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141. 13/10/2025 Ilja Gogić (University of Zagreb, Croatia)
Title: Spectrum-shrinking maps and nonlinear preservers on matrix domains
Abstract: The celebrated Kaplansky–Aupetit conjecture asks whether every surjective linear map between unital semisimple Banach algebras that shrinks the spectrum must be a Jordan homomorphism. While the conjecture has been resolved in specific settings (most notably for von Neumann algebras by Aupetit and for algebras of bounded linear operators on Banach spaces by Sourour), it remains widely open, even for C*-algebras. In contrast, spectrum-preserving maps are often more accessible, and a natural question is whether results in that setting can be extended to the spectrum-shrinking case. However, existing results indicate that such generalizations are typically far more delicate. Motivated by this, the talk investigates continuous spectrum-shrinking maps from various subsets Xₙ of the complex matrix algebra Mₙ with values in another matrix algebra Mₘ. The classes of domains Xₙ under consideration include structural matrix algebras (i.e. subalgebras of Mₙ containing all diagonal matrices), the sets of normal and singular matrices, and matrix Lie groups such as GL(n), SL(n), and U(n). Our first objective is to determine when such spectrum-shrinking maps automatically preserve the spectrum. Building on this, and Šemrl’s influential nonlinear characterization of Jordan automorphisms of Mₙ (when n ≥ 3) as continuous maps preserving both spectrum and commutativity, our second objective is to establish an analogous nonlinear preserver theorem for maps Xₙ → Mₙ. This is based on joint work with Alexandru Chirvasitu (University at Buffalo) and Mateo Tomašević (University of Zagreb).
Future talks:
142. 20/10/2025 Victor Roca i Lucio (Paris Cité University, France)
143. 27/10/2025 Michiel Smet (Ghent University, Belgium)
144. 03/11/2025 Xiaomin Tang (Heilongjiang University, China)
145. 10/11/2025 Ginevra Giordani (University of L'Aquila, Italy)
146. 17/11/2025 Yulia Zaitseva (HSE University, Russia)
147. 24/11/2025 Gerardo Martín Escolano (University of Granada, Spain)
148. 01/12/2025 Vicent Pérez Calabuig (University of Valencia, Spain)
149. 08/12/2025 Azamat Saydaliyev (Institute of Mathematics, Uzbekistan)
150. 15/12/2025 Cristina Draper (University of Málaga, Spain)
----. 22/12/2025 XX Non-Associative Day in Online´25
151. 05/01/2026 Dimas José Gonçalves (Federal University of São Carlos, Brazil)
152. 12/01/2026 Ramón González Rodríguez (University of Vigo, Spain)
153. 19/01/2026 Dimitar Grantcharov (University of Texas at Arlington, USA)
154. 26/01/2026 Bernardo Leite da Cunha (University of Santiago de Compostela, Spain)
155. 02/02/2026 Zahra Nazemian (University of Graz, Austria)
156. 09/02/2026 Hans Cuypers (Eindhoven University of Technology, Netherlands)
157. 16/02/2026 Davide Ferri (University of Torino, Italy)
158. 23/02/2026 Saikat Goswami (Institute for Advancing Intelligence, India)
159. 02/03/2026 Solomon Vishkautsan (Tel-Hai Academic College, Israel)
160. 09/03/2026 Lucia Bagnoli (National Institute for Pure and Applied Mathematics, Brazil)
161. 16/03/2026 Carsten Dietzel (University of Caen Normandy, France)
162. 23/03/2026 István Heckenberger (Philipps University Marburg, Germany)
163. 30/03/2026 Willian Franca (Federal University of Juiz de Fora, Brazil)
164. 06/04/2026 Rong Tang (Jilin University, China)
165. 13/04/2026 Maria Ferrara (University of Campania Luigi Vanvitelli, Italy)
166. 20/04/2026 Michael Lau (Laval University, Canada)
167. 27/04/2026 Abdenacer Makhlouf (University of Haute Alsace, France)
Ivan Kaygorodov • Salvatore Siciliano • Mykola Khrypсhenko • Jobir Adashev