Thematic Month at CIRM in Complex Geometry

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

The award provides partial support for the participation of U.S.-based Mathematicians in a conference in Pure Mathematics titled "Thematic Month: Complex Geometry", to be held at CIRM, Luminy (France) from January 28 to March 01, 2019. The main theme of the conference is Geometry; one of the cornerstones of modern Mathematics with broad applications, ranging from String Theory to Cryptography. Through newly discovered, deep connections between various active areas of research in Geometry, including Arithmetic, Algebraic and Complex Differential Geometry, each subject has witnessed unexpected and groundbreaking advances. The conference aims to facilitate interactions among researchers in these diverse fields to further these developments. Such activities have proved to be of unparalleled importance for geometers in these interconnected areas, specially for those in early stages of their careers. The event supported by this award is composed of a master class (1 week long) and 4 international conferences, each one week long: Singular Metrics in Kaehler Geometry (week 2), Birational Geometry and Hodge Theory (week 3), Entire Curves, Rational Curves and Foliations (week 4), and Ball Quotient Surfaces and Lattices (week 5). The last couple of years have been witness to important progress in our understanding of the geometry of complex algebraic varieties, and more generally Kaehler varieties. The aim of this conference is to facilitate the gathering of experts of international stature in various active areas of research. The aim of the Master Class is the introduction of techniques and theories that will be used throughout the conference. This will mainly consist of three courses: Hodge theory, K3 surfaces and special metrics on manifolds. During the second week, the goal is to study various geometric problems where the theory of singular metrics play an important role. This includes the following topics: Singular Kaehler-Einstein varieties and their moduli, Positivity in Complex Geometry and Generalized Yau-Tian-Donaldson Conjecture. The aim of the third week is to investigate various methods in Algebraic Geometry with a view towards applications in Birational Geometry and Moduli spaces. The following topics will be of particular importance: Hodge theory and Moduli of higher dimensional varieties. The goal of the fourth week is to gather specialists in different fields working on the geometry of algebraic and transcendental curves in complex varieties. Topics include: jet spaces and foliations, Special Varieties and Nevanlinna theory. Despite an intensive search for finding a geometric construction for ball quotient surfaces, very few examples have been obtained with explicit equations. Recently Cartwright and Steger have introduced new algorithms for such constructions, leading to the completion of the classification of fake projective planes. The focus of the final week will be a detailed analysis of this fundamental work and its applications. Webpage for the conference: https://conferences.cirm-math.fr/2060.html This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.