Idris Assani


place: Born in Niger, but from Benin

M.S. (1981) , University Paris Dauphine , Commerce (1981);

The Doctorat 3 eme cycle 1981 - Pure mathematics- University Pierre and Marie
Curie- Paris 6-
thesis: Multivalued Conditional Expectation and Multivalued Martingales; Advisor: R. Pallu de la Barriere.
Doctorat es Sciences 1986- Pure mathematics- University Pierre et Marie Curie Paris 6-
thesis: Contribution to the Ergodic Theory of Operators, and Multivalued Maps with Values in a Banach Space; Advisor: A. Brunel

: Professor of Mathematics at the University of North Carolina-Chapel Hill.


Idris Assani earned the Master of Sciences , University Paris Dauphine , Commerce (1981); Doctorat 3eme cycle, University Paris 6,-adviser (R. Pallu de la Barriere)-Pure Math (1981); and in 1986 Doctorat d'Etat , University Paris 6, adviser (A. Brunel) -Pure Math.

A Mathematician's eye for quality shows that though he was an excellent researcher, Dr. Assani ran into North Carolina racism in the 1990's. Here is what happened:

"I came to the USA in 1988 knowing very little about the country and trusting the UNC Chapel Hill Math department who invited me. But soon enough I find myself forced to go to courts and to the AMS Council to have my work and abilities recognized. My legal actions were settled in 1995 year I was finally promoted to the rank of Associate Professor with tenure. As part of the settlement (may be To make up for all that has gone wrong) I was allowed to apply for promotion to Full Professor one year later. I was promoted to Full Professor after a full review (more than 2/3 yes) on July 1 1996. I then became the first black mathematician tenured associate professor and the first to be promoted to the rank of Full professor at the oldest public university in the country (more than 200 years old). I am certainly the only one in the history of the department to be promoted from Associate to Full professor in one year.The struggle is not over as mentalities are very difficult if not impossible to change and it is not easy to stay here. I used my struggle to open up the admission of Black graduate students in the department. I was told that there was only one Black student in the entire history of the department who got a PHD and it was before I came to Chapel Hill. There are now 3 black graduate students in the department preparing Masters and PHD."

Idris Assani's papers are referenced below. However, after picking one of his papers as one of the best, I asked Dr. Assani what were his "favorite" works of his own. He said,

"Most of my favorite recent papers were written during this period [late 1990s]. You picked the Duke Mathematical Journal paper Strong laws for weighted sums of independent identically distributed random variables.(which extends with new methods results obtained jointly by J. Bourgain (1994 Fields medalist), H. Furstenberg,Y. Katznelson and D. Ornstein. Another one is Multiple recurrence and almost sure convergence for weakly mixing dynamical systems that gives the best possible result to date on H. Furstenberg famous conjecture on a.e. multiple recurrence for dynamical systems. Another one was presented to the one hour invited AMS address I gave in October 1998. It is a preprint submitted now to the Journal d"Analyse mathematique "Wiener -Wintner dynamical systems" . The paper is in postcript font and can be downloaded by clicking on my webpage on "Winston Salem meeting Abstract and preprint" then on Finally another recent preprint is "Multiterm return time theorem for weakly mixing systems" to appear in Annales de l'Institut Henri Poincare. On the older papers I could pick Rota's alternating procedure with nonpositive operators and others which solved questions raised by my adviser "Antoine Brunel" in the two papers that appeared in Canadian journal of mathematics and Canadian Bulletin of Mathematics."

Dr. Assani's email:

Also see the web page: Who are the greatest Black Mathematicians?

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.

Areas of interest: Dynamics, Ergodic Theory


  1. Assani, Idris. Wiener Wintner Ergodic Theorems, World Scientific. Publishing Co., Inc., River Edge, NJ, 2003. xii+216 pp. ISBN: 981-02-4439-8


A listing of Dr. Assani's recent, but unpublished works can be found at his web site. According to Mathematical Reviews, Idris Assani has published 35 papers in Mathematics.

