• 21.04.26: Keyu Wang (University of Vienna)

Title:  Representations of Langlands dual algebras

Abstract: Two simple Lie algebras are called Langlands dual if their Cartan matrices are transposes of each other, as they appear as a pair in the Langlands correspondence. We are interested in the relationship between the representation theories of Langlands dual Lie algebras. The first part of the talk will focus on classical Lie algebras: we will recall their character theory and introduce the connection between Langlands dual algebras. In the second part, we will turn to quantum affine algebras, introduce the Frenkel–Hernandez conjecture, and briefly summarize the branching rule proved in joint work with Jingmin Guo and Jian-Rong Li.

• 28.04.26: Azzura Ciliberti (RUB)

Title:  A multiplication formula for cluster characters in gentle algebras

Abstract: Gentle algebras, introduced by Assem and Skowroński, are a well-loved class of algebras. They are string algebras, so their module categories are combinatorially described in terms of strings and bands, they are tiling algebras associated with dissections of surfaces, and they have many other remarkable properties. Furthermore, Jacobian algebras arising from triangulations of unpunctured marked surfaces are gentle. In the talk, I will present a multiplication formula for cluster characters induced by generating extensions in a gentle algebra A. This formula generalizes a previous result of Cerulli Irelli, Esposito, Franzen, Reineke. Moreover, in the case where A comes from a triangulation T, it provides a representation-theoretic interpretation of the exchange relations in the cluster algebra with principal coefficients in T.

• 05.05.26: details via email 

• 12.05.26: Narasimha Chary (IIT Kanpur)

Title:  The Gromov Width of Generalized Bott-Samelson varieties

Abstract:  The Gromov width of a symplectic manifold is a fundamental symplectic invariant that measures the size of the largest standard symplectic ball that can be symplectically embedded into the manifold. In this talk, we will first discuss known results on the Gromov width for specific classes of symplectic manifolds and methods to estimate it. Finally, we will focus on smooth generalized Bott-Samelson varieties, which provide a natural generalization of both Bott-Samelson varieties and flag varieties. This talk is based on work with Stéphanie Cupit-Foutou and with Yogendra Singh. 

• 19.05.26: Fang Yang (MPIM Bonn)

Title:  Correspondences between Quantum Grothendieck Rings and Derived Hall Algebras of Type A

Abstract: Hernandez and Leclerc established an isomorphism between quantum Grothendieck rings and derived Hall algebras associated with arbitrary Dynkin quivers. Under this correspondence, the bar involution applied to the q,t-character of a standard module in the quantum Grothendieck ring can be expressed as a mathbb{Z}[t,t^{-1}]-linear combination of q,t-characters of standard modules. In the case of type A quivers, we show that these coefficients are in fact polynomials in (t-t^{-1}) with coefficients in \mathbb{Z}. Building on this result, we aim to prove that the corresponding analogues of Kazhdan–Lusztig polynomials reduce to powers of (-t^{-1}). This is joint work with Alessandro Contu.

• 02.06.26: Sean Monahan (TUM)

Title:  Horospherical varieties with quotient singularities

Abstract: Horospherical varieties are a vast generalization of both toric and flag varieties which have a hands-on combinatorial description using so-called "coloured fans", generalizing the correspondence between toric varieties and polyhedral fans. I will briefly introduce these objects and highlight a combinatorial characterization for when horospherical varieties have quotient singularities.

• 09.06.26: details via email 

• 16.06.26: Mrigendra Kushwaha (University of Delhi)

Title:  

Abstract:

• 23.06.26: Martina Lanini (Università di Roma Tor Vergata)

Title:  

Abstract:

• 30.06.26: details via email 

• 07.07.26: details via email