About

Research

Below are links to my papers and preprints.
Actual published articles may change slightly from the version available here.

  • Generalizations of Furstenberg's Diophantine result

  • Accepted. Ergodic Theory and Dynamical Systems.
    This paper generalizes H. Furstenberg's result about density of an irrational point in the one-torus under the x2 x3 multiplicative semigroup to a much sparser class of sequences. The proof uses ideas from the effective proof of Furstenberg's theorem by Bourgain-Lindenstrauss-Michel-Venkatesh and p-adic analysis.

  • On mixing and sparse ergodic theorems

  • Submitted.
    This paper deals with Bourgain's sparse ergodic theorem for the case of the horocyclic flow (and general one-parameter unipotent flows on homogenuous spaces). In particular, we show that the exceptional set of the point which their average along polynomial sample times do not equidistribute is a lower dimensional subset. Moreover, we show that such an estimate is free of the actual spectral gap of the homogenuous space. The proof uses ideas from homogenuous dynamics (primarily Ratner's theorems and quantitative mixing), automorphic representation theory, harmonic analysis and number theory.

  • Quantitative disjointness of unipotent flows from nilflows and applications

  • Work in progress.
    The paper shows a quantitative disjointness statement of unipotent flows from nilflows, based on the proof of the uniform Wiener-Wintner theorem and the results of Green,Tao and Ziegler regarding nilcharacters. We show applications including a quantitative return times theorem and equidistribution along sprase sampling over quasi-crystals in horospherical subgroups.

  • Equidistribution of spheres in horospheres

  • Work in progress.
    We show a quantitative theorem regarding equidistribution of large spheres in maximal horospherical subgroups, which is an analouge of the classical result of Van-der-Corput regarding equidistribution of projections of large spheres in the torus.

Teaching

This year (2016-2017) I am teaching the following courses:

  • Fall Semester - Infintisimal Calculus I - Prof. Ron Livne.
  • Spring Semester - Advanced Calculus II (vector calculus and differential geometry) - Prof. Noam Berger.

I have previously been a teaching assistant in the following courses at the Hebrew University:

2015-2016

  • Fall Semester - Infintisimal Calculus I - Prof. Mike Hochman
  • Spring Semester - Calculus for computer science - Dr. Yves Godin.

2014-2015

  • Fall Semester - Infintisimal Calculus I - Prof. Mike Hochman
  • Spring Semester - Not teaching, on research visit to UC-Berkeley.

2013-2014

  • Fall Semester - Mathematics for Chemistery students - Mr. Itamar Zwick
  • Spring Semester - Calculus for computer science - Dr. Yves Godin.

2012-2013

  • Fall Semester - Group theory and basic algebra - Prof. Aner Shalev.
  • Spring Semester - Calculus for computer science - Prof. Raz Kupferman.

2011-2012

2010-2011

2009-2010

  • No teaching this year.

2008-2009

  • Spring Semester - Introduction to Differential Geometry for undergraduate students - Dr. Jake Solomon.

Notes

Not intended for publication.

Contact Me

I am available by e-mail at firstname.lastname@mail.huji.ac.il

Office address:
Ross Buliding 35,
Einstein Institute of Mathematics
Edmond J. Safra Campus
The Hebrew University of Jerusalem
Givat Ram. Jerusalem, 9190401 Israel