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$Description: Description: Description: Description: Description: Description: Description: K:\wellicon.gif$ Idris Assani

Affiliation

Department of Mathematics

University of North Carolina at Chapel Hill

Position

Professor, Department of Mathematics

Education

Doctorat es Sciences ,Pure Math., University Paris 6, adviser (A. Brunel) -Pure Math, 1986

Doctorat 3eme cycle, Pure Math,University Paris 6,-adviser (R. Pallu de la Barriere)-Pure Math, 1981.

Bachelors , Commerce , University Paris Dauphine, 1981.

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Mailing Address

Department of Mathematics

CB 3250, Phillips Hall

University of North Carolina at Chapel Hill

Chapel Hill, NC 27599-3250 USA

Location

Phillips Hall, Room 305 A

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TEACHING INFO

Office hours (Spring 2012) –Tuesday 11:30 am to 12:30 pm, -Wed 11:00 am -noon and by appointment.

Course: Math 521. Tu –Th 9:30- 10:45

Contacts

Email : assani@math.unc.edu

assani@email.unc.edu

FAX : (919) 962 2568

Research Interests

Ergodic Theory Seminar
Winston-Salem meeting: Abstracts and Preprints
Almost everywhere phenomena in Ergodic Theory and Dynamical Systems, Recently
Connections between ergodic theory and Harmonic Analysis
Wiener Wintner type problems
Return times, nonconventional ergodic averages, mixing of all orders.

Past work includes convergence problems for positive operators.

Honors, Awards.

IBM junior award, UNC Chapel-Hill
   University Council Research grant , UNC Chapel-Hill
   NSF grant (principal Investigator) 1990-1997
   NSF, AMS travel grant to the 1st inter. Conf. in South Africa.Summer 1997
   Teaching Award, "Favorite Faculty" , UNC Chapel-Hill.1996
   Invited one hour-address-AMS meeting-Winston-Salem- October 1998.
NSF Grant 2000-2001-"On line teaching and learning in Mathematics".(project director- PI)
NSF Grant for 2003,2004, 2006,2007,2008, 2009 Ergodic Workshop
Member of the Committee of Academic Tenure and Employment Security of the AMS 2001-2004
Member of FITAC UNC Chapel Hill-2001-2004
Member of the Faculty Council UNC Chapel Hill
Marquis who's who,
Serv ed on the Panel Review for Howard University Mathematical Program, 2001
Served on the 2005, 2006, 2007 (Chair) NSF Graduate fellowshipPanel-
Finalist The Benjamin Banneker award, 2006

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Publications from 1982-1990 (Mathscinet- http://www.ams.org/mathscinet)

Publications and Preprints-1990-present

<>BOOK: 1) Wiener Wintner Ergodic theorems: 228 pages, World Scientific Pub Co; 2003
ISBN: 9810244398
Editor Proceedings       2) Chapel Hill Ergodic Workshops: American Mathematical Society, Contemporary Mathematics, Vol 356, 2004.
                                      3) Ergodic Theory and Related Fields, American Mathematical Society, Contemporary Mathematics Vol. 430, 2007 <>
                                       4) Ergodic Theory , American mathematical Society, Contemporary Mathematics, vol 485, 2009.

   1) Minimal Convergence on Lp spaces ,
        Ergodic Theory and Dynamical Systems ,10, 411-421, 1990
    2) An equivalent measure for some nonsingular transformations and applications,
         Studia Mathematica, 97, 1-12, 1990 (with J.Wos)
    3) The helical trasnform as a connection between ergodic theory and harmonic analysis
         Trans of the Amer. Math. Soc., vol 331, 1,p.131-142, 1992 (with K. Petersen)
    4) Some connections between ergodic theory and harmonic analysis
     Proc. of the Int. Conf. in Prob. and Erg. Th. . Evanston, Illinois, 1991(with K. Petersen and H. White)
    5) Universal weights from dynamical systems to mean bounded positive operators
       Proc. of the Int. Conf. in Prob. and Erg. Th. Evanston, Illinois, 1991.
    6) A Wiener-Wintner property for the helical transform"
        Erg. Th. and Dyn. Sys. , 12, 185-194,1992
    7) The Wiener-Wintner property for the helical transform of the shift on [0,1]Z,
       Erg. Th. and Dyn. Systems 12, 659-672, 1992.
    8) The return times and the Wiener Wintner property for Mean bounded positive operators
       Erg. Th. and Dyn. Systems 12, 1-12, 1992
    9) The helical transform and the a.e. convergence of Fourier Series,
         Illinois Journal of mathematics, vol 37, 1, 123-147, 1993
10) Uniform Wiener-Wintner Theorems for weakly mixing dynamical systems
         (preprint 1993- unpublished-available)
11) Wiener Wintner return times ergodic theorem,
          Israel J. of Math , 92, p.375-395 , 1995 (with E. Lesigne and D. Rudolph)
12) Strong laws for weighted sums of iid random variables,
         Duke Math. J., vol 88, 217-246 , 1997.
13) Convergence of the pSeries for Stationary Processes
         Proc. of the New York Journal of Math. Conference, Vol 3A, p. 15-30, 1997
14) A weighted pointwise ergodic theorem
        Annales de l'Institut Henri Poincare , vol 34,n 1, 139-150,1998.
15)" Multiple recurrence and almost sure convergence of weakly mixing dynamical systems ",
         Israel J. of Math., vol 103, 111-125, 1998.
16) Corrections to " A Wiener-Wintner property for the helical transform"
        Erg. Th. and Dyn. Sys.,vol 18,1331-1333 (1998).
17) A note on the equation y=(I-T)x in L1
       Illinois J. of Math. vol 43, 3, (1999) p. 540-541;
18) Multiterm return time theorem for weakly mixing systems
         Annales de L'Institut Henri Poincare,vol 36,2,153-165,(2000).
19) Wiener Wintner theorems,
        Kluwer Encyclopaedia of Mathematics , accepted (May 2000).
20) Properties of Wiener Wintner dynamical systems(with K. Nicolaou)
       Bull. Soc. Math. France, 129, (3), 2001, p. 361-377.
21) Spectral Characterization of Wiener Wintner Dynamical systems,Compte Rendus de l'Academie des Sciences
         t. 332, Serie I, p.321-324, 2001.
22) Spectral Characterization of Ergodic Dynamical Systems,
      ContemporaryMathematics , 284, 13-22, 2001.
23) Spectral Characterization of Wiener Wintner Dynamical Systems
       Erg.. Th. and Dynamical Systems, 24, 2, 347-365, 2004 , pdf file
24) Wiener Wintner Dynamical Systems
       Erg. Th.. and Dyn. Syst,23, 1637-1654, 2003.
25) Pointwise convergence of averages along cubes, preprint 2003,math.DS/0305388, , pdf file, dvi file
25') Pointwise convergence of averages along cubes II, preprint 2003,math.DS/0305403 pdf file
      dvi file
25'') Pointwise convergence along cubes for measure preserving systems. (preprint 2003).
     , pdf.file, dvi.file.
       Most parts of these papers have been combined in a single paper
    "Pointwise convergence of ergodic averages along cubes " (preprint 2004)
      available pdf .

