Profile decomposition theorem is a refinement of the Banach-Alaoglu (weak compactness) theorem in presence of a given set of quasi-isometries. We define a class of co-compact embeddings of Banach spaces that yields a clear structure for bounded divergent sequences. This is a generalization, on the functional-analytic level, of the concentration compactness principle of Lions. Applications include Sobolev, Jawerts Strichartz and Moser-Trudinger embeddings.
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
Abstract:
We consider a locally finite (Radon) measure on SO(d,1)/Gamma
invariant under a horospherical subgroup of SO(d,1) where Gamma is a discrete, but not necessarily geometrically finite, subgroup. We show that whenever the measure does not observe any additional invariance properties then it must be supported on a set of points with geometrically degenerate trajectories under the corresponding contracting 1-parameter diagonalizable flow (geodesic flow). This is joint work with Elon Lindenstrauss.
Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract: A spanning tree of a graph G is a subgraph with the same vertex set which is a tree. In 1981, McKay proved an asymptotic result regarding the number of spanning trees in random k-regular graphs. In this talk we will discuss an analogous result for certain random simplicial complexes (All terms will be explained in the talk).
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The talk is based on a joint work with Lior Tenenbaum.
Repeats every week every Sunday until Sat Feb 01 2020 except Sun Oct 27 2019.
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
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" .
Repeats every week every Sunday until Sat Feb 01 2020 except Sun Oct 27 2019.
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
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
Repeats every week every Sunday until Sat Feb 01 2020 except Sun Dec 29 2019.
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
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.
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.
Title:
Limit theorems of optimal transportation and teleportation
Abstract:
I’ll review the fundamental definitions in optimal transport theory and discuss limit theorems along with applications to regularity of flows and, if time permit, a novel application to optimal networks,
Manchester Building (Hall 2), Hebrew University Jerusalem
Physical systems are regularly studied as spatial point sets, and so understanding the structure in such sets is a very natural problem. However, aside from several special cases, describing the manner in which a set of points can be arranged in space has been historically challenging. In the first part of this talk, I will show how consideration of the configuration space of local arrangements of neighbors, and a few simple results in metric geometry, can shed light on essential challenges of this problem, and in the classification of data more generally.
