Recent work of Galkin and Shinder suggests that if a cubic 4-fold X is rational then the variety F of lines on X is birational to Hilb(K3). I’ll compare this to Hassett’s notion of X having an associated K3 surface, which turns out to be equivalent to saying that F is birational to a moduli space of sheaves on a K3 surface. The key technical tool is the Mukai lattice that Richard Thomas and I i...

In this paper, we show how the Weil descent attack of Gaudry, Hess and Smart can be adapted to work for some hyperelliptic curves defined over fields of odd characteristic. This attack applies to a family of hyperelliptic and superelliptic curves over quadratic field extensions, as well as two families of hyperelliptic curves defined over cubic extensions. We also show that those are the only f...

We find out for which t shells of selfdual lattices and of theirs shadows are spherical t-designs. The method uses theta series of lattices, which are modular forms. We analyse fully cubic and Witt lattices, as well as all selfdual lattices of rank at most 24.

In this paper, we will study the existence of periodic solutions for the delay evolution integrodifferential equations in a general Banach space with unbounded operator. @ 2004 Elsevier Ltd. All rights reserved.

Article history: Received 19 August 2014 Received in revised form 19 September 2014 Accepted 29 September 2014 Available online 22 October 2014

We prove the conjectural relationship recently proposed in [16] between certain special cubic Hodge integrals of the Gopakumar–Mariño–Vafa type [27, 36] and GUE correlators.