This is an introduction to tropical geometry in two talks, mainly in case of curves. The stress will be put on the applications in complex and real algebraic geometry. At the end a few other approaches will be discussed briefly.
On November 10, 2025, the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences will host the Atanasoff Memorial Day event - a new initiative of the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences and the International Center for Mathematical Sciences (ICMS-Sofia) at the IMI-BAS. The organizers' ambition is to hold the Atanasoff Memorial Lecture Series program every year, thus commemorating the memory of John Vincent Atanasoff (1903–1995) - a computer pioneer, inventor of a model of an electronic digital computer and renowned as the "Bulgarian father of the electronic computer". It aims to celebrate the intersection of mathematics, computation, and the sciences of complexity — the very domains that unite topology, geometry, and machine learning in the 21st century.
On November 10, 2025, at 10:00 a.m. in Room 403 of IMI–BAS, Professor Ernesto Lupercio will deliver a public lecture titled “The Algebra of Avalanches: From Sandpiles to the Hidden Symmetries of the Universe.” Professor Lupercio, chair of the research group “Topological, Computational, and Algebraic Aspects of Complex Systems” at ICMS–Sofia, is an internationally recognized mathematician and recipient of the ICTP Ramanujan Prize and the Marcos Moshinsky Research Award.
The workshop brings together a focused group of researchers working across non-Kähler complex geometry, Hodge-theoretic and categorical structures, quantum and irregular phenomena, and mirror symmetry. The goal is to clarify and refine a set of ideas that appear as “atomic” components across these areas, and to create space for concentrated discussion and collaboration. The program combines extended sessions, research talks, and blackboard discussions. The setting is intended to be mathematically rigorous, collegial, and oriented toward identifying new structures and open directions.
November 5, 2025, 16:30 Sofia time, Room 403, IMI-BAS and online via Zoom..
A closer look at the definition of atoms and functoriality - seminar talk by Roy Magen (ICMS, IMI-BAS).
November 4, 2025, 3:00 PM, Room 403, IMI-BAS and online via Zoom..
Seminar by Prof. Ludmil Katzarkov on Recent Advancements in the Theory of Atoms.
Leonardo Cavenaghi, IMI-BAS
Tuesday, November 4, room 403, IMI-BAS. 13:00
Linear systems on complex algebraic curves have been an interesting and rich area of study for a long time. It is known that a real structure on the initial curve induces a real structure on the varieties parameterizing these linear systems. In this talk, I will first present the classical Brill-Noether theorems for these varieties, and then address some fundamental topological questions in the real setting including the case of real trigonal curves.
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.
International Center for Mathematical Sciences
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Acad. G. Bonchev St. bl.8
1113 Sofia, Bulgaria
Tel. +359 2 9793822
icms-office@math.bas.bg
Copyright 2020 ICMS | All Rights Reserved
