Department of Mathematics and Philosophy

Iraj Kalantari

Iraj Kalantari

Emeritus Professor


Ph.D., Cornell University (Logic, Anil Nerode)

M.S., Cornell University (Applied Mathematics, Lawrence Payne)

B.S., University of Wisconsin, River Falls (Mathematics/Physics, Curt Larson)

Contact Information:

456 Morgan Hall

Research Interests:

Research: My main area of interest is computability. In particular, my work has been in computability in topology and in analysis where the objects of interest have been those that are computable, those that are incomputable, and those that are computably incomputable.

Research with graduate students: I am interested in working with students who are directed, or who become directed, in pursuing a Ph.D. focusing on aspects of computability in mathematics.

Research with undergraduate students: I am interested in helping students find a specific theorem in a junior or senior level mathematics course, and researching it. This research could include the history of, the variety of the proofs for, and the applications of that theorem. Students would be expected to consult various textbooks and accessible journals to gather and examine different proofs or applications, and to write a paper on their findings. I am also interested in helping students develop a computer animation/study of a theorem and its proof, or of a phenomenon in dynamical systems or cellular automata (or similar areas). Students would write a paper and a program demonstrating thoughtful understanding of the theorem, its proof, and its computer illustration.

Selected Publications:

  • Kalantari, I., & Welch, L. (2013). When series of computable functions with varying domains are computable. MLQ Math. Log. Q.59, no. 6, 471–493.
  • Kalantari, I., & Andreev, F. (2012). Collinearity of iterations and real plane algebraic curves. Voronoi Diagrams in Science and Engineering (ISVD), pp. 126-131.
  • de Biasi, S. C., Kalantari, B., & Kalantari, I. (2011). Mollified zone diagrams and their computation. Transactions on computational science. XIV, 31–59, Lecture Notes in Comput. Sci., 6970, Springer, Heidelberg.
  • Enayat, A., & Kalantari, I. (2010). Preface [The proceedings of the IPM 2007 Logic Conference]. Held in Tehran, June 10–17, 2007. Ann. Pure Appl. Logic 161, no. 6, 709–710.
  • Kalantari, I. (2007). Induction over the continuum. Induction, algorithmic learning theory, and philosophy, 145–154, Log. Epistemol. Unity Sci., 9,; Springer, Dordrecht.
  • Kalantari, I., & Welch, L. (2006). Specker's theorem, cluster points, and computable quantum functions. Logic in Tehran, 134–159, Lect. Notes Log., 26, Assoc. Symbol. Logic, La Jolla, CA
  • Andreev, F., Kalantari, B., & Kalantari, I. (2004). Animation of mathematical concepts using polynomiography. Proceeding SIGGRAPH '04, ACM SIGGRAPH, Educators program, p. 27 (
  • Kalantari, I., & Welch, L. (2004). A blend of methods of recursion theory and topology: a Π  0 1 tree of shadow points. Arch. Math. Logic 43, no. 8, 991–1008.
  • Kalantari, I., & Welch, L. (2004). Density and Baire category in recursive topology. MLQ Math. Log. Q. 50, no. 4-5, 381–391.
  • Kalantari, I.&  Welch, L. (2003). A blend of methods of recursion theory and topology. Ann. Pure Appl. Logic 124, no. 1-3, 141–178. 
  • Kalantari, I., & Welch, L. (1999). Recursive and nonextendible functions over the reals filter foundation for recursive analysis. II. Ann. Pure Appl. Logic 98, no. 1-3, 87–110.
  • Brattka, V., & Kalantari, I. (1998). A bibliography of recursive analysis and recursive topology. Handbook of recursive mathematics, Vol. 1, 583–620, Stud. Logic Found. Math., 138, North-Holland, Amsterdam. 
  • Kalantari, I., & Welch, L. (1998). Point-free topological spaces, functions and recursive points filter foundation for recursive analysis. I. Computability theory. Ann. Pure Appl. Logic 93, no. 1-3, 125–151.
  • Kalantari, B., & Kalantari, I. (1997)Zaare-Nahandi, Rahim. A basic family of iteration functions for polynomial root finding and its characterizations. J. Comput. Appl. Math. 80, no. 2, 209–226. 
  • Kalantari, I., & Weitkamp, G. (1987). Effective topological spaces. III. Forcing and definability. Ann. Pure Appl. Logic 36, no. 1, 17–27.
  • Kalantari, I., & Weitkamp, G. (1985). Effective topological spaces. II. A hierarchy. Ann. Pure Appl. Logic 29, no. 2, 207-224.
  • Kalantari, I., & Weitkamp, G. (1985). Effective topological spaces. I. A definability theory. Ann. Pure Appl. Logic 29, no. 1, 1-27.
  • Jockusch, C.G., Jr., & Kalantari, I. (1984). Recursively enumerable sets and van der Waerden's theorem on arithmetic progressions. Pacific J. Math. 115, no. 1, 143-153.  
  • Kalantari, I., & Remmel, J. B. (1983). Degrees of recursively enumerable topological spaces. J. Symbolic Logic 48, no. 3, 610-622.
  • Kalantari, I., & Leggett, A. (1983). Maximality in effective topology. J. Symbolic Logic 48, no. 1, 100-112. 
  • Kalantari, I., &  McDonald, G. (1983). A Data Structure and an Algorithm for the Nearest Point Problem, IEEE Transactions on Software Engineering, Vol. 9, no. 5, pp. 631-634.
  • Kalantari, I. (1982). Major subsets in effective topology. Patras Logic Symposion (Patras, 1980), 77-94, Stud. Logic Foundations Math., 109, North-Holland, Amsterdam-New York.  
  • Kalantari, I. (1981). Effective content of a theorem of M. H. Stone. Aspects of effective algebra (Clayton, 1979), pp. 128-146, Upside Down A Book Co., Yarra Glen, Vic.
  • Kalantari, I., & Retzlaff, A. (1977). Maximal vector spaces under automorphisms of the lattice of recursively enumerable vector spaces. J. Symbolic Logic 42, no. 4, 481-491.