Repeats every week every Sunday until Sat Feb 01 2020 except Sun Oct 27 2019.
11:00am to 1:00pm
Location:
Ross 70
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
Driven by recent technological advancements, behavior and brain activity can now be measured at an unprecedented resolution and scale. This “big-data” revolution is akin to a similar revolution in biology. In biology, the wealth of data allowed systems-biologists to uncover the underlying design principles that are shared among biological systems. In my studies, I apply design principles from systems-biology to cognitive phenomena. In my talk I will demonstrate this approach in regard to creative search.
Repeats every week every Sunday until Sat Feb 01 2020 except Sun Dec 29 2019.
2:00pm to 4:00pm
Location:
Ross 70
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.
Repeats every week every Sunday until Sat Feb 01 2020 except Sun Oct 27 2019.
4:00pm to 6:00pm
Location:
Ross 70
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" .
Abstract: I will present some results that state that under certain topological conditions, any action of a countable amenable group with positive topological entropy admits off-diagonal asymptotic pairs. I shall explain the latest results on this topic and present a new approach, inspired from thermodynamical formalism and developed in collaboration with Felipe García-Ramos and Hanfeng Li, which unifies all previous results and yields new classes of algebraic actions for which
A countable group is said to be homogeneous if whenever tuples of elements u, v satisfy the same first-order formulas there is an automorphism of the group sending one to the other. We had previously proved with Rizos Sklinos that free groups are homogeneous, while most surface groups aren't. In a joint work with Ayala Dente-Byron, we extend this to give a complete characterization of torsion-free hyperbolic groups that are homogeneous.
In the mid-18th century,Euler derived his famous equations of motion of an incompressible fluid, one ofthe most studied equations in hydrodynamics. More than 200 years later, in1966, Arnold observed that they are, in fact, geodesic equations on the(infinite dimensional) Lie group of volume-preserving diffeomorphisms of amanifold, endowed with a certain right-invariant Riemannian metric.