  1. Assani, Idris Properties of Wiener Wintner Dynamical Systems, Ergodic Theory and Dynamical systems. Bull. Soc. Math. France 129 (2001), no. 3, 361--377.
  2. Assani, Idris Caractérisation spectrale des systèmes dynamiques du type Wiener-Wintner. (French) [Spectral characterization of Wiener-Wintner dynamical systems] C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 4, 321--324.
  3. Assani, I. Spectral characterization of ergodic dynamical systems. Council for African American Researchers in the Mathematical Sciences, Vol. IV (Baltimore, MD, 2000), 13--22, Contemp. Math., 284, Amer. Math. Soc., Providence, RI, 2001.
  4. Assani, I. Multiple return times theorems for weakly mixing systems. Ann. Inst. H. Poincaré Probab. Statist. 36 (2000), no. 2, 153--165.
  5. Assani, I. A note on the equation $Y=(I-T)X$ in $L\sp 1$. Proceedings of the Conference on Probability, Ergodic Theory, and Analysis (Evanston, IL, 1997). Illinois J. Math. 43 (1999), no. 3, 540--541.
  6. Assani, I. A weighted pointwise ergodic theorem . Ann. Inst. H. Poincaré Probab. Statist. 34 (1998), no. 1, 139--150.
  7. Assani, I. Multiple recurrence and almost sure convergence for weakly mixing dynamical systems . Israel J. Math. 103 (1998), 111--124.
  8. Assani, I. Convergence of the $p$-series for stationary sequences . New York J. Math. 3A (1997/98), Proceedings of the New York Journal of Mathematics Conference, June 9--13, 1997, 15--30 (electronic).
  9. Assani, I. Corrections to: "A Wiener-Wintner property for the helical transform" [Ergodic Theory Dynam. Systems {12} (1992), no. 2, 185--194; MR 93h:28023]. Ergodic Theory Dynam. Systems 18 (1998), no. 5, 1331--1333.
  10. Assani, I. Strong laws for weighted sums of independent identically distributed random variables. Duke Math. J. 88 (1997), no. 2, 217--246.
  11. Assani, I.; Lesigne, E.; Rudolph, D. Wiener-Wintner return-times ergodic theorem . Israel J. Math. 92 (1995), no. 1-3, 375--395.
  12. Assani, I. The Wiener-Wintner property for the helical transform of the shift on $[0,1]\sp {Z}$ . Ergodic Theory Dynamical Systems 12 (1992), no. 4, 659--672.
  13. Assani, I. The helical transform and the a.e. convergence of Fourier series . Illinois J. Math. 37 (1993), no. 1, 123--146.
  14. Assani, I. A Wiener-Wintner property for the helical transform . Ergodic Theory Dynamical Systems 12 (1992), no. 2, 185--194.
  15. Assani, I. The return times and the Wiener-Wintner property for mean-bounded positive operators in $L\sp p$ . Ergodic Theory Dynamical Systems 12 (1992), no. 1, 1--12.
  16. Assani, Idris; Petersen, Karl; White, Homer Some connections between ergodic theory and harmonic analysis . Almost everywhere convergence, II (Evanston, IL, 1989), 17--40, Academic Press, Boston, MA, 1991.
  17. Assani, Idris Universal weights from dynamical systems to mean-bounded positive operators on $L\sp p$ . Almost everywhere convergence, II (Evanston, IL, 1989), 9--16, Academic Press, Boston, MA, 1991. )
  18. Assani, Idris; Petersen, Karl The helical transform as a connection between ergodic theory and harmonic analysis. Trans. Amer. Math. Soc. 331 (1992), no. 1, 131--142.
  19. Assani, I.; Wo\'s, J. An equivalent measure for some nonsingular transformations and application . Studia Math. 97 (1990), no. 1, 1--12.
  20. Assani, I. Minimal convergence on $L\sp p$ spaces . Ergodic Theory Dynamical Systems 10 (1990), no. 3, 411--420.
  21. Assani, I. Rota's alternating procedure with nonpositive operators . Adv. Math. 77 (1989), no. 2, 183--188.
