The geodesic flow on a normal cover of a compact hyperbolic surface admits a "random walk" on the group of decks transformations $G$. In this talk, I'll provide some recent results which connect this walk to the geometric properties of the cover and $G$.
In the last 35 years, geometric flows have proven to be a powerful tool in geometry and topology. The Mean Curvature Flow is, in many ways, the most natural flow for surfaces in Euclidean space. In this talk, which will assume no prior knowledge, I will illustrate how mean curvature flow could be used to address geometric questions.
Manchester Building (Hall 2), Hebrew University Jerusalem
Let u be a harmonic function on the plane. The Liouville theorem claims that if |u| is bounded on the whole plane, then u is identically constant. It appears that if u is a harmonic function on the lattice Z^2, and |u| < 1 on 99,99% of Z^2, then u is a constant function. Based on a joint work with A. Logunov, Eu. Malinnikova and M. Sodin.
Speaker: Benny Sudakov, ETH, Zurich
Title: Subgraph statistics
Abstract:
Consider integers $k,\ell$ such that $0\le \ell \le \binom{k}2$. Given
a large graph $G$, what is the fraction of $k$-vertex
subsets of $G$ which span exactly $\ell$ edges? When $G$ is empty or
complete, and $\ell$ is zero or $\binom k 2$,
this fraction can be exactly 1. On the other hand if $\ell$ is not one
these extreme values, then by Ramsey's theorem, this
fraction is strictly smaller than 1.
The systematic study of the above question was recently initiated by
Manchester Building (Hall 2), Hebrew University Jerusalem
The proof of decoupling grew out of an area of Fourier analysis called restriction theory. In this talk, we will describe some of the basic problems and tools of restriction theory, especially wave packets, which are a crucial idea in the proof of decoupling.
Title: Local root numbers for Heisenberg representations
Abstract: On the Langlands program, explicit computation of the local root numbers (or epsilon factors) for Galois representations is an integral part. But for arbitrary Galois representation of higher dimension, we do not have explicit formula for local root numbers. In our recent work (joint with Ernst-Wilhelm Zink) we consider Heisenberg representation (i.e., it represents commutators by scalar matrices) of the Weil
The general theme is game dynamics leading to equilibrium concepts.
The plan is to deal with the following topics (all concepts will be defined, and proofs / proof outlines will be provided):
(1) An integral approach to the construction of calibrated forecasts and their use for Nash equilibrium dynamics.
(2) Blackwell's Approachability Theorem and its use for correlated equilibrium dynamics (regret-matching).
(3) Communication complexity and its use for the speed of convergence of uncoupled dynamics.
The general theme is game dynamics leading to equilibrium concepts.
The plan is to deal with the following topics (all concepts will be defined, and proofs / proof outlines will be provided):
(1) An integral approach to the construction of calibrated forecasts and their use for Nash equilibrium dynamics.
(2) Blackwell's Approachability Theorem and its use for correlated equilibrium dynamics (regret-matching).
(3) Communication complexity and its use for the speed of convergence of uncoupled dynamics.
Abstract: Modal logic is used to study various modalities, i.e. various ways in which statements can be true, the most notable of which are the modalities of necessity and possibility. In set-theory, a natural interpretation is to consider a statement as necessary if it holds in any forcing extension of the world, and possible if it holds in some forcing extension. One can now ask what are the modal principles which captures this interpretation, or in other words - what is the "Modal Logic of Forcing"?
