He visited the Department of Mathematics, University of Memphis from 5th Jan 2015 to 5th March 2015. During this period he gave a Colloquium talk entitled 'Almost isometric ideals in Banach spaces'. He also gave a talk in the Analysis seminar, entitled,'On a theorem of Shintani and Ando'. He had regular research interactions with Professor F Botelho of the Department of Mathematics. They collaborated on the algebraic reflexivity problem for operator ideals and obtained some positive results.
His visit was conducted under the subject “Profinite groups: endomorphisms, automorphisms, profinite completions and applications” and was partially supported by a grant from the Simons Foundation. Prof. David Moldavanskii was his main host-contact.
During this period, the main activities consisted of:
- A presentation of the research problems: the aim here was to introduce the subject and create contact and interaction with Lecturers, M. Sc. and Ph. D. students.
Listing research in progress, papers published or in preprint form
Below is the description of a result that we have obtained, which is part of a work in progress.
"During my stay I had regular interactions with Professor Juan J. Font on some preserving problems in the context of function spaces. In fact, preserving problems concern the question of determining or describing the general form of all trans- formations of a given structure which preserve something in connection with the underlying structure such as norm, spectrum, spectral-radius, etc. For instance, we can point out the famous Banach-Stone theorem which characterizes linear isome- tries between C(X)-spaces as weighted composition operators.
"It is a great opportunity for me to receive a travel grant from International Mathematical Union-Simons Foundation to visit Professor Wilhelm Winter at University of Muenster, Germany from May 16, 2015 to July 16, 2015. The main purpose of my visit is to study connections between dynamical systems and the classification program of C*-algebras via the Focus Programme on C*-algebras at University of Muenster.
I participated in the weekly seminar organized by the group of Professor Wilhelm Winter.
During his visit of University of Santiago de Compostela Prof. Omirov obtained - jointly with Prof. Manuel Ladrasome- general results on the second group of cohomology of semisimple Leibniz algebras. These results were designed in the form of a manuscript which is added in website: arxiv.org. Moreover, he continue the study of irreducible components of the variety of solvable Leibniz algerbas. After obtaining the final planed results on this direction Prof. Omirov is planning to write a paper.
I started my project by studying about two combinatorial concepts: Hilbert Depth and Hilbert Regularity.