25’’’) The final version of this paper is accepted in Journal d’Analyse Mathematique.

      J. Analyse Math. 110 (2010),241–269. and can be seen here pdf
26) An L1 counting problem in ergodic theory
     (preprint 2003) (with Z. Buczolich and D. Mauldin), math.DS/0307384,
    . Journal d'Analyse Mathematique, vol XCV, 221-241, 2005.
    pdf
27) Duality and the one sided ergodic Hilbert transform, (preprint 2003)
      Contemporary Mathematics 357, "Chapel Hill Ergodic Workshops", 81-90, 2004. pdf
28) Counting and convergence in ergodic theory, (preprint 2004)
      (with Z. Buczolich and D. Mauldin), Acta Univ. Carolinae, 45, 2004, 5-21.
29) Poitnwise convergence of nonconventional averages, (preprint 2003)
    Coll. Math., vol 102, 2, 245- 262, 2005.
     pdffile
30) Averages along cubes for not necessarily commuting measure preserving transformations.
      Contemporary Math., vol.430, 1-19, 2007 pdf
31) On the one sided Ergodic Hilbert transform (with M. Lin),
   Contemporary Mathematics, vol.430, 20- 39, 2007, pdf
32) On A. Zygmund 's differentiation conjecture (preprint 2006).
        math.CA/0609827
33) The (Lp, Lq) bilinear Hardy Littlewood function for the tail (with Zoltan Buczolich)
        Isr. J.Math., vol. 179, 173-188, 2010.

34) A maximal inequality for the tail of the bilinear Hardy-Littlewood function
(with Zoltan Buczolich)
Contemporary Mathematics, vol 485, 7-11, 2009.

35) The (L1, L1) bilinear Hardy-Littlewood function and Furstenberg averages
(with Zoltan Buczolich), Revista Matematica Iberoamericana 26.3 (2010), 861-890.

36) Pointwise characteristic factors for the multiterm return times theorem.

(with K. Presser), accepted in Erg. Th. And Dyn. Syst. pdf- 2011

ERGODIC THEORY WORKSHOPS ORGANIZED:
Summer 2002:
February 2003:
February 2004.:
Proceedings: Chapel Hill Ergodic Theory workshops; Contemporary Mathematics, Vol 356, 2004.
February 2005:
February 2006
Proceedings: Ergodic Theory and Related Fields: Contemporary Mathematics, Vol 430, 2007

February 2007:
February 2008:

February 2009

Proceedings: Ergodic Theory , American Mathematical Society, Contemporary Mathematics, vol 485, 2009.

April-29-May 02-2010

March 17-21- 2011

March 22-25- 2012

STUDENTS :

1) PHd students
Katerina Nicolaou (PHD) - "Some properties of Wiener Wintner dynamcial systems"- May 2001.
David Duncan (PHD) - " A Wiener Wintner double recurrence theorem"- November 2001.

2) Masters of Sciences

Emmanuel Bonuedie- Minimality of interval exchange transformations- 2011.

Carole Agyemanh Prempeh,- Cutting and Stacking in ergodic theory- 2011.

      Kim Noonan- Birkhoff's theorem and the return times for the tail.- 2003.
      Kim   Presser - "J. Bourgain's return times theorem" - 1995
      Leonard Choup -"Mean Convergence of (1/N) Sum T^n f S^ng when S and T Commute, and T, S, with T S^(-1) have Finitely Many
      Ergodic Components" - May 2001

<> 3) Undergraduate Honors Projects
      Tom Peng - "The central limit theorem" -1998 (Highest honors)
      Elaina Blanks - "Continuous Nowhere differentiable functions- 2000 (honors).
      Ben Dodson - " R. C. Vaughan's proof of the Bombieri-Vinogradov theorem"- 2005 (Highest Honors)
      Megan Somerday- "On Littlewood conjecture" . April 2006 - Honors
      Erica Zuhr. Henderson Prize- "On the Besicovich set". April 2007- Honors

Chase Debnam: “Lebesgue Differentiation theorem“ . April 2010- Honors

COLLABORATION -UNC Chapel Hill and the Kwame Nkrumah University of Science and Technology (Kumasi- GHANA)

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