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Scholarly Interest Report
         
Michael D Boshernitzan
Professor
Professor of Mathematics
 
e-mail:michael@rice.edu
 
  • B.S. Mathematics (1972) Moscow State University, Moscow, USSR
  • M.S. Ergodic Theory (1974) Hebrew University, Jerusalem, Israel
  • Ph.D. Hardy Fields (1981) Weizmann Institute of Science, Rehovot, Israel
 
Primary Department
   Department of Mathematics
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Research Areas
 Ergodic Theory, Hardy Fields, Number Theory
 
Teaching Areas
 Algebra, Topology, Number Theory, Complex Analysis.
Ergodic Theory, Combinatorics
 
Selected Publications
 Refereed articles
 

M. Boshernitzan "Subgroup of interval exchanges generated by torsion elements and rotations." Proceedings of the Proc. Amer. Math. Soc., 144 (2016) : 2565–2573.

 
 

M. Boshernitzan, J. Chaika "Dichotomy for arithmetic progressions in subsets of reals." Proc. Amer. Math. Soc., 144, No 2, (Dec. 2016) : 5029–5034.

 
 

M. Boshernitzan, N. Frantzikinakis, M. Wierdl "Under recurrence in the Khintchine recurrence theorem." Journal D'Analyse Math. (2017) In Progress

 
 

M. Boshernitzan, D. Berend, G. Kolesnik,

Analytically defined uniformly dense sequences, Journal of Number Theory, 156(2015), 38-51

 
 

M. Boshernitzan, D. Berend, G. Kolesnik,

Analytically defined uniformly dense sequences, Journal of Number Theory, 156(2015), 38-51

 
 

M. Boshernitzan, Subgroup of interval exchanges generated by torsion elements and rotations, Proceedings of the AMS, in Press (accepted in May 2015)

 
 

J. Athreya, M. Boshernitzan,"Ergodic Properties of Compositions of Interval Exchange Maps and Rotations", Nonlinearity 26 (2013), 417-421.

 
 

J. Athreya, M. Boshernitzan,"Ergodic Properties of Compositions of Interval Exchange Maps and Rotations", Nonlinearity 26 (2013), 417-421.

 
 

M. Boshernitzan, A. Besbes, D. Lenz,  Delone sets with finite local complexity: linear repetivity versus positivity of weights, Discrete Comput. Geom. 49 (2013), no. 2, 335–347.

 
 

M. Boshernitzan, J. Chaika, Diophantine properties of IETs and general systems: quantitative proximality and connectivity",  Invent. Math. 192 (2013), no. 2, 375–412.

 
 

M. Boshernitzan, A condition for weak mixing of induced interval exchange transformations, Contemporary Mathematics 567 (2012), 53–65. (Special volume Dynamical Systems and Group actions, dedicated to Anatoli Stepin on the occasion of his 70th birthday).

 
 

M. Boshernitzan, J. Chaika, "Borel-Cantelli sequences", Journal d’Analyse Mathmatique 17 (1), (2012) 321–345.

 
 

(with D. Damanik) Pinned Repetitions in Symbolic Flows: Preliminary Results, AIMS Proceedings. Discrete Contin. Dyn. Syst. 2009, Dyn. Systems, Di erential Equations and Applications.
7th AIMS Conference, suppl. (2009), 869-878 (arXiv:0808.2200 [22]).

 
 

M. Boshernitzan, J. Chaika,  Diophantine properties of IETs and general systems: quantitative proximality and connectivity. Mar 2010,  arXiv:0910.5422.  

 
 

(with D. Damanik) The repetition property for sequences on tori generated by polynomials or skew-shifts,

Istael J. Math 174(2009), 189-202.

 
 

(with D. Ralston) Continued fractions and heavy sequences. Proc. Amer. Math. Soc. 137 (2009), no. 10, 3177--3185.

 
 
(with E. Glasner) On two recurrence problems, Fund. Math. 206 (2009), 113-138

 
 

MR2448017 Berend, Daniel; Boshernitzan, Michael D. Nilpotent groups are round. Israel J. Math. 167 (2008), 49--61.

 
 MR2417481 Boshernitzan, Michael; Wierdl, Máté Almost-everywhere convergence and polynomials. J. Mod. Dyn. 2 (2008), no. 3, 465--470 37Axx
 
 Boshernitzan, Michael and Chaika, Jon. The densest sequence in the unit circle.
 
 MR2434741 Boshernitzan, Michael; Damanik, David Generic continuous spectrum for ergodic Schrödinger operators. Comm. Math. Phys. 283 (2008), no. 3, 647--662. 81Q10 (47B36 47B80)
 
 arXiv:0808.2200 Pinned Repetitions in Symbolic Flows: Preliminary Results. Michael Boshernitzan (Rice), David Damanik (Rice). math.DS.
 
