Understanding the Virtual Fundamental Class

• Grant number: 25/22006-8
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: February 09, 2026
• End date: August 08, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Fabio Ferrari Ruffino
• Grantee: Lucas Novo da Silva
• Supervisor: Andrea Tobia Ricolfi
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Scuola Internazionale Superiore di Studi Avanzati (SISSA), Italy
• Associated to the scholarship: 24/15412-7 - Ulrich Bundles, BP.MS

Abstract

With the present project, the candidate aims to be introduced to enumerative geometry, first by acquiring familiarity with the classical approach, and afterwards by learning the basic theory about the virtual fundamental class. As relevant applications of the modern approach, the applicant will study the first notions about Gromow-Witten theory, Donaldson-Thomas theory, and Pandharipande-Thomas theory, which can be thought of as modern analogues to the classical Schubert calculus on Grassmannians. (AU)