Conference: Higher dimensional algebraic geometry

University Of California-San Diego, La Jolla CA

Investigators

Abstract

This award supports participation in the conference "Higher dimensional algebraic geometry" which will take place at the University of California San Diego from January 10 - 14, 2024. The conference is organized by Paolo Cascini (Imperial College), Brian Lehman (Boston College), Dragos Oprea (University of California San Diego, local organizer) and Chenyang Xu (Princeton University). The event will feature talks by approximately 25 leading mathematicians. There will also be opportunities for early-career mathematicians to disseminate their work. The conference will spotlight the latest breakthroughs in birational geometry and higher dimensional algebraic geometry. The past few years have witnessed significant progress in various subdisciplines of higher-dimensional algebraic geometry. However, due to the pandemic, there have been limited opportunities to disseminate these advances. The current conference seeks to remedy this situation. It also aims to foster collaborations and to facilitate connections within the mathematical community. This award will provide partial support to the travel expenses of mathematicians who do not have federal support or who are students, postdoctoral researchers, or belong to under-represented groups. Algebraic varieties are geometric objects defined by polynomial equations. Understanding the structure of algebraic varieties is a central question in algebraic geometry with far-reaching implications in nearby fields (commutative algebra, differential geometry, symplectic geometry, mathematical physics, computational geometry, number theory, etc). In birational geometry, the focus is on classifying complex projective varieties up to birational equivalence. The Minimal Model Program aims to generalize the classification results in dimension two to higher-dimensional varieties. The field was profoundly transformed by the work of James McKernan and his collaborators. The topics of the conference will include some of the most exciting recent advances in the area, such as K-stability and Fano varieties, MMP for foliations and Kahler varieties, boundedness results for Calabi-Yau varieties, birational geometry in positive and mixed characteristic, mirror symmetry and others. The website for the conference is https://lehmannb3.wixsite.com/james-60. 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.