Abstract:
Measure equivalence of countable groups is a measure theoretic analogue
of quasi-isometry.
For example, any two lattices in the same Lie group are by definition
measure equivalent.
We prove that any countable group that is measure equivalent to Out(Fn)
is virtually isomorphic to Out(Fn). This is a joint work with Camille
Horbez.
Ornstein and Shields (Advances in Math., 10:143-146, 1973) proved that Brownian motion reflected on a bounded region is an infinite entropy Bernoulli flow and thus Ornstein theory yielded the existence of a measure-preserving isomorphism between any two such Brownian motions. For fixed h >0, we construct by elementary methods, isomorphisms with almost surely finite coding windows between Brownian motions reflected on the intervals [0, qh] for all positive rationals q. This is joint work with Terry Soo.
Abstract:
Recently Uri Gabor refuted an old conjecture stating that any
finitary factor of an i.i.d process is finitarly isomorphic to an
i.i.d process. Complementing Gabor's result,
in this talk, which is based on work in progress with Yinon Spinka,
we will prove that any countable-valued process which is admits a
finitary a coding by some i.i.d process furthermore admits an
$\epsilon$-efficient finitary coding, for any positive $\epsilon$.
Here an ``$\epsilon$-efficient coding'' means that the entropy
In the lecture I will describe basic notions of computational complexity:
Boolean functions, basic algorithmic tasks, Boolean circuits, P, NP, randomness, quantum circuits, noisy quantum circuits, bounded depth circuits, and more.
If time permits I will describe some (or more realistically one) mathematical challenge in the field and briefly
describe some examples (more realistically, one example) on how theory meets reality.
האי-שוויון האיזופרימטרי קובע שמבין כל הגופים בעלי נפח 1 במרחב אוקלידי N-מימדי, הגוף בעל שטח הפנים הקטן ביותר הוא כדור. יתר על כן, גוף קמור מנפח 1 ששטח פניו קרוב לשטח הפנים של כדור קרוב בעצמו, במובן מתאים, להיות כדור. לטענה זו יש היסטוריה ארוכה והיא היתה מוכרת, בגירסה זו או אחרת, כבר בימי קדם, אך הוכחה מלאה ניתנה רק בסוף המאה ה-19 ותחילת המאה ה-20, והכללות שלה מעסיקות מתמטיקאים עד היום.
Title: Optimal growth of frequently oscillating subharmonic functions.
Abstract: In this talk I will present Nevanlinna-type tight bounds on the minimal possible growth of subharmonic functions with a large zero set. We use a technique inspired by a paper of Jones and Makarov.
Abstract: In this talk, I'll show the invalidity of finitary counterparts for three main theorems in classification theory: The preservation of being a Bernoulli shift through factors, Sinai's factor theorem, and the weak Pinsker property. This gives a negative answer to an old conjecture and to a recent open problem.
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.
