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Geometry and Mathematical Physics

∙ Integrable systems in relation with differential, algebraic and symplectic geometry, as well as with the theory of random matrices, special functions and nonlinear waves, Frobenius manifolds • Deformation theory, moduli spaces of sheaves and of curves, in relation with supersymmetric gauge theories, strings, Gromov-Witten invariants, orbifolds and automorphisms
• Quantum groups, noncommutative Riemannian and spin geometry, applications to models in mathematical physics
• Mathematical methods of quantum mechanics
• Mathematical aspects of quantum Field Theory and String 
• Symplectic geometry, sub-riemannian geometry

• Geometry of quantum fields and strings

Kähler Geometry Seminar

The Kähler Geometry seminar is jointly organized by researchers in ICTP and SISSA. In the academic years 2018/19 and 2019/20 the seminar was structured as a working group in Kähler Geometry, studying special curvature properties of Kähler manifolds.

This year the Kähler geometry seminar will start with a series of introductory talks, that will serve as an overview of some of the main themes in the study of Kähler metrics.

  • Title: Kähler metrics and curvature problems in Kähler geometry
    when: Friday, November 13, 2020 - 14:00
    speaker: Carlo Scarpa
    abstract: This seminar is an introduction to various curvature problems in Kähler geometry. We will start by recalling the basic definitions, some standard examples, and we will look at classic existence and non-existence results for the constant scalar curvature equation.

  • Title: Constant scalar curvature metrics on compact Riemann Surfaces
    when: Friday, November 20, 2020 - 14:00
    speaker: Carlo Scarpa
    abstract: We will see an analytic proof of the existence of constant scalar metrics on compact Riemann surfaces, after Kazdan-Warner and Fine. The proof will be fairly detailed, to highlight some features of the problem that appear also in higher-dimensional situations.

  • Title: The Kempf-Ness Theorem in Kähler Geometry
    when: Friday, November 27, 2020 - 14:00
    speaker: Enrico Schlitzer
    abstract: The Kempf-Ness theorem relates algebraic (GIT) quotients with certain symplectic quotients. We will review the construction of such quotients and prove the simplest version of the K-N theorem, in the affine case. The attempt to generalize this result to an infinite-dimensional setting led to the notion of K-stability.

  • Title: A variational approach to the study of the cscK equation
    when: Friday, December 11, 2020 - 14:00
    speaker: Carlo Scarpa
    abstract: Given a Kähler class on a compact complex manifold, Mabuchi showed in 1985 that there is a functional whose critical points (that are in fact minimizers) are solutions of the constant scalar curvature equation. In this talk we will give an overview of the study of this K-energy functional, that has brought in recent years many important results regarding the existence and uniqueness of cscK metrics.

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