Landau-Ginzburg Potentials via Projective Representations in Cluster Varieties
Institut des Hautes Etudes Scientifiques (IHES) via YouTube
Overview
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Explore the connections between cluster varieties, Landau-Ginzburg potentials, and projective representations in this 45-minute lecture by Béa de Laporte from the University of Cologne. Delve into the world of partial compactifications of Fock-Goncharov's cluster varieties, including flag varieties significant in algebraic group representation theory. Examine how these compactifications lead to Landau-Ginzburg potentials on dual cluster varieties, and how their tropicalizations define polyhedral cones parametrizing the theta basis. Discover a new interpretation of these potentials as F-polynomials of projective representations of Jacobian algebras. Follow the lecture's progression through introductory concepts, motivations, natural spaces, dual cluster varieties, examples, and results, culminating in a theorem and its proof. Gain insights into this collaborative work with Daniel Labardini-Fragoso, presented at the Institut des Hautes Etudes Scientifiques (IHES).
Syllabus
Introduction
Motivations
Natural Spaces
Dual Cluster Variety
Examples
Results
Cluster varieties
Example
Dual cluster varieties
Potential summation
Jacobian algebra
Theorem
Proof
Taught by
Institut des Hautes Etudes Scientifiques (IHES)