Solutions Spaces: a Geometric Approach

• Grant number: 25/16921-5
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2026
• End date: July 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Theory of Computation
• Principal Investigator: Benjamin Merlin Bumpus
• Grantee: Benjamin Merlin Bumpus
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• City of the host institution: São Paulo
• Associated researchers: Hugo Luiz Mariano

Abstract

Recent successes of Artificial Intelligence make it clear that there is relevant information in thestructure of solution spaces that can be exploited to great effect. However, theory is lagging behindpractical computing since solution spaces are not often treated as first-class mathematical objects incomputational complexity. This proposal aims to address this gap by combining tools from graph theoryand algebraic geometry and viewing solutions spaces as both graphs and algebraic varieties. Theproject deliverables include new results in structural graph theory, competitive practical algorithms (andimplementations thereof) and new insights into the geometry of solution spaces. (AU)