[geometry-ml:03492] MS seminar at Kavli IPMU -- Mauro Porta and Alastair Craw

[Todor Milanov]

Dear all,

I would like to announce the following two Mathematics and String theory seminars at Kavli IPMU

1) Speaker: Mauro Porta (U of Strasbourg)
Date:	Thu, Nov 15, 2018, 15:30 - 17:00
Place:	Seminar Room A

Title: Virtual classes in analytic geometry. 

Abstract: In this talk I will survey ongoing work with T. Y. Yu. In the first introductory part of the talk I will explain general motivations that lead to consider virtual classes and I will give examples arising from different areas. I will also explain how derived geometry can be successfully used to construct and sometimes compute virtual classes in these situations. In the second part of the talk, I will focus on the analytic aspects of the theory. I will review the main foundational results of derived analytic geometry and I will survey recent progresses in my joint work with T. Y. Yu on the construction of non-archimedean Gromov-Witten invariants. 


2) Speaker: Alastair Craw	(U of Bath)
Date:	Wed, Nov 21, 2018, 15:30 - 17:00
Place:	Lecture Hall

Title:	Birational geometry of symplectic quotient singularities

Abstract: For a finite subgroup G of SL(2,C), a well known construction of Kronheimer realises the minimal resolution S of the Kleinian singularity C^2/G as a quiver variety, and implies that the ample cone of S is a Weyl chamber in the root system of type ADE associated to G by the McKay correspondence. For any n>1, there is a natural generalisation to dimension 2n, namely, the Hilbert scheme X=Hilb^[n](S) of n points on S, which is itself a resolution of a symplectic quotient singularity C^{2n}/G_n; here, G_n is the wreath product of G with S_n. In dimension greater than two, minimal resolutions are not unique, so one expects the situation to be much more complicated. While this is the case, I'll explain why every projective, crepant resolution of C^{2n}/G_n is a quiver variety and, in addition, why the movable cone of X can be described in terms of an extended Catalan hyperplane arrangement of the root system associated to G. The Namikawa Weyl group arises naturally in this context, and it plays a key role. This is joint work with Gwyn Bellamy.



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Todor Eliseev Milanov
Associate Professor 
Kavli IPMU,  Japan

todor.milanov ＠ ipmu.jp