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Personalbild Abtin Daghighi

Abtin Daghighi

Forskare och lärare i matematik.

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Anknuten som övrig/annan befattning till Institutionen för matematik och matematisk statistik
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MIT-huset, plan 3, Matematik och matematisk statistik Umeå universitet, 901 87 Umeå

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)

Colloquium Mathematicum, Vol. 165, (2) : 225-240
Daghighi, Abtin; Gauthier, Paul M.

Forskargrupper

Gruppmedlem

Fall 2020 and Spring 2021: Analysis for Engineers

Syllabus

Canvas (course material)

Cambro

Schedule (Time-Edit)

Spring 2021: Discrete mathematics

Syllabus

Canvas (course material)

Fall 2021: Statistics for engineers