Joint IAS/PU Groups and Dynamics Seminar

Minimum Entropies of Braids

Chi Cheuk Tsang

Every braid can be thought of as a homeomorphism of a punctured disc. Morally, the more complicated a braid is, the more dynamics is contained in the corresponding homeomorphism, which one can quantify using topological entropy. In particular, one...

We prove ''reasonable'' quantitative bounds for sets in ℤ2

avoiding the polynomial corner configuration (x,y),(x+P(z),y),(x,y+P(z)), where P is any fixed integer-coefficient polynomial with an integer root of multiplicity 1. This simultaneously...

Teichmuller dynamics give us a nonhomogeneous example of an action of SL_2(R) on a space H_g preserving a finite measure. This space is related to the moduli space of genus g curves. The SL_2(R) action on H_g has a complicated behavior: McMullen...