Monday, 17 Nov 2025:
1. Sarjick Bakshi (Center for Excellence in Basic Sciences (UM-DAE CEBS), Mumbai, India)
Title: g-vectors of Plücker Coordinates
Cluster algebras, introduced by Fomin and Zelevinsky, are commutative algebras characterised by intricate combinatorial structures and have applications across geometry and Lie theory, including examples such as Grassmannians, double Bruhat cells, and open Richardson varieties. In this talk, we will explore the Frobenius categorification of cluster algebras with coefficients. Using the additive categorification framework developed by Jensen--King--Su, we will explicitly determine the g-vectors of Plücker coordinates for the Grassmannian variety with respect to the triangular initial seed. This talk is based on a joint work with Bernhard Keller https://arxiv.org/pdf/2410.01037.
2. Soumyadip Sarkar (Institute of Mathematical Sciences, Chennai, India)
Title: Crystal structure on the polynomial induction
We will talk about the restriction problem in algebraic combinatorics. The permutation group Sn can be naturally embedded inside GLn(C). Now we can take a irreducible polynomial representation of degree d of GLn(C) and restrict it to Sn and one can ask for a positive combinatorial formula for the restriction coefficients. It is an old problem in algebraic combinatorics. We will discuss the history and recent developments towards solving this problem.
3. Krishna Teja Ganduri (Indian Statistical Institute, Bengaluru, India)
Title: WEYL CHARACTER TYPE FORMULAS
Abstract. Fix g = g(A) any complex Borcherds–Kac–Moody (BKM) Lie algebra for a BKM Cartan matrix A, and a Cartan subalgebra h ⊂ g. Let L(λ) be the simple highest weight g-module with top weight λ ∈ h∗. This talk develops Weyl character type formulas for non-integrable quotients of Verma modules in the below two settings; these quotients yield weight-sets of all highest weight g-modules.
1) For higher order Verma modules, which we introduced and which subsume and generalize integrable L(λ) and parabolic Vermas. These formulas use certain semigroups inside Weyl groups in some cases in finite type, and follow from BGG type resolutions.
2) For seemingly unexplored “integrable” simple L(λ) with λ ∈ P± := μ ∈ h∗μ pairing with i-th simple root yields a Z≤0-multiple of |Aii|2, for rank 2 BKM g. P±-weights reveal all Chevalley–Serre relations in L(λ) ∀ λ ∈ h∗. Formulas in setting 1) yield characters of all quotients of the Verma module with top weight ρ ∈ P± (which is non dominant integral), in every negative An type cases (Aii = −2, Ai,i±1 = −1). Based on joint works with A. Khare and S. Pal ref: arXiv:2203.05515v2 and arXiv:2505.08102.
Tuesday, 18 Nov 2025:
4. Shushma Rani (Indian Institute of Science, Bengaluru, India)
Title: Weyl modules and CV modules in Lie superalgebras $\mathfrak{sl}(1|2)[t]$
In this talk, I will present the graded character of the Weyl modules and give its applications. We have constructed a short exact sequence of the CV modules in case of $\mathfrak{sl}(1|2)[t]$ and proved that these CV modules are isomorphic to the fusion product if generalised Kac modules.
5. Kaveh Mousavand (Okinawa Institute of Science and Technology, Onna, Japan)
Title: Brick-directed algebras and their applications
As a modern analogue and generalization of the representation-directed algebras, we introduce the notion of brick-directed algebras. We study some main properties of these algebras and show how this new family gives a vast generalization of the classical notion and also includes various types of algebras which are of infinite representation type. A key tool in our study is the notion of brick-splitting torsion pairs, which itself is a novel generalization of splitting torsion pairs. Through these generalizations, we obtain several interesting results on the modern and classical families of algebras. If time permits, we also discuss how brick-directed algebras give a full classification of those algebras whose lattice of torsion classes is trim. This is based on joint work with Sota Asai, Osamu Iyama, and Charles Paquette.
6. Chaithra P (Indian Institute of Science, Bengaluru, India)
Title: Marked chromatic polynomials and root multiplicities of BKM Lie superalgebras
We investigate the root multiplicities of Borcherds–Kac–Moody (BKM) Lie superalgebras through their denominator identities, deriving explicit combinatorial formulas in terms of graph invariants associated with marked (quasi) Dynkin diagrams. A central notion in our approach is that of marked multi-colorings and their associated polynomials, which generalize chromatic polynomials and provide an effective framework for computing root multiplicities.
