Mathematics Days in Sofia – 2026
Section “Geometry and Topology”
Participants
Invited Speakers
- Ludmil Katzarkov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Stefan Ivanov, Sofia University “St. Kliment Ohridski” and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Contributors
- Alexander Petkov, Sofia University “St. Kliment Ohridski”, Bulgaria
- Andrei Bengus-Lasnier, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Cornelia-Livia Bejan, Gheorghe Asachi Technical University of Iaşi, Romania
- François Bernard, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Ivan Minchev, Sofia University “St. Kliment Ohridski”, Bulgaria
- Katarina Lukić, University of Belgrade, Serbia
Leonardo Francisco Cavenaghi, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Mića Stanković, University of Belgrade, Serbia
- Milan Zlatanovic, University of Niš, Serbia
- Miroslav Maksimovic, University of Pristina, Kosovo
- Peter Petrov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Valdemar Tsanov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Vesko Valov, Nipissing University, Canada
Program and Abstracts
In this talk we will introduce a new approach to Minimal Model Program (MMP) based on atoms theory.
It is shown that on a compact ACYT 6-manifold with co-closed Lee form the curvature of the torsion connection is an SU(3) instanton if and only if the torsion is parallel with respect to the torsion connection.
We are going to present in this talk two sub-gradient estimates for the quaternionic contact (qc) heat equation on a compact qc manifold of dimension 4n+3, provided some positivity conditions are satisfied. These are qc versions of the prominent Li-Yau gradient estimate in Riemannian geometry. Another goal of this talk is to exhibit two Perelman-type entropy formulas for the qc heat equation on a compact qc-Einstein manifold of dimension 4n+3 with non-negative qc scalar curvature (e.g. compact 3-Sasakian manifold), as well as an integral sub-gradient estimate for the positive solutions of the qc heat equation.
Introduced by Pham and Teissier, the Lipschitz saturation of a complex analytic variety X is an algebraic construction which plays an important role in the study of the Lipschitz geometry of singularities. In the case of curves, in particular, two curve germs are bi-Lipschitz equivalent if and only if their Lipschitz saturations are isomorphic. It can therefore be viewed as a canonical representative of the bi-Lipschitz equivalence class of a curve germ. Moreover, the Lipschitz saturation of a curve is a toric curve, which can be determined algorithmically from its characteristic exponents.
In higher dimensions, this object also encodes strong topological information about the Lipschitz geometry of the singularity, but it becomes much more difficult to describe, and no algorithmic method is known for computing it in general. In a joint work with Giles Flores and Chavez, we show, however, that the Lipschitz saturation can be computed explicitly in arbitrary dimension in the case of toric singularities
In this talk, we briefly review core concepts in quantum cohomology and the quantum differential equation to explain how information extracted from these frameworks can be applied to questions in birational geometry.
This presentation is based on ongoing joint work with Ludmil Katzarkov and Maxim Kontsevich.
These are the results of joint work with prof. Milan Zlatanović.
After reviewing briefly the history of problem, the main theorem of Izmestiev and Akopyan will be formulated. The main steps of the proof will be discussed, with the results needed for them. Some applications will be mentioned during the talk as well.
The Hilbert quotient Y of a complex projective manifold X by the action of a connected reductive linear algebraic group G is the projective spectrum of the ring of G-invariants in the homogeneous coordinate ring of X. It can be obtained alternatively as the symplectic reduction for the action of a maximal compact subgroup K of G: Y is the quotient by K of the Kempf-Ness set M (the 0-fiber of a suitable momentum map). The Kempf-Ness set is not algebraic, only the quotient is. In this talk, I will preset a construction of certain special algebraic submanifolds of M with finite morphisms to Y, in case X admits an action by a larger reductive group. The construction uses compatible symmetric subgroups and has applications to invariant theory.
