--- robots: noindex, nofollow --- # Lodha conference 16-20th of November 2026 All the talks in the Harish Chandra seminar room. Breakfast is served at 9:30 **Monday 16 Nov** 10:00-11:00 Indranil Biswas: Homogeneous vector bundles on the upper-half plane 11:00-11:30 Tea 11:30-12:30 Ignacio Vergara: The Dixmier problem and its recent solution 12:30-15:00 Lunch 15:00-16:00 Prahlad Vaidyanathan: Values of Rokhlin Dimension for Integer Actions 16:00-16:30 Tea 16:30-17:30 Ishan Patri **Tuesday 17 Nov** 10:00-11:00 Penelope Azuelos: Virtually abelian subgroups of hierarchically hyperbolic groups 11:00-11:30 Tea 11:30-12:30 Partha Sarathi Ghosh: Stability of the weak Haagerup property under graph products 12:30-15:00 Lunch 15:00-16:00 Tattwamasi Amrutan: Invariant Random Subgroups of C*-simple groups 16:00-16:30 Tea 16:30-17:30 Lizzy Teryoshin: Groups with the fixed-point property **Wednesday 18 Nov** 10:00-11:00 Forrest Glebe 11:00-11:30 Tea 11:30-12:30 Mahesh Krishna: Group-Frames for Banach Spaces 12:30-15:00 Lunch *Afternoon free* **Thursday 19 Nov** 10:00-11:00 Soumyashant Nayat 11:00-11:30 Tea 11:30-12:30 Bratati Som: Conjugacy problem for Dehn twists of free products of free abelian groups 12:30-15:00 Lunch 15:00-16:00 Damian Osajda 16:00-16:30 Tea 16:30-17:30 David Gao 18:30 CONFERENCE DINNER (in our cafeteria) **Friday 20 Nov** 10:00-11:00 Ben Hayes 11:00-11:30 Tea 11:30-12:30 Radhika Gupta: Finite index rigidity for free-by-cyclic groups 12:30-15:00 Lunch 15:00-16:00 Aareyan Manzoor 16:00-16:30 Tea 16:30-17:30 Darius Alizadeh End --- Titles and abstracts (this is a pretty broad spectrum conference, please keep that in mind when preparing your talk): --- Name: Tattwamasi Amrutam Title: Invariant Random Subgroups of C*-simple groups. Abstract: Let Gamma be a countable discrete C*-simple group. Let $\mu$ be an invariant random subgroup. We show that $\mu$-a.e subgroup H is C*-simple. This is a joint work with Mehrdad Kalantar. --- Name: Pénélope Azuelos Title: Virtually abelian subgroups of hierarchically hyperbolic groups Abstract: Hierarchically hyperbolic groups form a vast family of groups satisfying a coarse but highly organised form of non-positive curvature. Notable examples include hyperbolic groups, mapping class groups, compact special groups and many Artin groups. In this talk, I will discuss recent joint work with Mark Hagen in which we investigated the behaviour of their virtually abelian subgroups, proving in particular a coarse analogue of the CAT(0) flat torus theorem and flat closing problem for this class of groups. --- Name: Indranil Biswas Title: Homogeneous vector bundles on the upper-half plane. Abstract: Cowen and Douglas classified a class of linear operators on a Hilbert space using holomorphic Hermitian vector bundles on a domain in the complex plane (Acta Math. 1978). We classify all equivariant holomorphic Hermitian vector bundles on the upper-half plane. This is done by extracting some linear algebraic data. Joint work with Gadadhar Misra. --- Name: Partha Sarathi Ghosh Title: Stability of the weak Haagerup property under graph products Abstract: The weak Haagerup property for groups is an approximation property that generalizes the Haagerup property (which itself is a generalization of amenability). On the other hand, a graph product of finitely many groups over a finite simplicial graph is a combinatorial construction that interpolates between the free product and the direct product of groups. In joint work with Shubhabrata Das, we showed that any graph product of finitely many groups, each satisfying the weak Haagerup property with $\Lambda_{WH}=1$, also satisfies the weak Haagerup property. --- Name: Radhika Gupta Title: Finite index rigidity for free-by-cyclic groups Abstract: We show that a free-by-cyclic group with infinite order monodromy is finite index rigid, that is, any two isomorphic finite index subgroups have the same index. This is joint work with Nir Lazarovich. --- Name: Mahesh Krishna Title: Group-Frames for Banach Spaces Abstract: Frames generated by unitary representations of groups, commonly known as group frames, have been extensively studied in the context of Hilbert spaces. In this talk, we present the first systematic study of frames for Banach spaces arising from isometric invertible representations of discrete groups. We characterize these group frames through left and right regular representations, Gram matrices, and group matrices acting on classical sequence spaces. Furthermore, we identify a rich class of functional-vector pairs, obtained from the double commutant of the underlying representation, that generate group frames for Banach spaces. These results provide a new framework for extending the theory of group-generated frames beyond the Hilbert space setting and reveal new connections between Banach space geometry, operator algebras, and representation theory. --- Name Bratati Som Title: Conjugacy problem for Dehn twists of free products of free abelian groups Abstract: Dehn twist automorphisms of groups are defined in terms of graph-of-groups decompositions and provide algebraic analogues of Dehn twist homeomorphisms of surfaces. In this talk, we will discuss the key steps in an algorithm for solving the conjugacy problem for Dehn twists of free products of free abelian groups, mainly using a canonical splitting of the mapping torus associated to a Dehn twist. This is based on joint work with Amir Weiss Behar and Chris Karpinski. --- Name: Lizzy Teryoshin Title: Groups with the fixed-point property Abstract: A group G is said to have the fixed-point property if every action of G on a compact convex set has a fixed point. Work of Oliver from 1975 classified which finite groups have the fixed-point property. In the case of infinite groups, the Schauder–Tychonoff theorem establishes that the integers have the fixed-point property, but this has not been shown for any other infinite, finitely generated group. In joint work with Nicolas Monod and Omer Tamuz, we establish a local transfer principle and use it to provide a new example of an infinite, finitely generated group belonging to this class of groups. --- Name: Ignacio Vergara Title: The Dixmier problem and its recent solution Abstract: It has been known since the 1950s that every uniformly bounded representation of an amenable group G on a Hilbert space is similar to a unitary representation. We say that G is unitarisable. The Dixmier problem asks whether the converse is also true: Is every unitarisable group amenable? A positive answer to this question was recently given by OpenAI. In this talk, I will give a brief introduction to the Dixmier problem, and then I will present the main ideas behind its solution. --- Name: Prahlad Vaidyanathan Title: Values of Rokhlin Dimension for Integer Actions Abstract: Rokhlin dimension is a notion of covering dimension for group actions on C*-algebras due to Hirshberg, Winter and Zacharias. We will describe this idea and what it is meant to achieve. We will then discuss actions of the integer group, and some recent results concerning the possible values that this dimension can take. --- Name: Title: Abstract: --- Name: Title: Abstract: --- Name: Title: Abstract: --- Name: Title: Abstract: ---