The following mini courses will be organized. The venue is Room 210, Run Run Shaw Building, Main Campus, The University of Hong Kong.

Date: September 11-15
Time: 9:45am - 10:45am
Speaker: Bernhard Keller
Affiliation: Université Paris Cité

Title: Additive categorification of cluster algebras with coefficients

Abstract: This lecture series is devoted to the construction of additive categorificiations of cluster algebras. After presenting additive categorification via cluster categories in the coefficient-free case, we will consider examples of Frobenius categorifications following Geiss-Leclerc-Schroeer (unipotent cells) and Jensen-King-Su (Grassmannians and positroids). We will then introduce the general framework of Higgs categories as developed by Yilin Wu. We will illustrate his constructions with examples from Goncharov-Shen's work, in particular the "basic triangle", which is the fundamental building block in their approach to higher Teichmueller theory. This material is taken from Miantao Liu's ongoing Ph. D. thesis.

Date: September 11-15
Time: 11:00am - 12:00noon
Speaker: Bernard Leclerc
Affiliation: CNRS Caen

Title: Monoidal categorification of cluster algebras

Abstract: A monoidal categorification of a cluster algebra A is a categorification of A via a monoidal category (in contrast to the more classical and fully developed approach involving additive 2-Calabi-Yau categories and quiver representations). After explaining the basic definitions, I will present the main examples coming from representation theory of affine Hecke algebras, quiver Hecke algebras and quantum affine algebras.

Date: September 25,26,28
Time: 2:00pm - 3:30pm
Speaker: Bernhard Keller
Affiliation: Université Paris Cité

Title: An introduction to relative Calabi-Yau structures

Abstract: Relative Calabi-Yau structures were first hinted at in a survey by Toën in 2014. Later, the theory was fully developed by Brav-Dyckerhoff in a paper from 2019. In this minicourse, we will first present the definition of left and right relative Calabi-Yau structures following Brav-Dyckerhoff and illustrate it on examples from algebraic geometry and cluster theory. We will then explain Brav-Dyckerhoff's gluing theorem and discuss its links to Fock-Goncharov's amalgamation construction. Finally, we will sketch Bozec-Calaque-Scherotzke's theorem linking relative Calabi-Yau completions to derived conormal bundles.