Courses at the Hyamfest
Ergodic Theory of Hyperbolic Groups
Lecturer: Danny Calegari
Assistant: Alden Walker
An introduction to the use of dynamical and probabilistic methods in geo-
metric group theory, especially as applied to hyperbolic groups. I hope to
discuss (central) limit theorems for random geodesics and random walks,
behaviour of characteristic functions (e.g. (stable) commutator length, w-
length, etc.) under random homomorphisms, and a few other topics if time
permits.
Invariants of Hyperbolic 3-Manifolds
Lecturer: Walter Neumann
Assistant: Christian Zickert
This short course will concentrate on number-theoretic invariants and num-
ber theoretic methods in the study of 3-manifolds. The first lecture will be
a brief introduction to algebraic number theory, followed by four lectures
on 3-manifolds, concentrating mostly on hyperbolic 3-manifolds.
Function Theory on Symplectic Manifolds
Lecturer: Leonid Polterovich
Assistant: Daniel Rosen
Function spaces associated to a symplectic manifold exhibit unexpected
properties and interesting structures, giving rise to an alternative intuition
and new tools in symplectic topology. These phenomena are detected by
modern symplectic methods such as Floer theory and are closely related
to algebraic and geometric properties of groups of Hamiltonian diffeomor-
phisms. I shall discuss these developments, their applications as well as
links to other areas such as group quasi-morphisms and quantum-classical
correspondence. All necessary symplectic preliminaries will be explained.
Notes, problem sets and video recordings of the lectures are available at:
http://www.ms.unimelb.edu.au/∼hyamfest/workshop.php
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