As part of this study, we introduce partially commutative Lie superalgebras (PCLSAs) as a tool for analyzing certain roots of BKM Lie superalgebras. We present a direct combinatorial proof of their denominator identity using ideas from Viennot’s heap theory, and we also characterize the roots of PCLSAs. This talk is based on joint work with Deniz Kus and R. Venkatesh https://arxiv.org/pdf/2503.11230.
Wednesday, 19 Nov 2025:
7. Arghya Sadhukhan (National University of Singapore, Singapore)
Title: Geometry of affine Deligne-Lusztig varieties corresponding to the maximal Newton stratum
A key approach to studying the special fiber of Shimura varieties involves the Newton stratification, indexed by the set B(G,\mu) of \sigma-conjugacy classes in the loop group. In many cases, the minimal stratum - generalizing the supersingular locus in Siegel modular variety - can be described explicitly as a union of classical Deligne–Lusztig varieties, with significant applications to the Kudla–Rapoport program, the Arithmetic Fundamental Lemma, and instances of the Tate conjecture. In this talk, I focus on the opposite extreme: the maximal element of B(G,\mu). I will present recent progress toward determining the dimension of the associated affine Deligne–Lusztig variety - which serves as a group theoretic model of the associated Newton stratum - and describe the geometry of its top-dimensional irreducible components, which include natural iterated fibrations over classical Deligne–Lusztig varieties.
8. Himanshi Khurana (Harish-Chandra Research Institute, Allahabad, India)
Title: Twisted Jacquet modules of a cuspidal representation of GLn(Fq)
Let G=GLn(Fq) be the general linear group over a finite field. The Jacquet module is an important tool for understanding the structure of representations of G. For a cuspidal representation of G, the Jacquet module is always trivial, which motivates the study of its twisted versions. In this talk, we will discuss recent results about the structure of twisted Jacquet modules for cuspidal representations of G. This is based on joint work with Kumar Balasubramanian and Krishna Kaipa.
9. Velmurugan S (Institute of Mathematical Sciences, Chennai, India)
Title: Eigenvalues of elements in double cover of symmetric and alternating groups.
For any irreducible representation $(\rho,V)$ and an element g of $G$, we show the complete list of eigenvalues of the operator $\rho(g)$. We verify a conjecture of Giannelli and Navarro for the double cover of symmetric and alternating groupswhich is as follows: Let $\chi$ be an irreducible character of $G$ with $\chi(1)$ divisible by a prime p. Suppose that $Res^G_P \chi$ contains a linear character of P, where P is a Sylow-p- subgroup of G. Then $Res^G_P \chi$ contains at least $p$ different linear characters of $P$. This is a work in progress with Amritanshu Prasad and Alexey Staroletov.
Thursday, 20 Nov 2025:
10. Sadhanandh Vishwanath (Chennai Mathematical Institute, Chennai, India)
Title: q-FI and q-rook categories
Representations of the category FI, comprising of finite sets and injections, has garnered significant attention for its role in studying representation stability and polynomial growth of S_n representations. Also, this framework allows us to treat compatible families of symmetric group representations as a unified object. Motivated by this, we aim to develop a q-analogue, the q-FI category, in which the symmetric groups are replaced by the Iwahori–Hecke algebras of type A. We defined q-FI as a subcategory of the q-rook category, which we builded from L.Solomon’s works on Iwahori-Hecke algebras of rook monoids.
We have given a presentation and proved basis theorems for these categories, which can be interpreted diagrammatically as 'local' relations. Following Ben Elias work on Hecke type categories, we showed q-FI category has a (non-obvious) diagrammatic monoidal structure. By contrast a key relation for the q-rook category seems to be inherently nonlocal. The representation category of q-rook category is a lowest weight category, in the sense of S.Sam and A.Snowden and there is also a connection to recent work of R. Dipper and T. Geetha on a Schur-Weyl duality between Hecke algebras and q-partition algebras. In this talk, I will define q- FI and q-rook categories using their diagrammatic presentations and show q-rook category is a lowest weight category.
11. Souvik Pal (Indian Institute of Science, Bengaluru, India)
Title: Representations of Hamiltonian vector fields on a torus
In this talk, we recall the notion of Shen–Larsson modules over the Hamiltonian Lie algebra, also known as the Lie algebra of Hamiltonian vector fields on a torus and provide necessary and sufficient conditions for the irreducibility of these modules. If time permits, we shall then describe the Jordan-Hölder series of the reducible ones, which we call exceptional modules.