YoVDO

Universally Counting Curves in Calabi-Yau Threefolds - ICBS 2024

Offered By: BIMSA via YouTube

Tags

Enumerative Geometry Courses Algebraic Geometry Courses Gromov-Witten Invariants Courses Calabi-Yau Threefold Courses Curve Counting Courses

Course Description

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore a groundbreaking lecture on enumerative geometry and curve counting in complex threefolds. Delve into the foundations of modern enumerative geometry, from basic concepts like unique lines between points to more complex ideas such as the 27 lines on smooth cubic surfaces. Discover a novel approach to enumerative invariants based on the "Grothendieck group of 1-cycles" and a universal curve enumeration invariant. Learn how this new perspective simplifies the structure of curve counting in complex threefolds with nef anticanonical bundle, revealing that the group is generated by "local curves". Understand the implications of this generation result, including new cases of the MNOP conjecture that relates Gromov-Witten and Donaldson-Pandharipande-Thomas invariants. Gain insights into cutting-edge mathematical research presented by John Vincent Pardon at the International Congress of Basic Science 2024, offering a fresh perspective on curve counting in Calabi-Yau threefolds.

Syllabus

John Vincent Pardon: Universally counting curves in Calabi--Yau threefolds #ICBS2024


Taught by

BIMSA

Related Courses

Integer-Valued Gromov-Witten Type Invariants - Guangbo Xu
Institute for Advanced Study via YouTube
Introduction to Contact Geometry by Dheeraj Kulkarni
International Centre for Theoretical Sciences via YouTube
Real Gromov-Witten Theory
International Mathematical Union via YouTube
MTC and Twisted Hilbert Spaces
ICTP Mathematics via YouTube
Donaldson-Thomas and Gromov-Witten Invariants - Part 17
IMSA via YouTube