Venue: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
- Samuele Mongodi (Politecnico di Milano)
In 2010, Ghiloni and Perotti showed how a slice-regular function f from a real alternative algebra A to itself is induced, in a suitable sense, by a holomorphic function F from the complex numbers to the complexification of A; however, there is no evident "holomorphic" link between the values of f and the values of F.
I want to show, in the particular case where A is the algebra of quaternions H, how the set of values of F which induce a zero of f is actually a complex subspace of the complexification of H and how a number of properties of slice-regular functions can be therefore deduced from the classical properties of holomorphic functions.
Moreover, this approach gives an identification of the set of imaginary units of H with a complex submanifold of a (complex) grassmannian, or, in other words, how we obtain a natural complex structure on such set which is compatible with slice-regularity; this point of view is linked to the work of Gentili, Salamon, Stoppato on the twistorial lift of a slice-regular function.
If time permits, I'll hint also to the general approach for the case of an associative algebra.
Contact person: Sonia Mazzucchi
The speaker is guest of the Research in Pairs program