The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on **June 13****, 20****23** at **1****:00 pm (UTC+3) ** in Room **478** of IMI.

A talk on:

## Functions holomorphic over finite-dimensional complex commutative algebras

** **will be delivered by **Marin Genov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences.**

Everybody is invited.

**Abstract. **Every morphism 𝜑:𝐴 →𝐵 in the category of finite-dimensional complex commutative associative unital (Banach) algebras gives rise to a structure sheaf of functions of a single 𝐴-variable and taking values in 𝐵 and whose differential respects the 𝐴-module structure of 𝐵. Even though these are holomorphic mappings of several complex variables, it turns out they also share many features of the theory of holomorphic functions of a single complex variable. At the same time this also enables the construction of relative complex analysis and relative (on the level of coefficients and in the sense of Grothendieck) complex-analytic geometry. In this talk I will discuss some basic aspects and questions of the local analytic theory.