And I am in this photo!
Prof T N Venkataramana was also an invited speaker.
| Name of the Speaker | Abstract |
|---|---|
| T N Venkataramana, ICTS, Bengaluru 5 lectures | Title: A Proof of the Margulis Superrigidity Theorem Abstract: We shall review the proof of the Margulis superrigidity theorem following the paper by Margulis, Invent. Math. 1984, developing the necessary background. A brief outline is given below. Rank of a semisimple Lie group, Irreducible lattices, Uniform & non-uniform Lattices, Rank 1 vs Higher rank, Examples, Arithmeticity theorem with proof, Zariski dense subgroups, Furstenberg measure, Amenable subgroups, Existence of equivariant measurable maps, Induced representations, Rationality of equivariant measurable maps. Proof of the superrigidity theorem. |
However, he unfortunately, he could not be present during the school. The rest of the speakers were as follows.
| Name of the Speaker | Abstract |
|---|---|
| Pranab Sardar, IISER Mohali 1 lecture | Title: On some rigidity theorems in geometric group theory Abstract: The rigidity theorems of Mostow, Margulis and others for lattices in semisimple Lie groups inspired many such rigidity type results in geometry and topology. In this expository lecture, we will survey some such theorems related to geometric group theory. |
| Pralay Chatterjee, IMSc Chennai 3 lectures | Title: Introduction to Lattices Abstract: Semisimple Lie groups, Lattices in Lie groups, Some generalities on lattices in Lie groups, |
| Riddhi Shah (RS) 1 lecture | Title: The structure of automorphism groups and lattices in Lie groups Abstract: We study the structure of groups of automorphisms of a connected Lie group; namely, we identify certain conditions under which they are almost algebraic, and discuss some applications and examples (joint work with S.G. Dani - https://arxiv.org/abs/2504.18641). We explore the structure of lattices in a connected Lie group and discuss some properties of automorphisms which keep a lattice invariant (joint work with Rajdip Palit and Manoj B. Prajapati - Geometry, and Dynamics 17 (2023), 185-213 - https://doi.org/10.4171/GGD/672 ) |
| C. S. Rajan (CSR), Ashoka University 3 lectures | Title: Harmonic superrigidity Abstract: The lectures will serve as an introduction to the rigidity results of Corlette and Gromov-Schoen. |
| Marc Bourdon, Université de Lille, France 4 lectures | Title: Lie groups and quasi-isometries Abstract: In geometric group theory, one studies groups as geometric objects, and tries to determine whether an algebraic property is a geometric one. In this setting, the natural maps between groups are the so-called quasi-isometries (QI). A class of groups is said to be QI-rigid if every finitely generated group that is QI to a group in the class, is virtually isomorphic to (another) group in the class. Geometric group theory started in the 80’s when Gromov proved that the class of nilpotent groups is QI-rigid. In the 90’s the subject focused on semisimple groups; it culminated when a combination of works allowed to establish that the class of lattices in a given semisimple group is QI-rigid. Since then, geometric group theory has developed several interactions with other fields of mathematics. It has been used to solve some old open problems (e.g. in 3-manifold topology). A major problem in geometric group theory is to classify connected Lie groups up to QI. One knows that every simply connected Lie group is QI to a completely solvable Lie group, i.e. to a closed subgroup of the upper triangular real matrix group. In 2018 Cornulier conjectured that two QI completely solvable groups must be isomorphic. This is currently open, even in the smaller class of nilpotent Lie groups. During the talks, I plan to introduce some QI-invariants for Lie groups, and illustrate them with examples. These invariants include the growth rate, the rank, and the L^p-cohomology. The examples of groups that will be discussed include the nilpotent groups, the Heintze groups, the abelian-by-abelian solvable Lie groups. Some known results about their QI classification will also be presented. The following notes were folllowed: Lie groups and quasi-isometries, Notes d’un mini-cours à IISER Mohali (Penjab) en juillet 2025 |
| Arghya Mondal 2 lectures | Title: Mostow rigidity Abstract: The Mostow Prasad Rigidity Theorem says if two finite volume hyperbolic manifolds of dimension greater than or equal to 3 are homotopy equivalent then they are isometric. We will give a complete proof of this statement for closed hyperbolic 3-manifolds. Then we will indicate how the proof can be extended in the general case. |