Department of Mathematics and Statistics Artur Sowa

Research Area(s)

  • Quantum Harmonic Analysis
  • Applications of Mathematics in Quantum Technologies 2.0
  • Post-Quantum Cryptography

Research Topics

  • Quantum Systems: theory, modelling and simulation; Complex Networks; Operator Equations
  • Harmonic analysis of signals; Riemann's zeta and Broadband Redundancy; fast-transform bases; nonlinear oscillators
  • Data Encryption 

     

Current and Recent Graduate Students

  • Elias Hassani Sangani (Ph.D. student, co-supervised by Dr. Francis Bui and Dr. Jonathan Norton) is conducting research in cryptography and cybersecurity.
  • Madeline Berezowski (Ph.D. student) is exploring new ways of analyzing quantum observables and their dynamics.
  • Mandana Bidarvand (Ph.D. student, co-supervised by Dr. Shahedul Khan) is investigating the mathematics of infinite arrays of qubits.
  • Elias Hassani Sangani successfully defended his M.Sc. thesis "An Information Security System for Image Encryption Applications: Architecture and Performance Evaluation" on 21 August 2023. Elias' research work has been co-supervised by Dr. Francis Bui (College of Engineering) and Dr. Jonathan Norton (College of Medicine). Elias will continue as a PhD student at the College of Engineering at USask, and will work under the joint supervision of these three supervisors. 
  • Qi Guo successfully defended his M.Sc. thesis "Logistic Operator Equation and the Induced Stochastic Process for Complex System Modelling" on 21 August 2018.
  • Izabela Vlahu successfully defended her PhD thesis "The Orthogonal Band Decomposition of the Finite Dirichlet Matrix and Its Applications" on 13 December 2017. Izabela's research work was co-supervised by Prof. Paul Babyn (then @ Department of Medical Imaging, U of S).
  • Arash Shamloo successfully defended his PhD thesis "Mathematical Modelling of Nano-Electronic Systems" on 11 December 2014.

Current and Recent Teaching

Math 436/818 Mathematical Modelling II (T2 2023-24), a course focused on quantum system modelling

Math 818: The Q+ Seminar (T1, 2023-24), a graduate research seminar focused on quantum harmonic analysis 

Math 438.3/838.3 Methods of Applied Mathematics II, (T2 2022-23), a course focused on operator theory 

Math 436.3/818.3 Mathematical Modelling II (T2 2021-22), a course focused on quantum system modelling

Recent preprints

  • Analysing matrix operators via harmonic analysis on [the group of positive rationals]

Peer-Reviewed Publications

Other publications

Patents

  • Method of Enhancement of the Visual Display of Images and Other Visual Data Records, US Patent Number 7194143, issue date 3/20/07.
    The patent can be looked up here.

