Regularity in one hypercomplex variable

Abstract: Since the 1930s, several function theories have been introduced over the algebra of quaternions and other alternative algebras. The aim of such constructions is to recover in higher dimensions the refined tools available in the theory of holomorphic functions of one complex variable. The peculiar properties of the higher-dimensional algebras considered are reflected in the different theories introduced.

A relatively recent breakthrough was the introduction of the class of slice regular functions of one quaternionic variable by Gentili and Struppa in 2006. This study, generalized to alternative $*$-algebras by Ghiloni and Perotti in 2011, has rapidly developed into a full-fledged theory.

The talk will overview the general problem of function theory in one hypercomplex variable, the main features of the theory of slice regular functions and its applications to open problems from other areas of mathematics.

complex variablesrings and algebras

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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