I am a researcher and part-time teacher in pure mathematics.
My licentiate thesis treated the maximum principle for a generalization of complex analytic functions to generic embedded Cauchy-Riemann manifolds. Title: The Maximum Principle for Cauchy-Riemann Functions and Hypocomplexity (2012). My doctoral thesis was a continuation of my licentiate thesis, it primary subject is a subspecialty of partial differential equations, namely locally itegrable structures, and the schwerpunkt was maximum principles, hypoelliticity and uniqeness conditions for various generalizations of holomorphic functions om submanifolds. Title: Regularity and Uniqueness-related Properties of Solutions with Respect to Locally Integrable Structures (2014).
Following my dissertation my primary field or research has been the theory of polyanalytic functions and their various generalizations. I am currently also in collaboration with Per Åhag in the analysis group (that is within a specialty different from that of polyanalytic functions).
Selected recent publications:
A. Daghighi, S.G. Krantz, Local Maximum Modulus Property for Polyanalytic Functions, Complex Anal. Oper. Theory, 10 (2016), no.2, 401-408
A. Daghighi, F. Wikström, Level sets of certain subclasses of alpha-analytic functions, J. Partial Differential Equations, Vol 30 (2017), no.4, 281-298
A. Daghighi, A local maximum principle for locally integrable structures, Communications in Contemporary Mathematics, Vol. 19, no.1, (2017)
A. Daghighi, On A Uniqueness Condition For CR Functions On Hypersurfaces, Bulletin of Mathematical Analysis and Applications, Vol. 10, no 1, (2018), 68-79
A. Daghighi, Polyanalytic functions on subsets of Z[i], Aust. J. Math. Anal. Appl., vol.15, no.1, (2018), 1-26
A. Daghighi, A necessary condition for weak maximum modulus sets of 2-analytic functions, Collect. Math., vol. 69, no. 2, (2018), 173-180
A. Daghighi, Local characterization of q-analytic functions in terms of hypoanalytic functions, Folia Mathematica, Vol. 20, no.1, (2018), 28-37
A. Daghighi, A sufficient condition for locally open polyanalytic functions, Complex Variables and Elliptic Equations, (2019), Vol 64, iss. 10, 1733-1738
A. Daghighi, P.M. Gauthier, An algebra of polyanalytic functions, Colloqium Math., DOI: 10.4064/cm8274-9-2020, (2020)