Title: The Modal Logic of Forcing (Part III) 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"?

I will review homological mirror symmetry for the torus, which describes Lagrangian Floer theory on T^2 in terms of vector bundles on the Tate elliptic curve --- a version of Lekili and Perutz's works "over Z", where t is the Novikov parameter. Then I will describe a modified form of this story, joint with Lekili, where the Floer theory is altered by a locally constant sheaf of rings on T^2 (an "F-field").

Title: Interpolation sets and arithmetic progressions Abstract: Given a set S of positive measure on the unit circle, a set of integers K is an interpolation set (IS) for S if for any data {c(k)} in l^2(K) there exists a function f in L^2(S) such that its Fourier coefficients satisfy f^(k)=c(k) for all k in K. In the talk I will discuss the relationship between the concept of IS and the existence arithmetic structure in the set K, I will focus primarily on the case where K contains arbitrarily long arithmetic progressions with specified lengths and step sizes.

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 original result. Furthermore, we will describe certain limiting frequencies

Quantum computation ================== 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. I will give some definitions, provide some basic results, and sketch some open problems.

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.

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. We describe an algorithm for the evaluation of such sums under periodic boundary conditions, provide a rigorous error analysis, and discuss its implications on the computational cost and choice of parameters.

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