International Intensive Courses

dedicated to Dirac operators, Hypercomplex and Harmonic Analysis

Please pay attention to the following rules for the online courses:


  1. It is highly appreciated if you use your real and complete name when entering the system. 

  1. Switch your microphone off when the lecture begins. You can switch it back when asking questions or replying. 

(!) un-authorized recording and distribution is illegal and it will be reported to the competent authorities.

Time zone converter

Most common time zones (recall, some countries changed already to Standard Time, or Winter Time):

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  2. CST (China Standard Time)

  3. EST zone (Eastern Standard Time)

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The online series of International Intensive Courses dedicated to Dirac operators, Hypercomplex and Harmonic Analysis are jointly organized by Chapman University, Politecnico di Milano, and University of Aveiro. These sequence of events will take place online and are directed to postgraduate students, young researchers, and all who wishes to expand their knowledge on current topics in these and related areas.

Courses will occur with a trimestral frequency. Interested participants are kindly request to register via the on-line form:

3rd Course - May 16 to May 27, 2022. November 23 to December 04, 2020.

(online platform ZOOM)

Lecturer: Professor Alexander Strohmaier, School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

Title: Dirac operators in Spectral Geometry and Mathematical Physics

Tentative schedule: (see below for a time converter)

Wednesday May 18,  14:30 - 15:30  (GMT)




Friday May 20,  14:30 - 15:30  (GMT)




Monday May 23,  14:30 - 15:30  (GMT)




Wednesday May 25,  14:30 - 15:30  (GMT)


Friday May 27,  14:30 - 15:30  (GMT) A

Reading List:

Nicole Berline, Ezra Getzler, Michèle Vergne: Heat Kernels and Dirac operators, Springer, 1992

Helga Baum, Ines Kath : Normally hyperbolic operators, the Huygens property and conformal geometry, Ann Glob Anal Geom 14, 315–371 (1996)

John Roe: Elliptic operators, topology and asymptotic methods, Second Edition, Chapman & Hall, 1999

Blaine Lawson, Marie-Louise Michelsohn: Spin Geometry, Princeton University Press, 1989

Lars Hörmander: The Analysis of Linear Partial Differential Operators I, II, III, Springer

Michael Taylor: Partial Differential Equations I, II, II, Springer, 2nd ed. 2011

Hitoshi Kumano-Go: Pseudo-Differential Operators, MIT Press, 1982

Bernd Thaller: The Dirac equation, Springer, 1992

Christian Baer, Nicolas Ginoux, Frank Pfaeffle: Wave Equations on Lorentzian Manifolds and Quantization, ESI Lectures in Mathematics and Physics, EMS Publishing House, 2007

Liangpan Li, Alexander Strohmaier: The local counting function of operators of Dirac and Laplace type, Journal of Geometry and Physics, Vol. 104, 204-228, (2016) 

Christian Bär, Alexander Strohmaier: Local Index Theory for Lorentzian Manifolds, 2020

Lecture 1. Basic notions of global Analysis: distribution sections of vector bundles, Dirac and Laplace operators

Lecture 3. Spectral theory of Dirac-type operators on closed Riemannian manifolds. Weyl laws, counting functions, eta invariants. Heat kernel methods vs FIO methods and the relation between them.

Lecture 5. Index theory. Sketch of the Atiyah-Singer index theorem and trace formulae

1st Course - November 23 to December 04, 2020. 

Lecturer: Professor Daniel Alpay, Chapman University, Orange, CA, USA

Title: A Course on Positive Definite Functions and Reproducing Kernel Spaces

2nd Course - December 06 to December 09, 2021. 

Lecturer: Professor David F. Walnut, George Mason University, Fairfax, VA 22030, USA

Title: Fundamentals of Time-Frequency Analysis and Wavelet Theory


Lecture 2. Geometry and Analysis of Dirac and Laplace operators: spin connection, compatibility, regularity

Lecture 4. Dirac type operators on space-times, relation to the Riemannian Dirac operator, fundamental solutions, Hadamard expansion and eta invariants.


This event is supported by the

International Society for Analysis, its Applications, and Computation