This course examines the intersection of Abelian Sandpile Theory and Tropical Geometry—two frameworks revealing how discrete local rules generate global geometric order. Offered by the Topological and Geometric Complexity Group at ICMS Sofia, the course welcomes doctoral students and researchers interested in the geometric foundations of complex systems.
The Symposium on Complex Systems, Data, and Topology is a four-day gathering exploring the frontiers of mathematics, machine learning, geometry, and real-world complexity. Set within the vibrant intellectual atmosphere of ICMS Sofia, the symposium brings together a select group of international researchers to discuss new ideas, paradigms, and tools shaping the future of science and computation.
The International Center for Mathematical Sciences – Sofia (ICMS-Sofia) hosts an international conference on Quantum Groups and Cluster Algebras between 15-19 December 2025 at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, with the financial support of the Simons Foundation, Republic of Bulgaria - Ministry of Education and Science and Institute of Mathematics and Informatics, and Bulgarian Academy of Sciences. The aim of this conference is to bring together researchers to share recent advances and promote further developments in the theory of Quantum Groups and Cluster Algebras.
Tropical sandpiles stand at the crossroads of mathematics, computer science, machine learning, algebra, physics, and mathematical logic. Originating from models of self-organized criticality, they reveal intricate combinatorial and geometric structures that echo through algebraic geometry and tropical mathematics. Their dynamics connect to complexity theory and algorithmic design in computer science, while also inspiring methods in statistical mechanics and the study of complex systems in physics. More recently, tropical sandpile models have begun to interact with approaches in data science and machine learning. At the same time, their formal underpinnings invite connections to logic and the foundations of computation — providing a common language where diverse disciplines converge.
September - October 2025
The research group “Theory of Atoms”'s Leonardo Kavenaghi will give series of lectures
The Theory of Atoms is a recent formalism introduced by Katzarkov, Kontsevich, Pantev, and Yu, which aims to integrate classical Hodge theory with symplectic geometry, seeking applications in birational geometry.
To properly understand it, we must gather concepts from many areas of knowledge, ranging from Gromov-Witten theory and enumerative algebraic geometry to classical and noncommutative Hodge theory. This series is designed to be an example-driven introduction, providing the essential background needed to understand this new theory.
Friday, September 5, room 358, IMI-BAS. 14:00
The research group “Theory of Atoms” will give two talks that will highlight recent advances.
On August 7, 2025, the Conference Celebrating the Consortium IMSAC was officially opened at the Institute of Mathematics and Informatics (IMI–BAS) in Sofia. The event honors the long-standing collaboration among leading mathematical institutes across the USA, Latin America, Asia, and Europe, united in the Institute of the Mathematical Sciences of the Americas Consortium (IMSAC). At the opening, Prof. Julian Revalski, Director of the International Center for Mathematical Sciences – Sofia (ICMS-Sofia), greeted the participants and emphasized the importance of international cooperation in advancing contemporary mathematics. Prof. Peter Boyvalenkov, Director of IMI-BAS, welcomed the guests to the institute and wished them a fruitful and inspiring conference. The opening of the conference also sets the tone for a vibrant month of mathematical activity inBulgaria and coincides with an important milestone — the end of the first year of the activities of the research group Theory of Atoms, led by Prof. Ludmil Katzarkov.
Y. Ruan (IASM, Hangzhou-China)
Tuesday, July 22, room 403, IMI-BAS. 15:00
The computation of higher genus GW-invariants of Compact Calabi-Yau 3-fold is one of the most difficult problems in geometry and physics. During last decade, there has been tremendous progress on the problem. I will survey these progress in the talk.
Leonardo Cavenaghi (IMI-BAS/ICMS)
Tuesday, July 22, room 403, IMI-BAS. 14:00
In this talk, we introduce the concept of atoms recently introduced by Katzarkov-Kontsevich-Pantev-Yu. Built from Gromov-Witten theory, they have been proven to be useful in understanding questions in birational geometry by examining the behavior of quantum cohomology under blowup (this is a theorem of H. Iritani, following a conjecture of M. Kontsevich).
Tuesday, July 8, room 403, IMI-BAS. 14:00
The research group “Theory of Atoms” will give two talks that will highlight recent advances.
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