讲座人简介：

Sibylle Schroll，德国科隆大学教授，代数表示论专家，主要研究同调代数、上同调理论，以及代数表示论和其他数学分支之间的联系，特别是最近在gentle代数的导出范畴及其几何模型方面做了多项重要工作。在Advances in Mathematics、Selecta Math. (N.S.)、Int. Math. Res. Not. IMRN、J. Lond. Math. Soc.、Math. Z.、Journal of Algebra等杂志发表论文40余篇。任Bulletin of the LMS的执行主编，Advances in Applied Mathematics、Quaestiones Mathematicae、Electronic Research Archive、Jahresbericht等杂志的编辑，也是Annales in Representation Theory (ART)的首任编辑之一。

讲座简介：

The Tamarkin-Tsygan calculus of an associative algebra is the comprehensive data ofits Hochschild homology and cohomology and their algebraic structures. In general, it isnext to impossible to obtain the comprehensive information of this calculus since alreadythe explicit calculation of the Hochschild homology and cohomology are of exceeding computational complexity. However, in certain cases, when there is much structural informationabout the algebras available, one might attempt such a calculation. The class of gentlealgebras constitutes such a case and in this talk, I will report on joint work with ChristianChaparro, Andrea Solotar and Mariano Suarez-Alvarez where we explicitly calculate thecomplete Tamarkin-Tsygan calculus for gentle algebras. For the purposes of the talk, wewill put a particular focus on the surface interpretation of the generators of the Hochschildcohomology. More precisely, gentle algebras are a class of monomial algebras which appearin many different settings such as cluster theory, N = 2 gauge theories and homologicalmirror symmetry of surfaces. In particular, in the context of the latter, there is a correspondence of the symplectic homology of the surface and the Hochschild cohomology of thegentle algebra. We will make this explicit by showing how the generators of the gradedcommutative algebra of the Hochschild cohomology of a gentle algebra can be seen in termsof the associated surface.