报告人： Bernhard Keller / 孔博恩
Affiliation: Universite Paris Cite / 巴黎西岱大学
摘要： Cluster algebras are certain commutative algebras with a very rich combinatorial structure. They were invented by Sergey Fomin and Andrei Zelevinsky in 2002, who were motivated by problems from Lie theory, in particular the study of Lusztig’s canonical bases and his notion of total positivity. Since then, it has turned out that cluster algebras also appear in a wide range of other subjects, from representation theory to mathematical physics, mirror symmetry and symplectic topology. Among the many methods developed to study cluster algebras is “additive categorification”, where the combinatorics of cluster algebras are lifted to the level certain (stably) 2-Calabi-Yau categories. In the case of cluster algebras with coefficients, these are the Higgs categories recently introduced by Yilin Wu. In this talk, after a historical survey and a basic introduction to cluster algebras, we will present the framework of additive categorification via Higgs categories and conclude with examples appearing in higher Teichmuller theory as approached by Fock-Goncharov, Jiarui Fei, Ian Le, … and Goncharov-Shen.
时间： 4pm, Friday, Dec. 19, 2025
地点： 18F Auditorium, SIMIS
Introduction to the speaker: Bernhard Keller is a renowned mathematician. He has made foundational contributions in the theories of differential graded categories, Hochschild cohomology and cluster algebras. He is a fellow of the American Mathematical Society, an ICM speaker in 2006 and has received the Sophie German Prize in 2014.
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