Members’ Colloquium

The Poisson-Furstenberg boundary  is a measure space that describes asymptotics of infinite trajectories of random walks. The boundary is non-trivial if and only if the defining  measure admits non-constant bounded harmonic functions.

The origin of...

We travel the years in order to understand the relationship between Nilpotency and Riemannian geometry: including Gromov's almost flat theorem for manifolds with bounded curvature and Fukaya-Yamaguchi's almost nilpotency of spaces with lower...

This colloquium will explore some fundamental issues in the mathematics of plasmas, focusing on the stability and instability of solutions to Vlasov-type equations, which are crucial for describing the behavior of charged particles in a plasma. A...

Expansion in graphs is a well studied topic, with a wealth of applications in many areas of mathematics and the theory of computation.

High dimensional expansion is a generalization of expansion from graphs to higher dimensional objects, such as...

A promenade in Serre's paper, plus some related results of mine.

Joint work with Amir Mohammadi, Zhiren Wang, and Lei Yang

Let Q be an indefinite ternary quadratic form. In the 1980s Margulis proved the longstanding Oppenheim Conjecture, stating that unless Q is proportional to an integral form, the set of values...

I will discuss some well-known and less-known papers of Turing, exemplify the scope of deep, prescient ideas he put forth, and mention follow-up work on these by the Theoretical CS community.

No special background will be assumed.

Triangulated surfaces are Riemann surfaces formed by gluing together equilateral triangles. They are also the Riemann surfaces defined over the algebraic numbers. Brooks, Makover, Mirzakhani and many others proved results about the geometric...

To any unital, associative ring R one may associate a family of invariants known as its algebraic K-groups. Although they are essentially constructed out of simple linear algebra data over the ring, they see an extraordinary range of information...

Structures which minimise area appear in numerous geometric contexts often related to degeneration phenomena. In turn, in many situations these structures also reflect the ambient geometry in some way (they are ‘calibrated’) and so they may provide...