# Abstract Rui-Jie Yang

**Rui-Jie Yang** will speak on

** Decomposition Theorem for semisimple local systems via non-abelian Hodge theory**

In algebraic geometry, the decomposition theorem of Beilinson-Bernstein-Deligne-Gabber is one of the foundational results concerning the topology of algebraic maps over complex numbers, which relies on the theory of weights for varieties over finite fields. In 1996 Kashiwara conjectured that the decomposition theorem should hold for any semisimple holonomic D-modules, which was proved by Sabbah and T. Mochizuki in a series of long papers via the theory of polarizable twistor D-modules. In this talk, I will explain a simple and new proof for semisimple local systems, building on a topological approach of de Cataldo-Migliorini and we only need Simpson’s classical non-abelian Hodge theory as inputs. This is joint with C. Wei.