Talk_id  Date  Speaker  Title 
15388

Thursday 9/6 3:00 PM

Daping Weng, MSU

Cluster DonaldsonThomas Transformation of Grassmannian
 Daping Weng, MSU
 Cluster DonaldsonThomas Transformation of Grassmannian
 09/06/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
Abstract: On the one hand, there is a 3d Calabi Yau category with stability conditions associated to a quiver without loops or 2cycles with generic potential, and one can study its DonaldsonThomas invariants. On the other hand, such a quiver also defines a cluster Poisson variety, which is constructed by gluing a collection of algebraic tori in a certain way governed by combinatorics. In certain cases, the DonaldsonThomas invariants of the former category can be captured by an automorphism on the latter space. In this talk, I will recall the cluster Poisson structure on the moduli space of configurations of points in a projective space, and state my result on constructing the corresponding cluster DonaldsonThomas transformation, and give a new proof of Zamolodchikov’s periodicity conjecture in the $A_m\boxtimes A_n$ cases as an application. If time permits, I will also talk about the generalization of this result to double Bruhat cells.

15393

Thursday 9/13 3:00 PM

Dylan Rupel, MSU

The Combinatorics of Compatible Pairs
 Dylan Rupel, MSU
 The Combinatorics of Compatible Pairs
 09/13/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
Abstract: Compatible subsets of edges in a maximal Dyck path were introduced by Lee, Li, and Zelevinsky as a tool for constructing nice bases for rank two cluster algebras. In this talk, I will present a generalization of this combinatorics and give two applications. The first application is a combinatorial construction of noncommutative rank two generalized cluster variables which proves a conjecture of Kontsevich. The second application gives a combinatorial description of the cells in an affine paving of rank two quiver Grassmannians, this part is joint work with Thorsten Weist.

15418

Thursday 9/20 3:00 PM

Matthew Mills, MSU

Green sequences and localacyclicity.
 Matthew Mills, MSU
 Green sequences and localacyclicity.
 09/20/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
In 2014 it was conjectured that the equality of the cluster algebra and upper cluster algebra is equivalent to the existence of a maximal green sequence. In this talk we will discuss a stronger result for cluster algebras from mutationfinite quivers with an emphasis on surface cluster algebras. Specifically we show that for all quivers from surface cluster algebras there exists a maximal green sequence if and only if the cluster algebra is equal to the cluster algebra if and only if the cluster algebra is locallyacyclic. We will also provide a counterexample to show that the result does not hold in general.

15398

Thursday 9/27 3:00 PM


Joint meeting with Notre Dame: open problem session

 Joint meeting with Notre Dame: open problem session
 09/27/2018
 3:00 PM  4:00 PM
 C304 Wells Hall
Abstract: we will discuss open problems in Cluster Algebras theory

15430

Thursday 10/4 3:00 PM

Dylan Rupel, MSU

Cell Decompositions for Rank Two Quiver Grassmannians
 Dylan Rupel, MSU
 Cell Decompositions for Rank Two Quiver Grassmannians
 10/04/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
A quiver Grassmannian is a variety parametrizing subrepresentations of a given quiver representation. Reineke has shown that all projective varieties can be realized as quiver Grassmannians. In this talk, I will study a class of smooth projective varieties arising as quiver Grassmannians for (truncated) preprojective representations of an nKronecker quiver, i.e. a quiver with two vertices and n parallel arrows between them. The main result I will present is a recursive construction of cell decompositions for these quiver Grassmannians. If there is time I will discuss a combinatorial labeling of the cells by which their dimensions may conjecturally be directly computed. This is a report on joint work with Thorsten Weist.

15431

Thursday 10/11 3:00 PM

Nick Ovenhouse, MSU

Introduction to Scattering Diagrams
 Nick Ovenhouse, MSU
 Introduction to Scattering Diagrams
 10/11/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
I will give basic definitions of scattering diagrams and wallcrossing automorphims, and finish by showing some examples related to rank2 cluster algebras.

16443

Thursday 10/18 3:00 PM

Dylan Rupel, MSU

Cluster Monomials and Theta Bases via Scattering Diagrams
 Dylan Rupel, MSU
 Cluster Monomials and Theta Bases via Scattering Diagrams
 10/18/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
In this talk I will add to Nick’s presentation from last time by describing a portion of the scattering diagram using cvectors and gvectors. Then I will present some examples of computing cluster monomials using broken lines. If there is time I will compute an element of the theta basis which is not a cluster monomial.

15442

Thursday 10/25 3:00 PM


MSUND Summit @ ND

 MSUND Summit @ ND
 10/25/2018
 3:00 PM  5:00 PM

We will be heading to Notre Dame to discuss open problems in the field. We will meet in room Hurley 258.

16462

Thursday 11/1 3:00 PM

Dylan Rupel, MSU

Cluster Monomials and Theta Bases via Scattering Diagrams
 Dylan Rupel, MSU
 Cluster Monomials and Theta Bases via Scattering Diagrams
 11/01/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
In this talk I will add to Nick’s presentation from last time by describing a portion of the scattering diagram using cvectors and gvectors. Then I will present some examples of computing cluster monomials using broken lines. If there is time I will compute an element of the theta basis which is not a cluster monomial.

16475

Thursday 11/15 3:00 PM

Daping Weng, MSU

More on Scattering Diagram and Theta Functions
 Daping Weng, MSU
 More on Scattering Diagram and Theta Functions
 11/15/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
Abstract: I will continue the discussion on scattering diagram and theta functions and relate them to the classical cluster theories. I will sketch GrossHackingKeelKontsevich’s proofs of positive Laurent phenomenon, sign coherence, and a weak version of the cluster duality conjecture.

15443

Thursday 11/29 3:00 PM

Greg Muller, University of Oklahoma

Scattering diagrams of marked surfaces
 Greg Muller, University of Oklahoma
 Scattering diagrams of marked surfaces
 11/29/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
Every cluster algebra has an associated 'scattering diagram': an affine space endowed with a (possibly very complicated) collection of 'walls'. The structure of this scattering diagram encodes essential information about the cluster algebra's exchange graph, Laurent coefficients, and theta functions. In this talk, I will discuss an ongoing project with Nathan Reading and Shira Viel to construct a scattering diagram associated to a triangulable marked surface. The affine space may be identified with the set of certain `measured laminations' on the surface, and the walls may be identified with certain forbidden subgraphs embedded in the surface, which we call `barricades'.

17483

Thursday 12/6 3:00 PM

Daping Weng, MSU

More on Scattering Diagram and Theta Functions
 Daping Weng, MSU
 More on Scattering Diagram and Theta Functions
 12/06/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
I will continue the discussion on scattering diagram and theta functions and relate them to the classical cluster theories. I will sketch GrossHackingKeelKontsevich’s proofs of positive Laurent phenomenon, sign coherence, and a weak version of the cluster duality conjecture.
