Workshop "Real algebraic geometry in Saint Petersburg"
October 11 - 15, 2021
This workshop will focus on real algebraic geometry, particularly in regards to applications to enumerative geometry and topology of real algebraic varieties. Additional related topics will include topology of tropical varieties, amoebas of algebraic varieties and extremal problems in real algebraic geometry.
The main intertwined themes we plan to address during the workshop are:
- (tropical) generalizations of Viro’s patchworking; applications to constructions of real algebraic varieties with a rich topology of the real part, of parabolic locus of affine real hypersurfaces;
- relations between combinatorial patchworking and tropical homology;
- real linear series on real algebraic curves and their Weierstrass points: upper bounds on their number, tropical constructions, special case of real inflection points of plane algebraic curves;
- totally real morphisms of varieties and curves, choreography of divisors on real algebraic curves after Viro, the separating semi-group of a real curve, generalisations of simple Harnack curves to higher dimensions;
- refined invariants of algebraic surfaces; relation between Göttsche-Shende invariants, Block-Göttsche invariants, and Mikhalkin’s quantum indices of real algebraic curves; generalizations to non-toric surfaces; relation of these invariants with Berkovich geometry and motivic integration;
- development of tropical techniques to compute recently discovered real and open enumerative invariants;
- geometry of amoebas of complex algebraic and analytic varieties;
- topology of tropical varieties; tropical intersection theory; tropical homology.
- Ilia Itenberg • Institut de Mathématiques de Jussieu - Paris Rive Gauche, Sorbonne Université
- Hannah Markwig • Eberhard Karls Universität Tübingen
Local institutions participating in the organization of the event
- St. Petersburg Department of Steklov Mathematical Institute of the Russian Academy of Sciences
- Leonhard Euler International Mathematical Institute in St. Petersburg
The conference is financially supported by a grant from the Government of the Russian Federation, agreements 075-15-2019-1619 and 075-15-2019-1620 and by a grant from Simons Foundation.