[Summer time:] UK, Portugal: 16:00; Spain, Italy, France, etc.: 17:00
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184. 24/08/2026 Alexander Zheglov (Lomonosov State University, Russia)
Title: Theory of normal forms of differential operators and some of its applications
Abstract: The theory of normal forms appeared in a series of my works with co‑authors as a convenient tool for studying quantum integrable systems (in a broad sense) — by this I mean rings of commuting operators of various natures. The normal forms of differential operators mentioned in the title are operators of a special type in a certain complete non‑commutative ring \hat{D}_n^{sym} (not the well‑known ring of formal pseudo‑differential operators!). They are obtained by conjugating the operators under study by an invertible operator (a generalised Schur operator), which is constructed from a chosen operator in the commutative ring. In my talk, I will give an overview of recent results obtained by myself and with co‑authors that follow from the theory of normal forms: an alternative classification of commutative rings of ordinary differential operators and the associated description of torsion‑free sheaves with zero cohomology on irreducible projective curves; a constructive one‑to‑one correspondence between solutions of the string equation and commuting ordinary differential operators; and the resulting proof of the Dixmier conjecture for the first Weyl algebra.
Future talks:
185. 31/08/2026 Shuai Hou (Jilin University, China)
186. 07/09/2026 Yannic Vargas (CUNEF University, Spain)
187. 14/09/2026 Mihalis Maliakas (National and Kapodistrian University of Athens, Greece)
188. 21/09/2026 Geoffrey Powell (University of Angers, France)
189. 28/09/2026 Frédéric Patras (Côte d'Azur University, France)
190. 05/10/2026 Silvia Properzi (Vrije Universiteit Brussel, Belgium)
191. 12/10/2026 István Heckenberger (Philipps University Marburg, Germany)
192. 19/10/2026 Simon Goodwin (University of Birmingham, UK)
193. 26/10/2026 Joost Vercruysse (Université Libre de Bruxelles, Belgium)
194. 02/11/2026 Diego Aranda-Orna (University of Oviedo, Spain)
195. 09/11/2026 Inna Entova-Aizenbud (Ben Gurion University of the Negev, Israel)
196. 16/11/2026 Anupam Singh (Indian Institute of Science Education and Research, India)
197. 23/11/2026 Sofiane Bouarroudj (New York University Abu Dhabi, United Arab Emirates)
198. 30/11/2026 Matevž Miščič (University of Ljubljana, Slovenia)
199. 07/12/2026 Ernesto Spinelli (Sapienza University of Rome, Italy)
200. 14/12/2026 Maria Matushko (Steklov Mathematical Institute of RAS, Russia)
Ivan Kaygorodov • Salvatore Siciliano • Mykola Khrypсhenko • Jobir Adashev