Zhaoting WEI (Indiana)
A differential graded category with geometric nature
I will talk about the "cohesive module", which is introduced by Jonathan Block, of a curved differential graded algebra A. In fact it is a bi-complex of graded modules of A.
The significance of cohesive module is that on a complex manifold X, it gives a DG enhancement of the bounded derived category of coherent sheaves on X. Conceptually the cohesive module gives a "de Rham-theoretic" construction of higher categories.
If time allows, I will also describe some of the applications of cohesive modules besides complex manifolds. Such examples include
-Higher Riemann-Hilbert correspondence
-Formal neighbourhood of closed embedding and so on.