The purpose of the conference is to celebrate the work of Anthony Iarrobino in algebra and geometry. The theme of the conference focuses on two threads: the Jordan type of Artinian algebras and the geometry of Hilbert schemes. Artinian algebras, characterized by their finite-dimensional structure, play a crucial role in various areas of mathematics, including representation theory, commutative algebra, and algebraic geometry. The Jordan type, associated with the Jordan canonical form, provides insights into the structure of these algebras.
The punctual Hilbert scheme, which parametrizes zero-dimensional subschemes of a fixed length in an algebraic variety, is a fundamental object in algebraic geometry with deep connections to combinatorics, singularity theory, and representation theory. Understanding the geometry of these schemes, particularly through the lens of Jordan types, opens new avenues for exploring the intricate relationship between algebra and geometry.
The conference aims to bring together leading researchers and young scholars to discuss recent advancements, share methodologies, and foster collaboration in this specialized but highly impactful area of mathematics. Topics will include the classification of Jordan types in various contexts, the role of Artinian algebras in deformation theory, and the geometric properties of punctual Hilbert schemes. By examining these themes, the conference seeks to deepen the understanding of the algebra-geometry interface and its implications for broader mathematical research.
