Fall Emphasis Semester 2020

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.

Here is an outline plan of the main events. More information will follow at the end of August 2020. To the extent possible, subject to proper social distancing protocols and travel restrictions, events will include an onsite aspect. We will use Zoom technology to facilitate remote participation as needed.

Hodge Theory and Rationality

Date: October 5th - 9th, 2020
Organizers: Dr. Philip Griffiths & Dr. Carlos Simpson
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.  

Quantum Toric Varieties 

Date: October 12th - 14th, 2020
Organizers: Dr. Philip Griffiths & Dr. Carlos Simpson
Abstract: TBA

Recent Applications of the Theory of O-minimal Structures to Various Questions in Hodge Theory

Date: November 13th - 20th, 2020
Organizers: Dr. Philip Griffiths & Dr. Carlos Simpson
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. 

Spring Emphasis 2021                                                                                    Short Courses and Seminars 2020 (TBA)