Inaugural Colloquium – Topological, Computational & Algebraic Aspects of Complex Systems

The research group “Topological, Computational & Algebraic Aspects of Complex Systems” launches its 2025 activity with a one-day colloquium at the International Center for Mathematical Sciences – Sofia (ICMS). Three talks will highlight recent advances in birational geometry, tropical sandpiles, and quantum toric geometry. All times below are UTC + 3 (Sofia).

Programme:

Abstracts:

Kyoung-Seog Lee, Combinatorially minimal Mori dream surfaces of general type

The study of minimal surfaces of general type has a long and beautiful history. However, they are still very mysterious objects and we do not know how to understand them systematically. In this talk, I will discuss how to use ideas of birational geometry to understand certain surfaces of general type. This talk is based on a joint work with JongHae Keum.

Mikhail Shkolnikov, Tropical sandpile as a scaling limit

We will start by discussing tropical sandpile model (the only known continuous mathematical realisation of self-organised criticality) which was discovered as a scaling limit of the classical sandpile model in the high-energy regime. This fact can be stated rigorously as certain theorems proven jointly with Nikita Kalinin, and one of these theorems at the level of point-wise convergence of renormalised toppling functions to some tropical series depending on the positions of single grain perturbations, as well as key points of its proof, will be explained in detail. If time permits, other versions of scaling limits (Hausdorff convergence of deviation loci to a tropical analytic curve defined by the series, and weak-* convergence of an appropriately regularised relaxed states to a distribution supported on this curve) will be demonstrated.

Ernesto Lupercio, Quantum Toric Geometry: a first approach

Quantum Toric Geometry (QTG) is a non-commutative enhancement of classical toric geometry in which the familiar algebraic torus is replaced by a quantum torus, leading to genuinely new moduli phenomena and rich links with mirror symmetry. After a brief review of toric fans and their quantum analogues, I will outline the Quantum Geometric Invariant Theory (QGIT) construction of quantum toric varieties, highlight how lattice data acquires modular parameters, and discuss wall-crossing and deformation questions that have no classical counterpart. The talk is based on joint work with Ludmil Katzarkov, Laurent Meersseman and Alberto Verjovsky. [arxiv.org]  https://arxiv.org/abs/2002.03876, sciencedirect.com, icms.bg

Practical information:

• Venue: ICMS, IMI-BAS, Acad. G. Bonchev 8, Sofia, Bulgaria
• Hybrid access: Zoom link will be e-mailed to registered participants.
• Registration: Please e-mail m.shkolnikov@math.bas.bg with subject “TCACS Colloquium”.

We look forward to seeing you at the first event of our 2025 series!