**Title:** Towards the Cone Conjecture for Hyperkahler Manifolds

**Speaker:** Misha Verbitsky, Higher School of Economics (Moscow)

**Date:** Friday, November 8, 2013

**Time:** 11:00am – 12:30pm

**Place:** Seminar Room 313, Simons Center

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**Abstract:** Let $M$ be a holomorphically symplectic manifold, and $K$ be its Kaehler cone. We show that all faces of the Kahler cone of $M$ are hyperplanes orthogonal to certain homology classes, called MBM classes. The MBM classes can be

characterized as homology classes which can be represented by a minimal curve in some deformation of $M$. For a deformation of a Hilbert scheme on $K3$, this result gives a simple proof of the Morrison-Kawamata cone conjecture (proven by Markman and Yoshioka in a forthcoming paper). This is a joint work with Ekaterina Amerik.

**Title:** Phase Structure of ALH Moduli Spaces

**Speaker:** Sergey Cherkis, University of Arizona

**Date:** Thursday, November 7, 2013

**Time:** 2:00pm – 2:30pm

**Place:** Seminar Room 313, Simons Center

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**Abstract:** Moduli spaces of instantons and monopoles provide a rich source of hyperkaehler geometries. Depending on the space on which the former are considered, their moduli spaces are realized as moduli spaces of quivers, bows, slings, or monowalls, leading to ALE, ALF, ALG, or ALH geometries. In this talk we focus on ALH case. We classify such moduli spaces and explore their phase structure.

**Title:** Hamiltonian Local Models for Symplectic Derived Stacks

**Speaker:** Chris Brav, IAS

**Date:** Wednesday, October 30, 2013

**Time:** 10:00am – 11:15am

**Place:** Seminar Room 313, Simons Center

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**Abstract:** We show that a derived stack with symplectic form of negative degree can be locally described in terms of generalised Darboux coordinates and a Hamiltonian cohomological vector field. As a consequence we see that the classical moduli stack of vector bundles on a Calabi-Yau threefold admits an atlas consisting of critical loci of regular functions on smooth varieties, and similarly for the stack of maps from an elliptic curve to a symplectic variety. This is joint work with Ben-Bassat, Bussi and Joyce.

**Title:** Four Point Amplitudes from Positivity

**Speaker:** Jaroslav Trnka, Caltech

**Date:** Wednesday, October 23, 2013

**Time:** 2:00pm – 3:30pm

**Place:** Seminar Room 313, Simons Center

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**Title:** Representations of Quivers With Loops

**Speaker:** Tristan Bozec, Université Paris-Sud 11, Orsay

**Date:** Wednesday, October 23, 2013

**Time:** 11:00am – 12:30pm

**Place:** Lecture Hall 102, Simons Center

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**Abstract:** This talk is about the properties of canonical and semicanonical bases in the case of quivers with loop(s). I will use these to define a new Hopf algebra “bigger” than the usual quantum groups. I will also try to give an idea of how Kashiwara crystals should be generalized in this case. Finally we’ll see what can be said in the context of Nakajima quiver varieties.

**Title:** Refined Knot Invariants and Hilbert Schemes

**Speaker:** Eugene Gorsky

**Date:** Tuesday, October 22, 2013

**Time:** 2:30pm – 3:30pm

**Place:** Seminar Room 313, Simons Center

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**Abstract:** Motivated by the string theory, M. Aganagic and S. Shakirov proposed a “refinement” to quantum invariants of knots, which can be formulated mathematically for torus knots using Macdonald polynomials. In a recent paper with A. Negut we proved that these “refined invariants” can be obtained as equivariant Euler characteristics of certain sheaves on the Hilbert scheme of points on the plane. Using localization at fixed points, one can get explicit formulae for these invariants. In some special cases, these results match a certain bivariate deformation of Catalan numbers defined by A. Garsia and M. Haiman.

**Title:** Mirror Symmetry in 3d N=2 Quiver Gauge Theories

**Speaker:** Peter Koroteev

**Date:** Friday, October 11, 2013

**Time:** 11:00am – 12:00pm

**Place:** Seminar Room 313, Simons Center

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**Abstract:** We study quiver gauge theories in 3d with N=2 supersymmetry and its vacua moduli space, which is a complex symplectic manifold. Then we realize the action of the mirror symmetry as a certain sympectomorphism of the SUSY vacua space. We identify many families of mirror quiver theories and discuss interesting connections with integrable spin chains. By gauging global symmetries of the quiver theories one may construct plethora quivers with Sp and SO gauge groups as well as their mirrors.

based on http://arxiv.org/abs/arXiv:1304.0779 and work in progress

]]>**Title:** Introduction to Quiver Gauge Theories

**Speaker:** Nikita Nekrasov

**Date:** Thursday, October 10, 2013

**Time:** 1:00pm – 2:00pm

**Place:** Lecture Hall 102, Simons Center

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**Title:** Hilbert Series of Coulomb Branch for N=2 Dimension 3 Field Theory

**Speaker:** Amihay Hanany, Imperial College London

**Date:** Tuesday, October 8, 2013

**Time:** 2:30pm – 3:30pm

**Place:** Seminar Room 313, Simons Center

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**Title:** N=2 gauge Theories and Quiver Representations

**Speaker:** Sergio Cecotti

**Date:** Thursday, October 3, 2013

**Time:** 2:30pm – 4:30pm

**Place:** Seminar Room 313, Simons Center

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**Abstract:** N=2 gauge theories are considered from the point of view of the representation theory of their (equivalence class) of quivers, or equivalently of basic (associative) algebra. The key observation is the strict relation between the Ringel theory of tame associative algebras and the N=2 SU(2) gauge theories. This can be generalized to an arbitrary gauge group, leading to a satisfactory algebraic theory of N=2 gauge models.