Idris Assani

Affiliation

Department of Mathematics

University of North Carolina at Chapel Hill

Position

            Professor, Department of Mathematics

Education

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

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

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 324 I.

  TEACHING INFO

Office hours (Fall 2007) --Monday-Wed 11:00 am -noon and by appointment.

 Course: Math 521 .

Contacts

Email : assani@math.unc.edu

          assani@email.unc.edu

Phone : (919) 962-9620

FAX : (919) 962-9620 or (919) 962 2568

Online Classroom

Online Math Help Center

Enter Online Classroom...

Enter Online Classroom.Instructor..

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 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

                  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 <>

   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,
      Contemporary Mathematics , 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 "
      available  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,   pdf
31) On the one sided Ergodic Hilbert transform (with M. Lin),
     Contemporary Mathematics,  vol.430 , 20- 39,  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)
       (Preprint 2007)

34)  A maximal inequality for the tail of the bilinear Hardy-Littlewood function (with Zoltan Buczolich)
       (preprint 2007)  accepted, to appear in Contemporary  Mathematics

35)  The (L1, L1) bilinear Hardy-Littlewood function for the tail (with Zoltan Buczolich)
       (in preparation)

    

  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

LIST of  REVIEWS :   List of math reviews

TECHNICAL REPORT  :"Teaching Linear Algebra using the Computer" (August 1998)

STUDENTS  :
 Current students:
   Undergraduate Honors  Projects  - Megan Somerday-  "On Littlewood conjecture" . April 2006  - Honors
                                                           - Erica Zuhr. Henderson Prize- "On the Besicovich set". April 2007- Honors

   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

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

     This page is under construction, please stay tuned...