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SUMMARY:The g-fan and the Gröbner fan of Gr(2\,n) and Gr(3\,6) - Lara Bos
 singer (Universidad Nacional Autonoma de Mexico (UNAM))
DTSTART:20211110T134500Z
DTEND:20211110T141500Z
UID:TALK164782@talks.cam.ac.uk
DESCRIPTION:In this talk I will discuss recent results of joint work with 
 Fatemeh Mohammadi and Alfredo N&aacute\;jera Ch&aacute\;vez. We show that 
 for the Grassmannains Gr(2\,n) and Gr(3\,6) there exist a unique maximal s
 implicial cone in the Gr&ouml\;bner fan (of a suitable ideal) whose inters
 ection with the tropical Grassmannian is the totally positive part of the 
 tropicalization. The initial monomial ideal of the maximal cone is the Sta
 nley-Reisner ideal of the g-fan (or cluster complex) associated with the c
 orresponding cluster algebra. Moreover\, there is family of Gr&ouml\;bner 
 degenerations associated with the maximal cone that is canonically isomorp
 hic to the cluster algebra with universal coefficients. This isomorphism y
 ields an identification of the rays of the totally positive tropicalizatio
 n with the cluster variables.
LOCATION:Seminar Room 1\, Newton Institute
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