Abstract: Substitution schemes provide a classical method for constructing tilings
of Euclidean space. Allowing multiple scales in the scheme, we introduce
a rich family of sequences of tile partitions generated by the substitution
rule, which include the sequence of partitions of the unit interval
considered by Kakutani as a special case. In this talk we will use new path counting
results for directed weighted graphs to show that such sequences
of partitions are uniformly distributed, thus extending Kakutani's

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.

Quantum computation
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You can hardly open the newspaper nowadays without seeing something about Quantum computation. But aside from the hype and the industry interest, this deceivingly simple model offers a surprisingly rich set of mathematical, physical and conceptual questions, which seem to touch upon almost any area of mathematics: from group representations, to Markov chains, Knot invariants, expanders, cryptography, lattices, differential geometry, and many more.

Title:
On the evaluation of sums of periodic Gaussians
Abstract:
Discrete sums of the form
$\sum_{k=1}^N q_k \cdot \exp\left( -\frac{t – s_k}{2 \cdot \sigma^2} \right)$
where $\sigma>0$ and $q_1, \dots, q_N$ are real numbers and
$s_1, \dots, s_N$ and $t$ are vectors in $R^d$,
are frequently encountered in numerical computations across a variety of fields.

Title:
A central limit type conjecture for the nodal statistics of quantum graphs
Abstract:

Theory of Computer Science Seminar

This talk provides a gentle, high level introduction to (the beautiful) Invariant Theory, that is aimed at non-experts. It will describe some of its main objects, problems and results. Read more about CS theory seminar: Avi Wigderson (IAS) : An invitation to Invariant Theory

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.

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.