TRINO

Solomiya Mizyuk (SISSA)

Venue: Thu, Feb 22, 15:00. SISSA, Room 134 (first floor).

Title:  Virtual class on a Quot scheme of points on a threefold

Abstract: We construct a semi-perfect obstruction theory on the Quot scheme of points corresponding to a vector bundle on a smooth projective threefold. We get a virtual class in the Chow group in degree zero and define the higher rank Donaldson Thomas invariants. All related definitions will be recalled.

Michele Graffeo (SISSA)

Venue: Wed, Mar 13, 15h00. UniTS, MIGe, Seminar room (building H2bis via Valerio 12/1, third floor).

Title: Integrable systems and the Cremona-cubes group

Abstract: The standard Cremona transformation is a classical object in algebraic geometry. In a joint work with G. Gubbiotti (University of Milan), we studied the algebraic entropy and the invariants of birational maps of the projective 3-space defined as the composition of the standard Cremona transformation with some special projectivities. Precisely, we consider projectivities acting on 12 points in the Reye configuration. These kind of maps appear for instance as the Kahan–Hirota–Kimura discretisation of the Euler top. In my seminar I will explain how such results can be obtained using classical techniques from algebraic geometry. If time permits, I will discuss some higher dimensional generalisations of this construction (joint work with G. Gubbiotti and M. Weinreich (Harvard)). 

Anna Barbieri (Università di Verona)

Venue: Wed, Mar 20, 14h00 . SISSA, Dubrovin Lecture Room (136, first floor).

Title:  Moduli spaces of stability conditions and of quadratic differentials

Abstract: The space of Bridgeland stability conditions is a complex manifold attached to a triangulated category D, parametrizing some t-structures of the category. In some cases, when D is constructed from a Ginzburg algebra of a quiver, it is isomorphic to a moduli space of quadratic differentials on a Riemann surface. I will review this correspondence, which is due to Bridgeland-Smith in the simple zeroes case and was extended in [BMQS] to higher order zeroes, to motivate a tentative construction of a smooth compactification of the stability manifold. This is based on joint works with M.Moeller, Y.Qiu, and J.So.

Paolo Stellari (Università di Milano)

Venue: Mon, May 13, 16h00. SISSA, Dubrovin Lecture Room (136, first floor).

Title:  Deformations of stability conditions with applications to very general Hilbert schemes of points and abelian varieties

Abstract: The construction of stability conditions on the bounded derived category of coherent sheaves on smooth projective varieties is notoriously a difficult problem, especially when the canonical bundle

is trivial. In this talk, I will illustrate a new and very effective technique based on deformations.

A key ingredient is a general result about deformations of bounded t-structures (and with some additional and mild assumptions). Two remarkable applications are the construction of stability conditions for very general abelian varieties in any dimension and for irreducible holomorphic symplectic manifolds of Hilb^n-type, again in all possible dimensions. This is joint work with C. Li, E. Macrì, Alex Perry and X. Zhao.

Felix Thimm (University of Oslo)

Venue: Tue, May 14, 10h00. SISSA, Dubrovin Lecture Room (136, first floor).

Title:  The 3-fold K-theoretic DT/PT vertex correspondence

Abstract: Donaldson-Thomas (DT) and Pandharipande-Thomas (PT) invariants are two curve counting invariants for 3-folds. In the Calabi-Yau case, a correspondence between the numerical DT and PT invariants has been conjectured by Pandharipande and Thomas and proven by Bridgeland and Toda using wall-crossing. For equivariant K-theoretically refined invariants, the DT/PT correspondence reduces to a DT/PT correspondence of equivariant K-theoretic vertices. In this talk I will explain our proof of the equivariant K-theoretic DT/PT vertex correspondence using a K-theoretic version of Joyce's wall-crossing setup. An important technical tool is the construction of a symmetized pullback of a symmetric perfect obstruction theory on the orginial DT and PT moduli stacks to a symmetric almost perfect obstruction theory on auxiliary moduli stacks. This is joint work with Nick Kuhn and Henry Liu.

Lars Halle (Università di Bologna)

Venue: Tue, May 28, 15h00. SISSA, Dubrovin Lecture Room (131, first floor).

Title:  TBA

Abstract: TBA