2019 Nov 11

Combinatorics: Barak Weiss (TAU)

10:00am to 12:00pm


C-400, CS building

Speaker: Barak Weiss (TAU)

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. 

2019 Oct 31

Groups & Dynamics seminar - Vincent Guirardel (Universite de Rennes 1) "Measure Equivalence rigidity for Out(Fn)"

10:00am to 11:00am


Ross 70
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
2019 Oct 29

Zemer Kosloff, Finitary isomorphisms of Brownian motions

2:00pm to 3:00pm

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.
2019 Nov 19

Tom Meyerovitch (BGU), Efficient finitary codings by Bernoulli processes

2:00pm to 3:00pm

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
2019 Oct 31

Basic Notions: Gil Kalai (HUJI) "Classical and quantum computation"

4:00pm to 5:15pm


Ross 70
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.
2019 Nov 20

Eshnav: Mike Hochman - The isoperimetric inequality

6:00pm to 7:00pm


Math 2 (Manchester building)

פרופ' מייק הוכמן: האי-שוויון האיזופרימטרי

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.