 

Boshernitzan M., Damanik D. "The repetition property for sequences on tori generated by polynomials or skew-shifts." Israel Journal of Mathematics.In Press

 
 Boshernitzan Michael, Glasner Eli. On two recurrence problems. Preprint 2008. Submitted to Fundamenta Mathematicae
 
 

Boshernitzan M., Ralston D. "Continued Fractions and Heavy Sequences." Proceedings of AMS.In Press

 
 

Berend, D., Boshernitzan, M. "Nilpotent Groups are Round." Israel J. of Math.In Press

 
 

Boshernitzan, M., Damanik D. "Generic Continuous Spectrum for Ergodic Schrodinger Operators." Commun. Math. Phys.Submitted

 
 M.Boshernitzan, G.Kolesnik, A.Quas, M.Wierdl, "Ergodic Averaging Sequences", J. d'Analyse Mathematique, 95 (2005), p. 63--1003.
 
 

M. Boshernitzan, A. Nogueira "Generalized Eigenfunctions of Interval Exchange Transformations." Ergodic Theory and Dynamical Systems, 24 (2004) : 697-705.

 
 

D. Berend, M. Boshernitzan, G. Kolesnik "Irrational Dilations of Pascal's Triangle." Mathematika, 48 (2003) : 159-168.

 
 

M. Boshernitzan, A. Goetz "A dichotomy of a two-parameter piecewise rotation." Ergodic Theory and Dynamical Systems, 23 (2003) : 759-770.

 
 

Yitwah Cheung, (M. Boshernitzan) "Hausdorff dimension of the set of nonergodic directions (with an Appendix by M. Boshernitzan)." Annals of Math., 158(2) (2003) : 661-678.

 
 

D. Berend, M.BoshernitzanM., G. Kolesnik "Distribution modulo 1 of some oscillating sequences |||." Acta Math. Hungar., 95, No.1-2 (April 2002) : 1-20.

 
 

D.Berend, M.Boshernitzan, G.Kolesnik "Distribution modulo 1 of some oscillating sequences, III." Acta Math. Hungar., 95(1-2) (April 2002)

 
 

M.Boshernitzan, C.R.Carroll "A generalization of Lagrange's theorem to interval exchange transformations." J. d'Analyse Mathematique, 72 (1997) : 21-44.

 
 

M.Boshernitzan, G.Galperin, T.Kruger, S.Troubetzkoy "Periodic billiard orbits are dense in rational polygons." Trans. Amer. Math. Soc., 350 (1998) : 2523-2535..

 
 Articles
 

M. Boshernitzan, V. Delecroix, Packing problem, quantitative recurrence in [0,1] and Lagrange spectrum of interval exchanges, preprint 2014, revised 2016

 
 

M. Boshernitzan, Approximate embedding of large polygons into Z2, revised 2014

 
 

M. Boshernitzan, D. Damanik, M. Lukic, J. Fillman "Ergodic Schrödinger operators in the infinite measure setting, preprint 2014." In Progress

 
 

M. Boshernitzan, "A Dichotomy for Projections of Planar Sets", preprint 2011 (revised)

 
Presentations
 Invited Talks
 

Invited lecture:  Banach limits associated with Hardy fields.  Dec. 13, 2016

Conference "Ergodic theory and its connections with Arithmetics and Combinatorics.  Luminy, Marseille, France   

 
 
Invited lecture. Packing problem and quantitative recurrence in [0, 1].  
Geometric and Probabilistic Methods in Group Theory and Dynamical Systems,  
Texas A&M University, College Station, TX.   November 9-12, 2015
 
 
 
 

Invited Lecture:  Optimal Constants for  Quantitave Poincare Recurrence in [0,1].

Ergodic Theorems and Applications in Probability,   Eilat, Israel. May 3-8, 2015.

 
 

Invited Lecture: Scales of functions and applications in ergodic theory, number theory and combinatorics. 2nd Workshop on Combinatorics, Number Theory and Dynamical Systems,

IMPA, Rio de Janeiro, Brazil, August 24--28, 2015.

 
 

Invited lectureCombinatorial properties of interval exchange transformation.

Ergodic Theory and Dynamical Systems - Toruń 2014.  Torun, Poland, 12-16 May 2014.

 

 
 

Two lectures in Max Plank Institute for Mathematics in Bonn, July 2014.  

 
 

Geometry, Dynamics, and Topology Days 2013, Eastern Illinois University.

Invited talk, "Combinatorial and diophantine properties of IETs".   April 19, 2013. 

 
 

May 15 -31, 2013. 

Invited speker in university Turku, Finland. Distinguished Lecture Series.

Includes  1 hour colloquium talk (Distinguished Lecture) and a topic course

(3 sessions of 1.5 hour each). Two weeks visit.

 

 
 

Invited Speaker. "Dichotomy for projections of planar sets".  South Padre Island. Fourth Discrete Geometry and Algebraic Combinatorics Conference, April 19, 2012.