  22. Assani, I. Estimates of positive linear operators on $L\sp p$ . Proc. Amer. Math. Soc. 104 (1988), no. 1, 193--196.
  23. Assani, I. Alternating procedures in uniformly smooth Banach spaces . Proc. Amer. Math. Soc. 104 (1988), no. 4, 1131--1133.
  24. Assani, I. Inégalites maximales et propriétés ergodiques ponctuelles . (French) [Maximal inequalities and point ergodic properties] Séminaire d'Analyse Fonctionelle 1985/1986/1987, 205--218, Publ. Math. Univ. Paris VII, 28, Univ. Paris VII, Paris, 1988.
  25. Assani, Idris; Mesiar, Radko On the a.e. convergence of $T\sp nf/a\sb n$ in $L\sb 1$-space, Proceedings of the 13th winter school on abstract analysis (Srní, 1985). Rend. Circ. Mat. Palermo (2) Suppl. No. 10 (1985), 57--61 (1986).
  26. Assani, I. Sur la convergence ponctuelle de quelques suites d'opérateurs, (French) [On the pointwise convergence of some operator sequences] Canad. Math. Bull. 30 (1987), no. 2, 134--141.
  27. Assani, I. Quelques théorèmes ergodiques dans les espaces $L\sp p\sb E$, (French) [Some ergodic theorems in $L\sp p\sb E$-spaces] Ann. Inst. H. Poincaré Probab. Statist. 23 (1987), no. 2, 209--224.
  28. Assani, I.; Courbage, M. On the loss of information in the transition from deterministic systems to probabilistic processes, Lett. Math. Phys. 12 (1986), no. 4, 257--265.
  29. Assani, I. Sur les opérateurs à puissances bornées et le théorème ergodique ponctuel dans $L\sp p[0,1]$, $1<p<+\infty$, (French) [Operators with bounded powers and the pointwise ergodic theorem in $L\sp p[0,1]$, $1 Canad. J. Math. 38 (1986), no. 4, 937--946.
  30. Assani, Idris Quelques propriétés mesurables de diverses suites d'un espace de Banach séparable $E$ dans $E\sp {N}$., (French) [Some measurable properties of various sequences of a separable Banach space $E$ in $E\sp {\bf N}$] Math. Scand. 58 (1986), no. 2, 301--310.
  31. Assani, I. On the punctual and local ergodic theorem for nonpositive power bounded operators in $L\sp p\sb{{C}}[0,1],\;1<p<+\infty$, Proc. Amer. Math. Soc. 96 (1986), no. 2, 306--310.
  32. Assani, Idris Sur une propriété borélienne des suites relativement faiblement complètes dans un espace de Banach, (French) [A Borel property of weakly complete sequences in a Banach space] C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 14, 691--694.
  33. Assani, Idris; Mesiar, Radko Sur la convergence ponctuelle de $T\sp nf/n\sp \alpha$, dans $L\sp p$., (French) [Pointwise convergence of $T\sp nf/n\sp \alpha$ in $L\sp p$] Ann. Sci. Univ. Clermont-Ferrand II. Probab. Appl. No. 3 (1985), 21--29.
  34. Assani, Idris Quelques résultats sur les opérateurs positifs à moyennes bornées dans $L\sb p$, (French) [Some results on $L\sb p$ mean bounded positive operators] Ann. Sci. Univ. Clermont-Ferrand II. Probab. Appl. No. 3 (1985), 65--72.
  35. Assani, Idris Une caractérisation des Banach réticulés faiblement séquentiellement complets, (French) [A characterization of weakly sequentially complete Banach lattices] C. R. Acad. Sci. Paris Sér. I Math. 298 (1984), no. 18, 445--448.
  36. Assani, Idris; Klei, Heinz-Albrecht Parties décomposables compactes de $L\sp{1}\sb{E}$, (French) [Decomposable compact subsets of $L\sp{1}\sb{E}$] C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 16, 533--536.
  37. Assani, Idris Quelques résultats liés aux ensembles décomposables de $L\sp{1}\sb{E}$, (French) [Some results concerning decomposable sets of $L\sp{1}\sb{E}$] C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 19, 641--644.


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