Dr Kristian Evans

Associate Professor

Mathematics

k.evans@swansea.ac.uk

Fluent Welsh Speaker

Office - 321
Third Floor
Computational Foundry
Bay Campus

Available For Postgraduate Supervision

About

My research interests lie in Analysis and Probability, in particular in pseudo-differential operators and Levy-type processes. I am co-author (with Niels Jacob) of a series of Analysis textbooks, entitled A Course in Analysis. In recent years, I have enjoyed developing new Statistics teaching provision in the Mathematics Department, however I have also taught a wide range of topics in Mathematics, including Complex Analysis. I have a genuine interest in teaching in an engaging and inclusive way and I like to share good practice where appropriate. I am also the Programme Director for our Mathematics, Applied Data Science and Actuarial Science programmes.

Publications

Research Highlights

Evans, K. & WILLIAMS, A. (2024). A Tool to Visualise and Interact with Probability Density Functions - Development and Case Study. MSOR Connections, 23(1), 15-28.
https://doi.org/10.21100/msor.v23i1.1504, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa67698
Evans, K. & Jacob, N. (2022). Some Geometric Observations on Heat Kernels of Markov Semigroups with Non-local Generators. In A.M. Candela, M. Cappelletti Montano, E. Mangino (Ed.), Trends in Mathematics (pp. 333-362). Springer International Publishing
https://doi.org/10.1007/978-3-031-20021-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa64994
https://link.springer.com/chapter/10.1007/978-3-031-20021-2_17
Evans, K. & Jacob, N. (2022). On Non-negative Solutions to Space-Time Partial Differential Equations of Higher Order. In Springer Proceedings in Mathematics and Statistics (pp. 85-107). Springer Nature Singapore.
https://doi.org/10.1007/978-981-19-4672-1_6, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa59047
Evans, K., Fry, H., & Jacob, N. (2021). Fundamental solutions in $\psi$-Bessel potential spaces of certain generators of transient Lévy processes. Revue Roumaine Mathematiques Pures et Appliquees, 66(1), 157-177.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa55969
http://imar.ro/journals/Revue_Mathematique/php/2021/Rrc21_1.php
Evans, K. & Jacob, N. (2020). A Course in Analysis Vol. V: Functional Analysis, Some Operator Theory, Theory of Distributions. World Scientific.
https://doi.org/https://doi.org/10.1142/11695, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa53554
https://www.worldscientific.com/worldscibooks/10.1142/11695
Evans, K. & Jacob, N. (2011). Variable order subordination in the sense of Bochner and pseudo-differential operators. Mathematische Nachrichten, 284(8-9), 987-1002.
https://doi.org/10.1002/mana.200810246, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8059
Evans, K. & Jacob, N. (2020). On Adjoint Additive Processes. Probability and Mathematical Statistics, 40(2), 205-223.
https://doi.org/10.37190/0208-4147.40.2.2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa48685
https://www.math.uni.wroc.pl/~pms/publications.php?nr=40.2
Evans, K. (2018). An Overview of the Pingo Audience Response System in Undergraduate Mathematics and Statistics Teaching. MSOR Connections, 17(1), 25
https://doi.org/10.21100/msor.v17i1.828, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa45005
https://journals.gre.ac.uk/index.php/msor/article/view/828
Jacob, N. & Evans, K. (2018). A Course in Analysis Vol. IV: Fourier Analysis, Ordinary Differential Equations, Calculus of Variations World Scientific.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43213
https://www.worldscientific.com/worldscibooks/10.1142/11078
Jacob, N. & Evans, K. (2017). A Course in Analysis Vol. III: Measure and Integration Theory, Complex-Valued Functions of a Complex Variable World Scientific.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa35868
http://www.worldscientific.com/worldscibooks/10.1142/10548

