Title: New bounds on the covering radius of a lattice.
We obtain new upper bounds on the minimal density of lattice coverings of R^n by dilates of a convex body K. We also obtain bounds on the probability (with respect to the natural Haar-Siegel measure on the space of lattices) that a randomly chosen lattice L satisfies L + K = R^n. As a step in the proof, we utilize and strengthen results on the discrete Kakeya problem. This is joint work with Or Ordentlich and Oded Regev.
Measure equivalence of countable groups is a measure theoretic analogue
For example, any two lattices in the same Lie group are by definition
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
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.
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.
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.