Elon Lindenstrauss "Arithmetic applications of diagonal flows" I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces, including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest, in particular CM points and integer points on spheres. I hope to cover parts of the following papers: Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.

Tentative syllabus 1. Mathematical models of classical and quantum mechanics. 2. Correspondence principle and quantization. 3. Classical and quantum computation: gates, circuits, algorithms (Shor, Grover). Solovay-Kitaev. Some ideas of cryptography 4. Quantum noise and measurement, and rigidity of the Poisson bracket. 5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code. 6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.

Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties. When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .

Title: Extending the Spectral Radius to Finite-Dimensional Power-Associative Algebras Abstract: The purpose of this talk is to introduce a new concept, the \textit{radius} of elements in arbitrary finite-dimensional power-associative algebras over the field of real or complex numbers. It is an extension of the well known notion of the spectral radius. As examples, we shall discuss this new radius in the setting of matrix algebras, where it indeed reduces to the spectral radius, and then in the Cayley-Dickson algebras, where it is something quite different.

The workshop will consist of four main mini-courses and several additional lectures, taking place on the shore of the Sea of Galilee, at Ohalo Manor Hotel.

Mini-Courses: Read more about Seminar on Random walks, equidistribution, and rigidity

Modern symplectic topology deals with objects of symplectic geometry indirectly, by associating to them auxiliary moduli spaces. This complicates its relation with homotopy theory. I will explain the overall framework that describes this relation (going back to Cohen, Jones and Segal), and some of the directions that are under investigation.

Most of the complications of classical topology have to do with torsion phenomena, say by looking at homology with modulo p coefficients. In principle, the same is true for symplectic topology, but the implications are only beginning to be explored. A particular impetus is provided by mirror symmetry, which links symplectic topology with arithmetic geometry.