## Artigos

### Isomorphisms of moduli spaces

We give infinitely many new isomorphisms between moduli spaces of bundles on local surfaces and on local Calabi–Yau threefolds. We also prove a local version of the Atiyah–Jones conjecture.

Autores:B. Callander, C. C. Amilburu, E. Gasparim, S. Barmeier

### Quantum Sheaf Cohomology, a Précis

We present a brief introduction to quantum sheaf cohomology, a generalization of quantum cohomology based on the physics of the (0,2) nonlinear sigma model.

Autor:J. Guffin

### Grothendieck Categories and their Deformations with an Application to Schemes

After presenting Grothendieck abelian categories as linear sites following [9], we present their basic deformation theory as developed in [14] and [10]. We apply the theory to certain categories of quasi-coherent modules over Z-algebras, which can be considered as non-commutative projective schemes. The cohomological conditions we require constitute an improvement upon [5].

Autor:W. Lowen

### Integrable systems from intermediate Jacobians of 5-folds

Given a cubic 4-fold Y, we provide an easy Hodge-theoretic proof of the following result of Iliev–Manivel: the relative intermediate Jacobian of the universal family of cubic 5-folds Z extending Y is a Lagrangian fibration.

Autor:D. Markushevich

### Real Determinant Line Bundles

This article is an expanded version of the talk given by Ch. O. at the Second Latin Congress on ”Symmetries in Geometry and Physics” in Curitiba, Brazil in December 2010. In this version we explain the topological and gauge-theoretical aspects of our paper” Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces” [15].

Autores:A. Teleman, C. Okonek

### Landau-Ginzburg Models, D-Branes and Mirror Symmetry

This paper is an introduction to D-branes in Landau-Ginzburg models and Homological Mirror Symmetry. The paper is based on a series of lectures which were given on Second Latin Congress on Symmetries in Geometry and Physics that took place at the Federal University of Paran ́a, Brazil in December 2010.

Autor:D. Orlov

### B-field transformations of Poisson grupoids

This is a survey devoted to the study of B-field transformations of multiplicative Poisson bivectors on a Lie groupoid G. We are concerned with B-fields given by multiplicative closed 2-forms on G. We extend the results in [5] by viewing Poisson groupoids and their B-field symmetries as special instances of multiplicative Dirac structures [24]. We also describe such symmetries infinitesimally.

Autor:C. Ortiz

### On the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds

In these notes we will provide a set of techniques which can help one to understand the proof of the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds. Precise definitions of multi-differential operators and polyderivations on an algebra are given, allowing to work on these concepts, when the algebra is an algebra of functions on a differentiable manifold, in a coordinate free description. Also, we will construct a cup product on polyderivations which corresponds on (Hochschild) cohomology to the wedge product on multivector fields. At the end, a proof of the above mentioned theorem will be given.

Autor:L. H. P. Pêgas

### “Parallel” Transport-Revisited

Parallel transport in a fibre bundle with respect to smooth paths in the base space B have recently been extended to representations of the smooth singular simplicial set Sing smooth(B). Inspired by these extensions, I revisit the development of a notion of ‘parallel’ transport in the topological setting of fibrations with the homotopy lifting property and then extend it to representations of Sing (B) on such fibrations. Closely related is the notion of (strong or ∞) homotopy action, which has variants under a variety of names.

Autor:J. Stasheff