Hodge Theory and its Applications
Hodge theory is a central subject in modern geometry. Originating in the 19th century works of Riemann, Jacobi, Picard, Poincaré and others, followed by topological ideas of Lefschetz, it was established in modern form in the middle of the 20th century in the monumental work of Sir William Vallance Douglas Hodge. Since then, it has blossomed both as a major subject in its own right and in many new directions in connection with Derived Categories, Derived Algebraic Geometry, Model Theory, Homological Mirror Symmetry, Mathematical Physics, Number Theory, Representation Theory and other areas of current mathematics.
We have organized a year entitled "Hodge Theory and its Applications" at the Institute of the Mathematical Sciences of the Americas (IMSA) at the University of Miami.
September 2020 - May 2021.
Below is an outline plan of the main events. IMSA is taking extra precautionary measures to ensure the well-being and safety of our visitors and personnel. All programs will be exclusively online. We will use Zoom technology to facility remote participation.
Hodge Theory and Rationality
Date: October 5th - 9th, 2020
Organizers: Dr. Philip Griffiths, Dr. Carlos Simpson, and The International Laboratory for Mirror Symmetry and Automorphic Forms, Higher School of Economics (Moscow, Russia)
Abstract: The study of Intermediate Jacobians was already one of the classical pathways by which Hodge theory had an impact on the study of birational geometry. In recent years this relationship has gained new momentum with a number of different techniques being proposed for the application of Hodge-type invariants such as Intermediate Jacobians and their generalizations, as well as categorical variants of these structures, to questions of rationality. This workshop will cover the latest results and techniques while also serving as an introduction to the applications of concrete aspects of Hodge theory.
To view the program schedule and video links, click here.
To view the abstracts of this program, click here.
Irrational Fans in Physics and Mathematics
Date: October 19th - 21st, 2020
Organizers: Dr. Ernesto Lupercio, Dr. Ludmil Katzarkov, and The International Laboratory for Mirror Symmetry and Automorphic Forms, Higher School of Economics (Moscow, Russia)
Abstract: Classically, rational fans and their relation to toric geometry have been very influential in XXI century geometry and topology. Various generalizations of this picture to the irrational case have arisen in various fields of mathematics and physics; the purpose of this conference is to bring together experts and beginners to talk about the state of the art in this rapidly growing field.
To view the program schedule and video links, click here.
To view the abstracts of this program, click here.
Recent Applications of the Theory of O-Minimal Structures to Various Questions in Hodge Theory
Date: November 16th - 20th, 2020
Organizers: Dr. Philip Griffiths, Dr. Carlos Simpson, and The International Laboratory for Mirror Symmetry and Automorphic Forms, Higher School of Economics (Moscow, Russia)
Abstract: In recent years the applications of model theory through the notion of o-minimal structure have led to new ideas and several breakthroughs in Hodge theory, in particular in the study of period mappings and period domains. The objective of this workshop is to bring together researchers on the cutting edge of model theory and o-minimal structures, with researchers interested in the study of period mappings, their geometry and arithmetic properties.
To view the program schedule and video links, click here.
To view the abstracts of this program, click here.
