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Double Bott-Samelson cells and cluster algebras

2019-06-27

Venue: Room 200-9, Yuquan Campus

Speaker: Dr. Linhui Shen, Department of Mathematics, Michigan State University

Abstract: 

We introduce the double Bott-Samelson cell associated to an arbitrary Kac-Peterson group G and a pair of positive braids (b, d). We prove that the double Bott-Samelson cells are affine varieties whose coordinate rings are upper cluster algebras. We describe the Donaldson-Thomas transformations on double Bott-Samelson cells. As an application, we obtain a new geometric proof of Zamolodchikov’s periodicity conjecture in the cases of type $\Delta \otimes A$. If time permits, I will further talk about its connections with Knot theory and quantum groups. Joint work with Daping Weng.