Members’ Colloquium

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...

A deep result of Furstenberg from 1967 states that if Γ is a lattice in a semisimple Lie group G, then there exists a measure on Γ

with finite first moment such that the corresponding harmonic measure on the Furstenberg boundary of G

is absolutely...

The Fourier uniformity conjecture seeks to understand what multiplicative functions can have large Fourier coefficients on many short intervals. We will discuss recent progress on this problem and explain its connection with the distribution of...

The problem of control of large multi-agent systems, such as vehicular traffic, poses many challenges both for the development of mathematical models and their analysis and the application to real systems. First, we discuss how conservation laws can...

I will discuss a result with Bonatti and Crovisier from 2009 showing that the C1 generic diffeomorphism f of a closed manifold has trivial centralizer; i.e. fg = gf implies that g is a power of f. I’ll discuss features of the C1 topology that enable...

Let G be an infinite discrete group. Finite dimensional unitary representations of G are usually quite hard to understand. However, there are interesting notions of convergence of such representations as the dimension tends to infinity. One notion —...