BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Simon Lentner (Universität Hamburg) DTSTART:20250618T090000Z DTEND:20250618T100000Z DTSTAMP:20260423T035630Z UID:EQuAL/42 DESCRIPTION:Title: P roving the Logarithmic Kazhdan-Lusztig Correspondence\nby Simon Lentne r (Universität Hamburg) as part of European Quantum Algebra Lectures (EQu AL)\n\n\nAbstract\nThe logarithmic Kazhdan-Lusztig correspondence by B. Fe igin and others is a conjectural equivalence between braided tensor catego ries of representations of quantum groups and of certain vertex algebras\, which are algebras with an analytic flavour that appear in quantum field theory. I will give a gentle introduction into the physics side and recall some previous result of mine that certain analytic operators called scree nings fulfill the relations of an associated Nichols algebra.\n\nIn arXiv: 2501.10735 I recently gave a proof of the conjectural category equivalence in quite general situations\, also including Nichols algebras beyond quan tum groups\, under the assumption that the vertex algebra side is analytic ally nice enough. The proof is based on joint work with T. Creutzig and M. Rupert\, in which we settled first small cases. The proof is almost compl etely algebraic and interesting in its own right\, the essential statement is: Every braided tensor category together with a big commutative algebra A\, such that the category of local A-modules is semisimple and the categ ory of A-modules contains no additional simple modules\, is equivalent to representations of a quantum group associated to a Nichols algebra\, which is determined by certain Ext1-groups. In a certain sense\, this is a cate gorical and braided version of the Andruskiewitsch-Schneider program\, and prominently uses important results in this area by I. Angiono and others. \n LOCATION:https://researchseminars.org/talk/EQuAL/42/ END:VEVENT END:VCALENDAR