All Research

Journal Articles

Evans, K. & WILLIAMS, A. (2024). A Tool to Visualise and Interact with Probability Density Functions - Development and Case Study. MSOR Connections, 23(1), 15-28.
https://doi.org/10.21100/msor.v23i1.1504, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa67698
Evans, K., Fry, H., & Jacob, N. (2021). Fundamental solutions in $\psi$-Bessel potential spaces of certain generators of transient Lévy processes. Revue Roumaine Mathematiques Pures et Appliquees, 66(1), 157-177.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa55969
http://imar.ro/journals/Revue_Mathematique/php/2021/Rrc21_1.php
Evans, K. & Jacob, N. (2020). On Adjoint Additive Processes. Probability and Mathematical Statistics, 40(2), 205-223.
https://doi.org/10.37190/0208-4147.40.2.2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa48685
https://www.math.uni.wroc.pl/~pms/publications.php?nr=40.2
Evans, K. (2018). An Overview of the Pingo Audience Response System in Undergraduate Mathematics and Statistics Teaching. MSOR Connections, 17(1), 25
https://doi.org/10.21100/msor.v17i1.828, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa45005
https://journals.gre.ac.uk/index.php/msor/article/view/828
Evans, K., Jacob, N., & Shen, C. (2015). SOME FELLER SEMIGROUPS ON C_∞(R^n×Z^m) GENERATED BY PSEUDO-DIFFERENTIAL OPERATORS. Mathematika, 61(2), 402-413.
https://doi.org/10.1112/S002557931500011X, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22138
Evans, K., Jacob, N., & Morris, O. (2014). On a class of Pseudo-Differential Operators on R^n x Z^m generating Feller Semigroups. Rev. Roumaine Math. Pures Appl., 59, 55-75.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa19855
Evans, K. & Jacob, N. (2012). Q-matrices as pseudo-differential operators with negative definite symbols. Mathematische Nachrichten, 286(5-6), 631-640.
https://doi.org/10.1002/mana.201100217, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa19853
Neate, A. & Evans, K. (2012). Mathematical Presentation and Communication Skills within the Core Curriculum. Further Work Developing Graduate Skills in HE Mathematics Programmes, 12-13.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43214
http://www.mathcentre.ac.uk/resources/uploaded/furthergradskills.pdf
Evans, K. & Jacob, N. (2011). Variable order subordination in the sense of Bochner and pseudo-differential operators. Mathematische Nachrichten, 284(8-9), 987-1002.
https://doi.org/10.1002/mana.200810246, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8059
Evans, K. & Jacob, N. (2007). Feller Semigroups Obtained by Variable Order Subordination. Revista Matemática Complutense, 20(2), 293-307.
https://doi.org/10.5209/rev_REMA.2007.v20.n2.16482, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa19852
http://www.springer.com/mathematics/journal/13163

Authored Books

Evans, K. & Jacob, N. (2020). A Course in Analysis Vol. V: Functional Analysis, Some Operator Theory, Theory of Distributions. World Scientific.
https://doi.org/https://doi.org/10.1142/11695, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa53554
https://www.worldscientific.com/worldscibooks/10.1142/11695
Jacob, N. & Evans, K. (2018). A Course in Analysis Vol. IV: Fourier Analysis, Ordinary Differential Equations, Calculus of Variations World Scientific.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43213
https://www.worldscientific.com/worldscibooks/10.1142/11078
Jacob, N. & Evans, K. (2017). A Course in Analysis Vol. III: Measure and Integration Theory, Complex-Valued Functions of a Complex Variable World Scientific.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa35868
http://www.worldscientific.com/worldscibooks/10.1142/10548
Jacob, N. & Evans, K. (2016). A Course in Analysis. Vol II: Differentiation and Integration of Functions of Several Variables, Vector Calculus World Scientific.
https://doi.org/10.1142/10059, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa29669
http://www.worldscientific.com/worldscibooks/10.1142/10059

Book Chapters

Evans, K. & Jacob, N. (2022). Some Geometric Observations on Heat Kernels of Markov Semigroups with Non-local Generators. In A.M. Candela, M. Cappelletti Montano, E. Mangino (Ed.), Trends in Mathematics (pp. 333-362). Springer International Publishing
https://doi.org/10.1007/978-3-031-20021-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa64994
https://link.springer.com/chapter/10.1007/978-3-031-20021-2_17

Conference Contributions

Evans, K. & Jacob, N. (2022). On Non-negative Solutions to Space-Time Partial Differential Equations of Higher Order. In Springer Proceedings in Mathematics and Statistics (pp. 85-107). Springer Nature Singapore.
https://doi.org/10.1007/978-981-19-4672-1_6, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa59047

Other Research Outputs

Jacob, N. & Evans, K. (2015). A Course in Analysis Vol. I: Introductory Calculus, Analysis of Functions of One Real Variable
https://doi.org/10.1142/9625, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23505
http://dx.doi.org/10.1142/9625

Taught Modules

MA-292 Statistical Data Analysis

This module concentrates on non-parametric statistics and techniques used to treat categorical data. In particular, the module covers a variety of statistical tests, criteria for choosing appropriate tests and the use of statistical software in order to deal with large data sets.
MA-301 Complex Analysis

The module approaches the theory of complex analytic functions; including concepts of Cauchy-Riemann equations, power series, Laurent series and residue calculus.
MA-M16 Probability and Statistics for Data Science

This module serves as an introduction to the concepts of probability and statistics required for Data Science. Both the theoretical concepts and practical examples will be explored throughout the module. Particular attention will be paid to applications using a programming language.
MAW301 Dadansoddi Cymhlyg

Mae'r modiwl hwn yn ystyried y theori o ffwythiannau analytig cymhlyg; gan gynnwys cysyniadau o hafaliadau Cauchy-Riemann, cyfresi pwer, cyfresi Laurent a chalcwlws gweddill.

Attachments

Courses in Analysis:

Dr Kristian Evans

Email address

Welsh language proficiency

About

Research Highlights

All Research

MA-292 Statistical Data Analysis

MA-301 Complex Analysis

MA-M16 Probability and Statistics for Data Science

MAW301 Dadansoddi Cymhlyg