• 28.10.25: details via email 

• 04.11.25: R. Venkatesh (IISc Bangalore)

Title:  Extending Dynkin’s classification beyond the finite case

Abstract: In his seminal 1952 work, Dynkin classified the semisimple subalgebras of finite-dimensional semisimple Lie algebras. To accomplish this, he introduced the notions of regular subalgebras and π-systems. A regular subalgebra is, by definition, one generated by root vectors. In this talk, I will focus on regular subalgebras of Kac–Moody algebras that are generated by root vectors corresponding to symmetric sets of real roots, and I will discuss how the classification of such subalgebras can be obtained beyond the finite-dimensional case.

• 11.11.25: details via email 

• 18.11.25: Ulrich Bauer (TUM)

Title:  Indecomposables in multiparameter persistence

Abstract: I will discuss various aspects of multi-parameter persistence related to representation theory and the decomposition into indecomposable summands, based on joint work with Magnus Botnan, Steffen Oppermann, Johan Steen, Luis Scoccola, Cameron Gusel, and Benedikt Fluhr. A classification of indecomposables is infeasible; the category of two-parameter persistence modules has wild representation type. We show that this is still the case if the structure maps in one parameter direction are epimorphisms, a property that is commonly satisfied by degree 0 persistent homology and related to filtered hierarchical clustering. Furthermore, we show that indecomposable persistence modules are dense in the interleaving distance, and that being indecomposable is a generic property of persistence modules. To this end, we establish suitable metric spaces of persistence modules that are complete under the interleaving distance and admit essentially unique decompositions. On the other hand, the two-parameter persistence modules arising from interleaved sets (relative interleaved set cohomology) have a very well-behaved structure that is encoded as a complete invariant in the extended persistence diagram. This perspective reveals some important but largely overlooked fundamental insights about persistent homology; in particular, it highlights the important fact that certain aspects of persistent homology are best captured at the level of chain complexes, in the derived category.

• 02.12.25: Lewis Topley (University of Bath)

Title:  Quantizations of nilpotent orbit closures in positive characteristics

Abstract: A quantization of a Poisson algebra is a noncommutative filtered algebra which recovers the Poisson algebra by the associated graded construction, which we call "taking the semiclassical limit". The quantization problem, which has its roots in the earliest formulation of quantum mechanics, asks us to invert this procedure. To be more precise, given a graded Poisson algebra, can we find/classify quantizations? In this talk I will consider quantizations of the algebras of regular functions over (normalisations of) closures of orbits in Lie algebras of reductive groups over fields of positive characteristic p > 0. It has long been expected that these quantizations should be related to a special class of representations of the reduced enveloping algebra: the so-called "minimal modules". I will explain that for gl_n a special class of minimal modules correspond bijectively to the quantizations of an orbit closure. One of our key innovations is a construction of quantizations as induced modules from a certain infinitesimal thickening of the scheme theoretic stabiliser of the p-character of the annihilator of a minimal module. This is a joint work with Matt Westaway (Bath) and Filippo Ambrosio (Jena).

• 09.12.25: details via email 

• 16.12.25: Jianrong Li (University of Vienna)

Title:  Boundary q-characters of finite-dimensional representations of quantum affine symmetric pairs

Abstract: Frenkel and Reshetikhin introduced q-characters for finite-dimensional representations of quantum affine algebras, providing a fundamental tool in their representation theory. Together with Tomasz Przezdziecki, we defined boundary q-characters for finite dimensional representations of quantum affine symmetric pairs of split types. In this talk, I will present a new joint work Tomasz Przezdziecki on evaluation modules for split quantum affine symmetric pairs. By computing the action of generators in Lu and Wang’s Drinfeld-type presentation on Gelfand–Tsetlin bases, we determine the spectrum of a large commutative subalgebra arising from this presentation. This leads to an explicit formula for boundary analogues of q-characters, which we interpret combinatorially in terms of semistandard Young tableaux. Our results show that boundary q-characters share familiar features with ordinary q-characters, such as a version of the highest weight property, while also exhibiting new phenomena, including an additional symmetry. 

• 13.01.26: Felix Röhrich (RWTH Aachen)

Title:  Imaginary vectors, Lusztig cones and the quantum Frobenius morphism

Abstract: In this talk, we present a study of the duals of Leclerc's imaginary vectors from the perspective of Lusztig's tight monomial cone. Previously, they were used by Kashiwara and Saito to show that there are elements in the canonical basis whose singular support is not irreducible, or by Baumann to show that the canonical basis is not fully compatible with the quantum Frobenius morphism and its splitting. However, in both cases quiver theoretic methods were used, limiting the results to the simply-laced case. Our approach works type-independently; as an application, we explain how Baumann's results can be extended to all finite types.

• 20.01.26:  Andrei Negut (ÉPFL)

Title:  Extremal monomials of q-characters

Abstract:  We prove a conjecture of Frenkel-Hernandez, which states that the monomials which appear in q-characters of finite-dimensional simple modules of quantum affine algebras are bounded by the orbit of the highest monomial under Chari's braid group action. Our proof is geometric, and uses certain quiver varieties associated to semisimple Lie algebras.

• 27.01.26: details via email