Balázs Szendrői's HomepageOrganiser: Balázs Szendrői
Mondays 13:15 – 14:45 in SR6
- December 9, Mate Telek (MPI Leipzig): Positive Solutions to Polynomial Systems via Tropical Geometry
- Tropical geometry establishes a connection between algebraic and polyhedral geometry, allowing to transform an algebraic variety into a polyhedral object, called tropical variety, that mimics essential properties of its algebraic counterpart. Recently, there has been increasing attention on the tropicalization of the positive part of algebraic varieties, i.e. the intersection of the variety with the positive real orthant. After a gentle introduction to tropical geometry, we will discuss real analogs of the Fundamental Theorem of Tropical Geometry and the Transverse Intersection Theorem. Building on these results, we will present an algorithm that provides lower bounds on the maximal number of positive real solutions of a parametrized polynomial equation system. The talk is based on joint work with Kemal Rose.
- January 13, 2025, Martin Kalck (Uni Graz): TBA
- January 20, 27, Sean Griffin
- March 2, Giulio Codogni (U Roma 2): Slope inequalities, effective positivity results for Hodge bundles and applications
- We will explain various higher dimensional generalizations of the Xiao-Cornalba-Harris slope inequality, and we will present several effective positivity results for Hodge bundles. We will talk about applications regarding the volume of integrable foliations, the volume and the ample cone of KSB moduli spaces, and the cardinality of the auotmorphism group of KSB fibrations. This is based on joint works with Zs. Patakfalvi, L. Tasin, F. Viviani
- March 9, Joshua Wen
Past talks
- October 14-November 11, Tamas Hausel (ISTA): Big algebras
- A series of lectures giving some background to the paper “Commutative avatars of representations of semisimple Lie groups” arXiv:2311.02711 and also more recent work on the anatomy of big algebras. For more, see https://hausel.ist.ac.at/749-2/
- September 30, Michael McBreen (Chinese University of Hong Kong): The Hamiltonian reduction of hypertoric mirror symmetry
- I will describe recent work with Vivek Shende and Peng Zhou, which relates the Fukaya category of a multiplicative hypertoric variety to the Fukaya category of its associated toric arrangement. This provides evidence for a general conjecture which describes the `hamiltonian reduction’ of a Fukaya category at singular values of the moment parameter. Despite the subject, the talk should be accessible to someone unfamiliar with the Fukaya category.
- April 29, May 27, June 3 / 10 / 24, Livia Campo: A birational perspective on Fano hypersurfaces and K-stability
- In this series of lectures I will first give an introduction to the
birational classification of Fano 3-folds via graded rings. I will
mostly focus on Fano hypersurfaces (i.e. defined by one equation in a
weighted 4-dimensional projective space). These are birationally
rigid, and I will present some major techniques to determine their
birational classes. Finally, I will then combine these facts to
discuss the existence of Kaehler-Einstein metrics on Fano 3-fold
hypersurfaces.
- In this series of lectures I will first give an introduction to the
- March 4 / 11, April 8 / 15, Noah Arbesfeld: Equivariant K-theory and Hilbert schemes
- First, I’ll give an introduction to computations in equivariant algebraic K-theory. Then we’ll apply these techniques to Hilbert schemes of points on surfaces and their generalizations. Some possible examples include nested Hilbert schemes and Nekrasov’s moduli spaces of crossed instantons.