Subhadip Dey
TIFR, Mumbai
October 16, 2025
Irreducible discrete subgroups of $G \times G$: Let $G$ be a noncompact semisimple real Lie group, and let $\Gamma$ be an irreducible discrete subgroup of $G \times G$, i.e., its projections to both factors are dense. We will highlight some structural questions and present some results showing that certain irreducible groups cannot be free products and are subject to strong constraints. Along the way, we will discuss examples of two quasi-isometric locally symmetric spaces with finitely presented fundamental groups, where one admits nontrivial bounded harmonic functions while the other does not, highlighting ergodic properties at infinity. This is based on joint work with Sebastian Hurtado.
TIFR, Mumbai
October 16, 2025
Irreducible discrete subgroups of $G \times G$: Let $G$ be a noncompact semisimple real Lie group, and let $\Gamma$ be an irreducible discrete subgroup of $G \times G$, i.e., its projections to both factors are dense. We will highlight some structural questions and present some results showing that certain irreducible groups cannot be free products and are subject to strong constraints. Along the way, we will discuss examples of two quasi-isometric locally symmetric spaces with finitely presented fundamental groups, where one admits nontrivial bounded harmonic functions while the other does not, highlighting ergodic properties at infinity. This is based on joint work with Sebastian Hurtado.