 
 

Diophantine and combinatorial Properties of IETs,  Eilat (Israel)  Workshop  (Ergodic Theorems, Group Actions and Applications),  Sunday 15 -- Friday 20 May, 2011,  Ben-Gurion University campus in Eilat (Israel).

 
 

"Quantitative recurrence and connectivity in erg. theory, Courant Institute, NY, Dec." (Dec 5, 2009)

 
 

http://iml.univ-mrs.fr/words2007/speakers.en.html

 
 

"Combinatorial and Diophantine Properties of Interval Exchange Trnsformations." conference in Dynamics in the Teichmuller Space and Applications to Rational Billiards, Marseille, France. (July 2003)

 
 Lectures
 

Colloquium. Scales of functions and applications in ergodic theory.  

Université de Rennes-1, Campus de Beaulieu,  France.  October 6, 2015.

 
 

"Combinatorial and Diophantine Properties of IETs",  Ergodic Theory Seminar, Hebrew University, Jerusalem, Israel, June 2, 2011

 
 

"Hardy fields and Ergodic Theory", Ergodic Optimization, BIRS workshop, Canada, Feb 6-11 2011.

 
 

"Local Complexity of Finite Sets",  Ergodic Theory seminar,  UIUC, December 6, 2011

 
 

"Weak mixing of induced IETs",   Billiards, Flat Surfaces, and Dynamics on Moduli  Spaces, Oberwolfach workshop, Germany,   May 8th - May 14th, 2011.

 
 

Diophantine and Combinatorial properties of IETs,  Dynamical Systems Seminar, Texas&AM University

 
 

"Hardy fields and Scales of functions. Applications." Colloquium Lecture, SFSU (San Francisco State University). (Sept. 10, 2008)

 
 Other
 

Colloquium lecture. An approach for construction of large scales of functions. Hardy fields. (in Russian). Colloquium lecture in Chernivitsi University, Chernivitsi, Ukraine, June 2, 2012.

 
 

Colloquium lecture. Combinatorial and Diophantine properties of interval exchange transformations. Institute of Mathematics, National Academy of Science of Ukraine, Kiev, Ukraine. May 25, 2012.

 
 

"Generic properties of interval exchange transformations." Institut de Mathematiques de Luminy, Marseille, France. (June 2001)

 
 

"Some extensions of LaGrange Theorem on the periodicity of the continued fraction expansions of quadratic irrationals." Special AMS session in Geometric and Symbolic Dynamical Systems., San Francisco, CA. (October 21, 2000)

 
 

"Combinatorial and Diophantine Properties of Interval Exchange Trnsformations." Colloquium Lecture, University of South California, LA. (November 10, 1999)

 
 

"Irrational Dilations of Pascal Triangle." AMS Special Session on Symbolic Dynamical Systems, University of North Texas, Denton, TX. (May 22, 1999) With D. Berend, G. Kolesnik

 
 

"Short Course on Asymptotic Distribution mod 1 (2 hours)." IV Joint Meeting AMS-SMM, University of North Texas, Denton, TX. (May 23, 1999)

 
 

"Diophantine properties of interval exchange transformations." Institut de Mathematiques de Luminy, Marseille, France. (June 1998)

 
 

"Quantitative recurrence results." Institut de Mathematiques de Luminy, Marseille, France. (July 1998)

 
 Seminar Speaker
 

3 hours course on interval exchange transformations, Torun University, Poland, May 2014

 
 Workshops
 

Scientific Committee Member + Minicourse.  "Minicourse: Combinatorial and Diophantine Properties of Interval Exchange Transformation." Workshop on Piecewise Isometries, Marseille-Lumini (IML), France. (June 2-15, 2002)

 
Supervised Theses & Dissertations
 David Ralston, Ph. D. Heaviness in Dynamics, and extension of Y. Peres lemma.. (2008) (Thesis Director)

 David Ralston, Ph. D. Heaviness in Dynamics.. (2008) (Thesis Director)

 Daniel Bernazzani, PhD Supervising PhD student D.Bernazzani. (2017) (Thesis Director)

 Jon Chaika, Ph. D. Interval Exchange Transformations: Applications of Keane's construction and disjointness. (Thesis Director)

Awards, Prizes, & Fellowships
 Research professor, Max Planck Institute, July 1-30, 2014, Max Planck Institute of Mathematics in Bonn (July 2014)

 MSRI membership for the Fall 2008, Reseach Professor, MSRI, Berkeley (Fall 2008)

 Visiting Professor, Institut de Mathematiques de Luminy, Marseille, France (May 25 - June 25, 2001)

Positions Held
 Research Professor, Max Planck Institute for Mathematics in Bonn, 1 month research position. (2014 - 2014)

 Visiting Professor, Princeton University, NJ. (2009 - 2009)

 Research Professor, MSRI member, MSRI, Berkeley. (2008 - 2008)