A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes

Pantev, Toen, Vaqui\'e and Vezzosi arXiv:1111.3209 defined $k$-shifted symplectic derived schemes and stacks ${\bf X}$ for $k\in\mathbb Z$, and Lagrangians ${\bf f}:{\bf L}\to{\bf X}$ in them. They have important applications to Calabi-Yau geometry and quantization. Bussi, Brav and Joyce arXiv:1305.6302 proved a 'Darboux Theorem' giving explicit Zariski or \'etale local models for $k$-shifted symplectic derived schemes ${\bf X}$ for $k<0$ presenting them as twisted shifted cotangent bundles. We prove a 'Lagrangian Neighbourhood Theorem' giving explicit Zariski or etale local models for Lagrangians ${\bf f}:{\bf L}\to{\bf X}$ in $k$-shifted symplectic derived schemes ${\bf X}$ for $k<0$, relative to the Bussi-Brav-Joyce 'Darboux form' local models for ${\bf X}$. That is, locally such Lagrangians can be presented as twisted shifted conormal bundles. We also give a partial result when $k=0$. We expect our results will have future applications to $k$-shifted Poisson geometry (see arXiv:1506.03699), to defining 'Fukaya categories' of complex or algebraic symplectic manifolds, and to categorifying Donaldson-Thomas theory of Calabi-Yau 3-folds and 'Cohomological Hall algebras'.Comment: 68 page

"El Padrí" de la Costa Brava

"El Padrí" de la Costa Brav

Brav Karl

For voice and piano. Based on the play by Holger Drachmann. Six numbers including Rytter-Visen , Maj-Visen , Zigeuner-Visen , Frier-Visen , Langfinger-Visen , and Rhinskvin. Plate number 12202.https://scholarexchange.furman.edu/krohn-album3/1006/thumbnail.jp

A Message from Jill Gonzales-Bravo, ATE-K President

A message from ATE-K President, Dr. Jill Gonzales-Brav

Braid groups and Kleinian singularities

We establish faithfulness of braid group actions generated by twists along an ADE configuration of $2$-spherical objects in a derived category. Our major tool is the Garside structure on braid groups of type ADE. This faithfulness result provides the missing ingredient in Bridgeland's description of a space of stability conditions associated to a Kleinian singularity.Comment: Section 4 from versions 1 and 2 has been deleted due to an error in the proof of Theorem 2. Renamed the paper and rewrote the other sections to reflect this chang