Home /  Recent developments in microlocal analysis


Recent developments in microlocal analysis October 14, 2019 - October 18, 2019
To apply for Funding you must register by: July 14, 2019 about 5 years ago
Parent Program:
Location: SLMath: Eisenbud Auditorium
Organizers LEAD Pierre Albin (University of Illinois at Urbana-Champaign), Nalini Anantharaman (Université de Strasbourg), Colin Guillarmou (Université Paris-Saclay)

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Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory, hyperbolic dynamical systems, probability… As this description shows microlocal analysis has become a very broad area. Due to its breadth, it is a challenge for researchers to be aware of what is happening in other parts of the field, and the impact this may have in their own research area. The purpose of this workshop is thus to bring together researchers from different parts of microlocal analysis and its applications to facilitate the transfer of new ideas. 
Keywords and Mathematics Subject Classification (MSC)
  • Microlocal analysis

  • elliptic partial differential equations (PDE)

  • hyperbolic PDE

  • Fredholm theory

  • singular spaces

  • hyperbolic dynamical systems

  • scattering theory

  • resonances

  • spectral gap

  • quantum chaos

  • inverse problems

  • general relativity

  • quantum field theory

  • nonlinear PDE

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
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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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Oct 14, 2019
09:15 AM - 09:30 AM
09:30 AM - 10:30 AM
  Loops, Toeplitz operators and representations
Richard Melrose (Massachusetts Institute of Technology)
10:30 AM - 11:00 AM
11:00 AM - 12:00 PM
  Deformation of spherical conical metrics
Xuwen Zhu (Northeastern University)
12:00 PM - 02:00 PM
02:00 PM - 03:00 PM
  Analysis on singular spaces
Jesse Gell-Redman (University of Melbourne)
03:00 PM - 03:00 PM
03:30 PM - 04:30 PM
  Reflections on fractional Laplacians
Rafe Mazzeo (Stanford University)
Oct 15, 2019
09:30 AM - 10:30 AM
  Asymptotic location of resonances for Schrödinger operators on infinite cylinders
Tanya Christiansen (University of Missouri)
10:30 AM - 11:00 AM
11:00 AM - 12:00 PM
  Quasimodes and completely integrable systems
Fabricio Macia (Universidad Politécnica de Madrid)
12:00 PM - 02:00 PM
02:00 PM - 03:00 PM
  Local Index Theory in Lorentzian Geometry
Alexander Strohmaier (University of Leeds)
03:00 PM - 03:00 PM
03:30 PM - 04:30 PM
  Lp norms via geodesic beams
Jeffrey Galkowski (University College London)
04:40 PM - 05:40 PM
  Viscosity Limits for 0th order operators
Maciej Zworski (University of California, Berkeley)
05:40 PM - 07:00 PM
Oct 16, 2019
09:30 AM - 10:30 AM
  Exact controllability for the Schr ̈odinger-Grushin equation
Nicolas Burq (Université Paris-Saclay)
10:30 AM - 11:00 AM
11:00 AM - 12:00 PM
  Dispersive estimates for the semi-classical Schrödinger equation inside a strictly convex domain
Oana Ivanovici (Sorbonne University)
Oct 17, 2019
09:30 AM - 10:30 AM
  Inverse problems for real principal type operators
Mikko Salo (University of Jyväskylä)
10:30 AM - 11:00 AM
11:00 AM - 12:00 PM
  Inverse boundary problems for semilinear elliptic PDE
Katya Krupchyk (University of California, Irvine)
12:00 PM - 02:00 PM
02:00 PM - 03:00 PM
  Recent progress on the Fried conjecture
Nguyen Viet Dang (Institut Camille Jordan)
03:00 PM - 03:00 PM
03:30 PM - 04:30 PM
  Systoles and Lagrangians of random complex projective hypersurfaces
Damien Gayet (Université Grenoble Alpes (Université de Grenoble I - Joseph Fourier))
Oct 18, 2019
09:00 AM - 10:00 AM
  Microlocal analysis of contact Anosov flows
Frederic Faure (Université Grenoble Alpes (Université de Grenoble I - Joseph Fourier))
10:00 AM - 10:30 AM
10:30 AM - 11:30 AM
  Semi-classical analysis of Schr ̈odinger equation on H-type groups
Clotilde Fermanian Kammerer (Université Paris-Est Créteil Val-de-Marne)
11:30 AM - 12:30 PM
  The inverse spectral problem for strictly convex domains
Hamid Hezari (University of California, Irvine)
12:30 PM - 02:00 PM