## Unni Namboodiri Lectures in Geometry and Topology

Unni Namboodiri (1956–1981) was a brilliant student of mathematics at the University of
Chicago. He died in an automobile accident in December 1981, just a few days after presenting
and defending his doctoral thesis *Equivariant vector fields on spheres*, written under the
direction of J. Peter May. The Unni Namboodiri Lecture Series was established in his memory
by his family.

### 2016–2017 Lectures

Mike Hill (UCLA)

#### Lecture 1

Friday, May 12, 2016, 4:00pm–5:00pm

#### Lecture 2

Monday, May 15, 2016, 4:00pm–5:00pm

#### Lecture 3

Tuesday, May 16, 2016, 4:30pm–5:30pm

### 2015–2016 Lectures

Yves Benoist (Université Paris-Sud)

On spectral gaps in simple Lie groups

#### Lecture 1: Dense subgroups in \(\mathrm{SL}(2,\mathbb{R})\), with N. de Saxce

Monday, May 16, 2016, 4:00pm–5:00pm in Ryerson 251

**Abstract**:
I will focus on proper Borel measurable dense subgroups of \(\mathrm{SL}(2,\mathbb{R})\)
and explain that their Hausdorff dimension is zero.
I will also explain why the convolution of sufficiently
many compactly supported continuous functions is differentiable.
We will see how these two questions are related.
The main tool will be a local spectral gap property.

#### Lecture 2: Random walk on \(\mathrm{SL}(2,\mathbb{R})\), with JF. Quint

Tuesday, May 17, 2016, 4:30pm–5:30pm in Eckhart 202

**Abstract**:
I will focus on random walks on \(\mathrm{SL}(2,\mathbb{R})\)
and explain the law of large numbers for the coefficients.
I will also focus on the regularity
of the stationary measure on the projective line.
We will see how these two questions are related.
The main tool will be a spectral gap property.

#### Lecture 3: Tempered homogeneous spaces, with T. Kobayashi

Thursday, May 19, 2016, 4:30pm–5:30pm in Eckhart 202

**Abstract**:
I will focus on unitary representations of \(\mathrm{SL}(n,\mathbb{R})\)
and give a criterion for the temperedness
of the regular representations on its algebraic homogeneous spaces.
I will also explain the relation between temperedness and induction.
We will see how these two questions are related.
The main tool will be a uniform spectral gap property.

Past Namboodiri Lecturers include: J. Frank Adams, William Thurston, Shing-Tung Yau, Daniel Quillen, Robert MacPherson, Simon K. Donaldson, Edward Witten, Mikhael Gromov, Gregory A. Margulis, Graeme Segal, Andrew J. Casson, Julius Shaneson, Nigel Hitchin, Dusa McDuff, Clifford Taubes, Alain Connes, Ib Madsen, Michael Hopkins, Yakov Eliashberg, David Gabai, Curt McMullen, Gang Tian, Michael Weiss, John Baez, Étienne Ghys, Nigel Higson, Mladen Bestvina, Douglas C. Ravenel, Danny Calegari, and Larry Guth.