This is a traditional conference celebrating the collaboration between many institutes in USA, Latin America, Asia and Europe included in the Institute of the Mathematical Sciences of the Americas Consortium (IMSAC). The conference will be held August 7-9, 2025, in Hall 403 of the Institute of Mathematics and Informatics, Sofia.
Ernesto Lupercio(IMI-BAS)
Friday, June 6, room 403, IMI-BAS. 16:00
In this course we will connect the theory of Topological modular forms with classical singularity theory. Other applications will be considered.Ludmil Katzarkov(IMI-BAS)
Friday, June 6, room 403, IMI-BAS. 15:00
We will make a connection between classical minimal model program and newly introduced theory of atoms.Series of lectures by Peter Dalakov (IMI-BAS and AUBG)
June 3, 6, 10, 13 2025, room 403, IMI-BAS. 14:00
Milan Zlatanovic (University of Niš)
Tuesday, May 13, room 403, IMI-BAS. 14:00
The goal of the conference is to bring together world-renowned and early-career researchers working in the field of algebraic geometry, low-dimensional topology, complex geometry and commutative algebra and foster discussions around singularities in topology, metric geometry, algebraic geometry, dynamical systems and mirror symmetry. The meeting also seeks to provide an opportunity for young scholars from Eastern Europe to engage with cutting edge research in the area.
Lecture Outline 1. Introduction to Binary Quadratic Forms and Conway’s Topographs We will begin with the basics of binary quadratic forms and their classification, followed by an introduction to Conway’s topographs—a visual and geometric framework for understanding them. Lecture Outline 2. Class Number Formula and Summation over Topographs Building on the first lecture, we will explore the class number formula and how summation identities arise naturally from the structure of topographs. Lecture Outline 3. Evaluation of Lattice Sums via Telescoping over Topographs The final lecture will focus on telescoping techniques, demonstrating how they can be used to evaluate intricate lattice sums—such as the one above—with geometric meaning.
In this talk, aimed at a general audience, we will describe recent results on the characterization of norm forms—a classical object in algebraic number theory—in terms of their values at integer points. These results answer natural questions and are related to still-open conjectures of Littlewood (from 1930) and of Cassels and Swinnerton-Dyer (from 1955). The proofs rely on studying the actions of maximal tori of algebraic groups on homogeneous spaces of arithmetic origin.
Aiming to understand the relation to other "refined invariants", and especially their possible interpretation in quantum theory, we explain how to obtain a quadratic, A1-version of Donaldson-Thomas invariants from the motivic refinements first introduced in Kontsevich-Soibelman. Following ideas from Behrend, Bryan and Szendroi, we provide predictions for these invariants in a few simple examples, mainly the computation of DT invariants of A3. Our main goal is to draw relationships with the literature, including works of Levine, Denef and Loser, Azouri, Pepin-Lehaulleur, Srinivas among others. We begin with a brief introduction to A1-enumerative geometry and in the end, we pose some further questions on possible extensions of our definitions. This is joint work with Johannes Walcher. We also comment on joint work in progress with Ran Azouri.
In this talk we will explain the role that the Lie algebras play in the construction of 6-dimensional compact quotient spaces M=G/Γ, where Γ is a lattice, endowed with an invariant complex structure with holomorphically trivial canonical bundle.
International Center for Mathematical Sciences
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
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