Ali Baklouti

LAMHA Closing Seminar 2024-2025

Pr. Hideyuki Ishi & Pr. Marcello Lucia

Name :

Pr. Hideyuki Ishi & Pr. Marcello Lucia

Title :

Pr. Hideyuki Ishi: On unitary representations of almost abelian exponential Lie groups.
Pr. Marcello Lucia: The class of second fundamental forms arising from minimal immersions in space forms.

Position :

Pr. Hideyuki Ishi : Graduate School of Mathematics, Nagoya University
Pr. Marcello Lucia : College of Staten Island, New York

Date :

June 03, 2025

Abstract

Pr. Hideyuki Ishi
Abstract: A Lie group is said to be almost abelian if it has a codimension-one normal commutative subgroup. An almost abelian Lie group is a solvable Lie group with rather simple structure, whereas this class contains non-type I groups such as the Mautner group. We consider the case where an almost abelian group G is exponential solvable. Then we can describe all the irreducible unitary representations of G via the Mackey machine. We shall discuss a criterion for the triviality of the kernel of the infinitesimal representation of a generic irreducible unitary representation of G.

Pr. Marcello Lucia

Abstract: The second fundamental form that may arise by considering minimal immersions of a fixed surface in a space form is subjected to various analytical constraints. Among those one, a central role is played by the Gauss-Codazzi equations, for which we will present several results.