» Center of Excellence in Complex and Hypercomplex Analysis

A group of mathematicians and physicists from the Schmid College of Science and Technology at Chapman University joined some of their national and international collaborators to form this Center of Excellence. The research conducted under the center's umbrella is mainly motivated by the latest results in Clifford and Hypercomplex Analysis and endeavors to find new ways in which this research can be applied in mathematics and physics. The members of this center of excellence draw on their research experience and use analytical and computational techniques to build sound differential and integral theories in this context, as well as possible applications in Quantum Physics and other interdisciplinary fields.

Complex Analysis is a classical branch of mathematics, having its roots in late 18th and early 19th centuries, which investigates functions of one and several complex variables. It has applications in many branches of mathematics, including Number Theory and Applied Mathematics, as well as in physics, including Hydrodynamics, Thermodynamics, Electrical Engineering, and Quantum Physics.

Clifford Analysis is the study of Dirac and Dirac type operators in Analysis and Geometry, together with their applications. In 3 and 4 dimensions Clifford Analysis is referred to as Quaternionic Analysis. Furthermore, methods and tools of Clifford Analysis are extended to the field of Hypercomplex Analysis.

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  • International Conference on Complex Analysis and Operator Theory

    Celebrating Daniel Alpay’s 60th birthday

    The “International Conference on Complex Analysis and Operator Theory - Celebrating Daniel Alpay’s 60th birthday” which will take place at Chapman University, Orange, California, November 4-7, 2016.


    The main topics of the conference are complex analysis, operator theory and other areas of mathematics which have been touched by Professor Daniel Alpay during his fertile scientific activity. This meeting will be the perfect occasion to celebrate his 60th birthday among friends and collaborators.

    Daniel Alpay has graduated in 1986 from the Weizmann Institute of Science with the Ph.D. thesis: "Reproducing kernel Krein spaces of analytic functions and inverse scattering".
    Since 1991 Daniel was a member of the Department of Mathematics, at Ben Gurion University, Beer-Sheva, Israel where he has been tenured since 1995. In December 2005, Daniel was awarded the Earl Katz family chair in algebraic system theory.
    Throughout his career, Daniel was an initiator and editor-in-chief of the journal, Complex Analysis and Operator theory published by Birkhauser whose first issue appeared in January 2007.
    Since 2005 he was also a co-editor of the subseries called "Linear Operators and Linear Systems" of the series "Operator Theory: Advances and Applications", as well as member of the editorial board of four other journals.
    His prolific career has spanned 230 papers and 6 books and counting.
    Daniel's current research interests include: Schur analysis in the setting of slice-hyperholomorphic functions, infinite dimensional analysis in the white noise space setting, and free analysis, rational functions and applications to linear system theory and wavelets, Schur analysis in the setting of bicomplex functions, operator theory and Riemann surfaces.

    There will be no registration fee, and we are happy to say that all the lunches and the social dinner will be provided.

    Committees:

    • Scientific: F. Colombo, D.C. Struppa, M.B. Vajiac, A. Vajiac
    • Organizing: I. Sabadini, M.B. Vajiac

    List of confirmed speakers: J. Behrndt, V. Bolotnikov, F. Colombo, J. Gantner, W. Helton, T. Hempfling, P. Jorgensen, H.T. Kaptanoglu, E. Kvaalen, D. Levanony, I. Lewkovicz, M. Mboup, A. Pinhas, I. Sabadini, B. Schneider, A. Sebbar, D.C. Struppa, M.B. Vajiac, A. Vajiac, D. Volok, A. Yger

    Directions and Travel Information

    Schedule of events

    Book of Abstracts

  • Chapman Faculty Members

    Yakir Aharonov Yakir Aharonov
    Research Interests: Quantum Physics
    Contact: Professor of Theoretical Physics, James J. Farley Professor of Natural Philosophy, Chapman University, Orange, California, USA
    Email: aharonov@chapman.edu
    Daniele Struppa Daniele C. Struppa
    Research Interests: Quaternionic and Hypercomplex Analysis, Microlocal Analysis
    Contact: Chancellor of Chapman University, Orange, California, USA
    Email: struppa@chapman.edu
    Jeff Tollaksen Jeff Tollaksen
    Research Interests: Quantum Physics
    Contact: Associate Professor of Physics, Chapman University, Orange, California, USA
    Email: tollakse@chapman.edu
    Adrian Vajiac Adrian Vajiac
    Research Interests: Quaternionic and Hypercomplex Analysis, Computational Algebra, Quantum Field Theory, Foundations of Geometry
    Contact: Associate Professor of Mathematics, Chapman University, Orange, California, USA
    Email: avajiac@chapman.edu
    Mihaela Vajiac Mihaela B. Vajiac, Director
    Research Interests: Quaternionic and Hypercomplex Analysis, Computational Algebra, Differential Geometry, PDEs, Integrable Systems
    Contact: Associate Professor of Mathematics, Chapman University, Orange, California, USA
    Email: mbvajiac@chapman.edu