Recent Invited Talks and Conference Presentations

  • (joint work with Jonas Fransson) Wielding the Dirichlet series to analyse the physics of bosons, 2024 CMS Summer Meeting, Saskatoon, 31 May - 3 June 2024 
  • Elias Hassani (joint work with) A post-quantum, post-AI data encryption method, 2024 CMS Summer Meeting, Saskatoon, 31 May - 3 June 2024 
  • Mandana Bidarvand (joint work with) Analyzing arrays of qubits via a multi-scale approach, 2024 CMS Summer Meeting, Saskatoon, 31 May - 3 June 2024 
  • Madeline Berezowski (joint work with) How Boson Dimers Reproduce Spin Projection Operators, 2024 CMS Summer Meeting, Saskatoon, 31 May - 3 June 2024 
  • Analysing operators that evade traditional computational approaches, Advanced Research & Technology Forum, MathWorks (Boston, MA, USA), 10 January 2024 (remotely)   
  • The physics of an array of boson sites expressed via the Dirichlet series, Friday Physics seminar, Department of Physics and Astronomy, Uppsala University, 8 December 2023 
  • Applying group duality in the analysis of operators, Department of Mathematics, Uppsala University, The PDEs and Applications seminar, 5 December 2023
  • New applications of harmonic analysis to quantum theory and engineering (version 2), Analysis of Complex Physical Systems Seminar, Department of Mathematics, University of Texas at Austin, 6 April 2022 (remotely)
  • New applications of harmonic analysis to quantum theory and engineering, Department of Physics and Engineering Physics, University of Saskatchewan, 25 January 2022
  • Quantum applications of harmonic analysis on the group of positive rationals, 75th+1 CMS Summer Meeting, Ottawa (remote platform), 7-11 June 2021
  • (P. Navez, A. Sowa, A. Zagoskin) Entangling continuous variables with a qubit array, The fifth AMMCS International Conference (AMMCS2019), Waterloo, Ontario, 18-23 August 2019
  • Perturbing Hamiltonians via automorphism of the torus, The fifth AMMCS International Conference (AMMCS2019), Waterloo, Ontario, 18-23 August 2019
  • Newer nonlocal transforms and their applications in quantum engineering, Saskatoon Summer Symposium: Quantum Engineering Meets Harmonic Analysis, Saskatoon, Saskatchewan, 12-16 August 2019
  • Qubits, wavelets, fractals, bands, CMS 2019 Regina, Regina, Saskatchewan, 7-10 June 2019
  • Mathematics and Industrial Enterprises...Activities Joined at the Hip (?), Keynote@ Canadian Undergraduate Mathematics Conference, CUMC 2018, Saskatoon, Saskatchewan, 11-15 July 2018
  • The Relevance of Harmonic Analysis in the Analysis of Quantum Systems, The Second International Conference on Mathematical Characterization, Control, Analysis and Applications of Complex Information and Systems (2nd CMCAA 2018), Beijing, China, 30 June-1 July 2018
  • Harmonic Analysis in Quantum Engineering 2.0, School of Mathematics, Beijing Institute of Technology, Beijing, China, 27 June 2018
  • The Role of Harmonic Analysis in Quantum Engineering, the Landau Seminar at the Department of Physics, Loughborough University, Loughborough, Leicestershire, England, 21 June 2018
  • Deploying Harmonic Analysis in Quantum and Nano Engineering, The Fields Institute, Focus Program on Nanoscale Systems and Coupled Phenomena, Mathematical Analysis, Modelling, and Applications, Toronto, Ontario, 14 May 2018; watch it here
  • The Broadband Redundancy and Its Applications, the Landau Seminar at the Department of Physics, Loughborough University, Loughborough, Leicestershire, England, 19 October, 2017
  • (A. Sowa, A. Zagoskin, and A. Balanov) A Nonlinear Master Equation Model for Quantum Metamaterials, The fourth AMMCS International Conference (AMMCS2017), Waterloo, Ontario, 20-25 August 2017
  • (B-Z. Li, A. Sowa) Numerical Methods for Analysis and Representation of Quantum States Associated with Integral Transform, The fourth AMMCS International Conference (AMMCS2017), Waterloo, Ontario, 20-25 August 2017
  • (S.A. Melli, A.P. Sowa, K.A. Wahid) Image Denoising via Redundant Quantum Channels, The fourth AMMCS International Conference (AMMCS2017), Waterloo, Ontario, 20-25 August 2017
  • (Q. Guo, A. Sowa) Examples of Quantum-dynamical Nonlaws and Their Properties, The fourth AMMCS International Conference (AMMCS2017), Waterloo, Ontario, 20-25 August 2017
  • Qualitative Analysis of Quantum States and Observables, the Landau Seminar at the Department of Physics, Loughborough University, Loughborough, Leicestershire, England, 28 June, 2017
  • Harmonic Analysis of Quantum States and Observables, EMN Quantum 2017, Vienna, Austria, 18-22 June, 2017
  • Searching for a spread-spectrum approach to some inverse problems, 10th International Conference on Scientific Computing and Applications (ICSCA 2016), The Fields Institute, Toronto, Ontario, 6-10 June 2016
  • Towards Quantum Image Processing, Saskatoon mini-Symposium: Applications of Quantum Engineering to Magnetic Resonance Imaging, Saskatoon, Saskatchewan, 18-19 August 2014
  • Linear Operators for the Analysis of Nonlinear Systems, 11th World Congress of Computaitonal Mechanics, 5th European Conference on Computaitonal Mechanics, Barcelona, Spain, 20-25 July 2014
  • Applying simulated quantum dynamics, Canadian Applied and Industrial Mathematics Society 2014 Annual Meeting, Saskatoon, Saskatchewan, 22-26 June 2014
  • Emerging applications of simulated quantum dynamics, International Focus Workshop on Metamaterials and Quantum Criticality, Loughborough, Leicestershire, UK, March 25, 2014
  • From nonlinear eigenvalue problems to fast transforms, number theoretic operators, and special quantum states, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland, November 21, 2013
  • Nonlinear oscillators and number theoretic quantum states, the Landau Seminar at the Department of Physics, Loughborough University, Loughborough, Leicestershire, England, October 30, 2013
  • Mathematical analogies between the eigenmodes of memristive nanosystems and some cryptography-specialized quantum states, BIT's 3rd Annual World Congress of Nanoscience and Nanotechnology-2013, Xi'an, China, September 28, 2013
  • Mathematical Models of Complex Phenomena, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, China, September 24, 2013
  • Operators resulting from the Dirichlet series, 2012 Canadian Mathematical Society Summer Meeting, Regina, Saskatchewan, June 2-4, 2012
  • Modelling with the Logistic Operator Equation, 3rd International Conference on Econophysics, Loughborough, England, September 23-29, 2011
  • A Fast-Transform Basis with Hysteretic Features, 24th Canadian Conference on Electrical and Computer Engineering, Niagara Falls, Ontario, May 8-11, 2011
  • Nonlinear eigenvalue problems with applications to quantum systems, 2010 Canadian Mathematical Society Winter Meeting, Vancouver, British Columbia, December 4-6, 2010
  • (F. Sage, A. Sowa), Numerical Quantum Chaos in Nonlocal Quantum Dynamics, presented (by FS) at the 1st Meeting of the Canadian Prairie Theoretical Physics Network, Lethbridge, August 25, 2010
  • Nonlinear quantum spectroscopy, OTAMP 2010, Fifth International Conference on Operator Theory Analysis and Mathematical Physics, Bedlewo, Poland, August 5 - 12, 2010
  • Nonlinear eigenvalue problems and quantum systems, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland, July 27, 2010
  • Quantum spectroscopy, nonlinear operator equations, etc., Fourth Annual Meeting of the Prairie Network for Research in Mathematical Sciences, Manitoba, April 30-May 2, 2010
  • On the topological characteristic of the spectra of some composite quantum systems, 2009 Canadian Mathematical Society Winter Meeting, Windsor, Ontario, December 5-7, 2009
  • On the noncommutative Schrödinger equation, Third Annual Meeting of the Prairie Network for Research in Mathematical Sciences, Saskatchewan, April 29-May 1, 2009
  • On the Stationary Solutions of the Noncommutative Schrödinger Equation, The Sixth IMACS International Conference on: Nonlinear Evolution Equations and Wave Phenomena, Georgia, USA, March 23-26, 2009
  • Exploiting the paradigm of quantum information in nanosystem modeling, The Sixth International Conference on Computational Methods of Science and Engineering, ICCMSE 2008, Greece, Sept. 25-30, 2008