Zdzislaw Brzezniak

Profile

Biography

I am a Professor at the Department of Mathematics, University of York, having joined in 2005. I hold a PhD degree in the area of PDEs conferred by the Jagellonian University, Krakow, Poland in 1988.

University roles

Former roles include:

• Chair of Graduate School Committee (from 2012 to 2015)
• A Member of Graduate School Committee (from 2017)

Research

Overview

Though fundamentally a Pure Mathematician, I do not like the distinction and I am interested in problems which come from applications and mathematical physics. Since the beginning of my PhD studies, my interests have been in Stochastic PDE's (SPDEs), turbulence and, in particular, in passive scalar equations.

I have a broad interest in maths which touches on geometric analysis and harmonic analysis. I am one of the world leaders in SPDEs theory and obtained fundamental results in the areas of geometric heat and wave equations, stochastic Navier-Stokes and Euler equations. I am well known for my work on the theory of stochastic integration, SPDEs in Banach spaces, and stochastic analysis on manifolds.

My results have been used by many mathematicians to develop the theory of nonlinear partial differential equations perturbed by noise and the analysis of infinite-dimensional manifolds, such as loop spaces, which are motivated in particular by quantum field theory, statistical physics and physics of ferromagnetic materials.

My research on stochastic geometric problems, especially those on the Landau-Lifshitz equations and Navier-Stokes equations are important to physicists and other non-mathematicians. In order to involve non-specialist audiences, I have co-organised many workshops and conferences, including:

• Harmonic analysis, stochastics and PDEs, 20-24 June 2022 at ICMS (Edinburgh)
• Stochastic Spin Systems: models, theory, simulation and real-world applications (Bielefeld 2017)
• The Indo-UK Workshop on Stochastic Partial Differential Equations and Application (Bangalore 2015)
• Nonlinear PDEs in Micromagnetism: Analysis, Numerics and Applications'' (Edinburgh 2013)

I was the main organiser of a six months long programme in 2010 on the Stochastic Partial Differential Equations at the Isaac Newton Institute; the others were K.D. Elworthy, M. Hairer, M. R{\"o}ckner, T. Souganidis and R. Tribe.

Research group(s)

Mathematical Finance and Stochastic Analysis Research Group

Geometry and Analysis Research Group

Mathematical Biology

Available PhD research projects

PhD supervision is available in any of the areas listed above or extensions or continuations of the projects listed below.

Examples of PhD project include:

1. Nimit Rana (2019), A few problems on stochastic geometric wave equations
2. Fabian Hornung (2018), Global solutions of the nonlinear Schrödinger equation with multiplicative noise
3. Gaurav Dharival (2017), A study of constrained Navier-Stokes equations and related problems
4. Tayfun Kok (2017), Stochastic Evolution Equations in Banach Spaces and Applications to the Heath-Jarrow-Morton-Musiela Equation
5. Javed Hussain (2016), Analysis Of Some Deterministic & Stochastic Evolution Equations With Solutions Taking Values In An Infinite Dimensional Hilbert Manifold
6. Liang Li (2014), A Study Of Stochastic Landau-Lifschitz Equations
7. Jiahui Zhu (2011), A Study of SPDEs w.r.t. Compensated Poisson Random Measures and Related Topics
8. Mikhail Neklyudov (2007), Navier-Stokes Equation and Vector Advection
9. Carl Chalk (2007), Nonlinear Evolutionary Equations in Banach Spaces with fractional time derivative
10. Yuhong Li (2004), Asymptotical Behaviour of 2D Stochastic Navier-Stokes Equations
11. Andrew Carroll (1999), The Stochastic Nonlinear Heat Equation

Supervision

Current Research Students

• Asma Alalyani - aasa525@york.ac.uk
• Dalal Alharbi - da761@york.ac.uk
• Hessa Alharbi - ha1204@york.ac.uk
• Liqiong Wang - lw540@york.ac.uk
• Youpeng Sun - ys1604@york.ac.uk