    External Faculty Members

    Fabrizio Colombo Fabrizio Colombo
    Research Interests: Functional Calculus, Applications to Physics, Compatibility Conditions, Symmetries, PDEs.
    Contact: Associate Professor, Politecnico di Milano, Italy
    Email: fabrizio.colombo@polimi.it
    Hendrik De Bie Hendrik De Bie
    Research Interests: Hypercomplex Analysis.
    Contact: Assistant Professor, Department of Mathematical Analysis, Universiteit Gent
    Email: hendrik.debie@ugent.be
    Maria Elena Luna Elizarraras Maria Elena Luna Elizarraras
    Research Interests: Clifford Analysis, Hypercomplex analysis.
    Contact: Professor, Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Mexico City, Mexico
    Email: eluna@esfm.ipn.mx
    Graziano Gentili Graziano Gentili
    Research Interests: Quaternionic Analysis
    Contact: Professor, Dipartimento di Matematica "U.Dini", Universita di Firenze, Italy
    Email: graziano.gentili@math.unifi.it
    Irene Sabadini Irene Sabadini
    Research Interests: Syzygies, Free Resolutions, Hilbert function, Duality Theorems.
    Contact: Associate Professor, Politecnico di Milano, Italy
    Email: irene.sabadini@polimi.it
    Ahmed Sebbar Ahmed Sebbar
    Research Interests: Complex Analysis, Number Theory, Differential Operators
    Contact: Professor, Exceptional Class, University of Bordeaux
    Email: Ahmed.Sebbar@math.u-bordeaux1.fr
    Michael Shapiro Michael Shapiro
    Research Interests: Clifford Analysis, Hypercomplex Analysis.
    Contact: Professor, Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Mexico City, Mexico
    Email: shapiro@esfm.ipn.mx
    Franciscus Sommen Franciscus Sommen
    Research Interests: Clifford Analysis.
    Contact: Professor, Department of Mathematical Analysis, Universiteit Gent
    Email: fs@cage.ugent.be
  • 2016: Series of 12 lectures on Operators of Infinite Order and Exact WKB Analysis, Professor Takashi Aoki, Kindai University

    Von Neumann Hall (545 W Palm), 9-11 a.m., August 22-26 and August 29th.

    Part I Differential operators, microdifferential operators and pseudodifferential operators of infinite order

    1. Introduction
    2. Algebraic definitions of pseudodifferential operators in complex analytic category
    3. Kernel functions
    4. Symbols of pseudodifferential operators and symbolic calculus
    5. Exponential calculus
    6. Applications

    Part II Exact WKB analysis

    1. Introduction
    2. WKB solutions of ODE of second order with a large parameter
    3. Borel sums of WKB solutions and connection formulas
    4. WKB solutions and microdifferential operators
    5. Higher-order equations and infinite-order equations
    6. Applications to special functions


    2014: Workshop on Integral transforms, boundary values and generalized functions

    Continuing the tradition established in the past two years, the Center of Excellence in Complex and Hypercomplex Analysis (CECHA) at Chapman University organized the Workshop during the period of October 17th to October 21st, 2014 with the topic: "Integral transforms, boundary values and generalized functions".

    The Organizing Committee and members of the CECHA:

    Schedule of the events and talks.

    List of speakers: D. C. Struppa, M.B. Vajiac, A. Vajiac, D. Alpay, M. Martin, P. Cerejeiras, D. Clahane, I. Sabadini, F. Colombo, G. Gentili, U. Kahler, M. Libine, C. Nolder, L. Cnudde, M. Shapiro, M.E. Luna-Elizarraras, A. Sebbar.


    2013: Workshop on Results in Mathematics and Physics obtained by Methods of Hypercomplex Analysis

    The Center of Excellence in Complex and Hypercomplex Analysis (CECHA) at Chapman University organized a Workshop during the period of November 7th 2013 to November 11th 2013, with the topic: "Results in Mathematics and Physics obtained by Methods of Hypercomplex Analysis".

    Schedule of Events

    The Organizing Committee and members of the CECHA:

    List of confirmed speakers:Daniele C. Struppa, Mihaela Vajiac, Adrian Vajiac, Maria Elena Luna Elizarraras, Michael Shapiro, Daniel Alpay, Craig Nolder, Irene Sabadini, Fabrizio Colombo, Graziano Gentili, Joao Morais, Matvei Libine, Thomas Hempfling, Dominic Rochon, Lander Cnudde.


    2012: Workshop on Function Theories for Bicomplex and Hyperbolic Numbers

    The Center of Excellence in Complex and Hypercomplex Analysis (CECHA) at Chapman University organized the workshop entitled Function Theories for Bicomplex and Hyperbolic Numbers, which took place at Chapman University, October 22-26, 2012, in the Sandhu Conference Center.

    Function Theories for Bicomplex and Hyperbolic numbers have recently gained momentum in the Mathematics and Physics communities. The goal of this workshop has been to provide and stimulate interaction and communication among the researchers whose scientific interests include these two areas of Mathematics.

    The talks and discussions were directly related to the Analysis of Bicomplex and Hyperbolic Numbers and their applications.

    The Organizing Committee and members of the CECHA:

    List of confirmed participants:Daniele C. Struppa, Adrian Vajiac, Mihaela Vajiac, Maria Elena Luna Elizarraras, Michael Shapiro, John Ryan, Dominic Rochon, Daniel Alpay, Franciscus Sommen, Uwe Kahler, Paula Cerejeiras, Matvei Libine, Sebastien Tremblay, Craig Nolder, Irene Sabadini, Fabrizio Colombo, Dana Clahane

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