 PM
  Reception
Nov 21, 2019
Thursday
09:30 AM - 10:30 AM
  Meanders and holomorphic differentials
Vincent Delecroix (Université de Bordeaux I)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Higher Teichmüller spaces and Anosov representations
Anna Wienhard (Max Planck Institute for Mathematics in the Sciences)
12:00 PM - 01:15 PM
  Lunch
01:15 PM - 02:15 PM
  Aspects of the cohomology ring of the moduli space of torsion-free sheaves on an irreducible nodal curve
Inder Kaur (Institute of Pure and Applied Mathematics (IMPA))
02:30 PM - 03:30 PM
  Degeneration of the Period Matrix and Shimura-Teichmuller Curves
Chaya Norton (University of Michigan)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Maximal surfaces in pseudo-hyperbolic spaces of rank 2
François Labourie (Universite de Nice Sophia Antipolis)
Nov 22, 2019
Friday
09:30 AM - 10:30 AM
  Holomorphic differentials and the geometry of dg-categories
Pranav Pandit (International Centre for Theoretical Sciences)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  On type-preserving representations of thrice punctured projective plane group
Sara Maloni (University of Virginia)
12:00 PM - 02:00 PM
  Lunch
03:00 PM - 04:00 PM
  Tea