Current and past research interests are

(1) anomalous random walks and travelling wave theory

(2) non-Markovian models of intracellular transport  and

(3) turbulence, combustion and stochastic dynamo

(4) financial modelling

Fedotov's major research interests lie in the general area of non-linear phenomena in statistical physics, random walk theory, front propagation theory and turbulent combustion. He is a coauthor of a book Reaction-Transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities, Springer Series in Synergetics, 450 p., 2010 (together with V. Mendez (Barcelona, Spain) and V. Hortshemke Fedotov was the Principal Investigator on EPSRC grant GR/M72241/01 which concerned with the large scale dynamics of reaction fronts in turbulent flow (1999-2001). As a recognition of his work in turbulence and combustion he was twice awarded a Senior Research Fellowship at Stanford University (1999-2004). He was an Invited Professor at Stanford University in 2006 and 2007. Fedotov has developed a stochastic approach to the problem of the growth of a magnetic field. The research was concerned with random advection/stochastic mixing, stochastic amplification of magnetic energy in the turbulent dynamo for subcritical case and magnetic waves in galaxies with memory effects. He was supported by The Royal Society Joint Project Grant Galactic magnetic field generation in subcritical case as a Project Leader. For a period of over 12 years, Fedotov's research is focused on the development of anomalous random walk models with reactions. Examples are (i) migration and proliferation dichotomy in tumor cell invasion; (ii) propagating fronts in reaction{transport systems with memory; (iii) superdiffusion and subdiffusion incide cells. He has been an Invited Professor at the Autonomous University of Barcelona in 2007, 2008,  2009 and 2012. Fedotov has been a Research Fellow of the Institute for Mathematics and its Applications, Minneapolis, USA in 2008 and a Fellow of the Isaac Newton Institute for Mathematical Sciences, Cambridge, for five months in 2010. He is regularly invited to be the keynote speaker at conferences on reaction-transport systems and fractional PDE's. Fedotov has been a Team Leader of EC Project FEPRE The Formation of Europe: Prehistoric Population Dynamics and the Roots of Socio-Cultural Diversity (2007-2010). This multidisciplinary 850,000 Euro project involved archeologists, demographers, physicists and applied mathematicians from France, Poland, Russia, Spain and the UK. It was concerned with development of the mathematical models of Neolithisation that includes both population migration and cultural diffusion involving several coexisting population types and variable environment.

Turbulence, combustion and stochastic dynamo

The research is concerned with random advection and stochastic mixing, non-premixed turbulent combustion, stochastic amplification of magnetic energy in the turbulent dynamo for subcritical case and magnetic waves in galaxies with memory effects. Sergei Fedotov was supported by EPSRC Research Grant (GR/M72241) “Large Scale Dynamics of Reaction Front in Turbulent Flow” as Principal Investigator (1999-2001). Total: £53,067. He was a Collaborator of DFG Project KL 611/6-1 in Wuppertal (1997/1998) and Project KL 611/6-2 in Berlin (1998) on combustion and detonation waves. He was a Team Leader of EC Project INTAS-94-2580 (1995-1997). Sergei Fedotov was twice awarded a Senior Research Fellowship at Stanford University to work at Center for Turbulence Research (1999-2004). Total: $48.000.  He was supported by The Royal Society Joint Project Grant “Galactic magnetic field generation in subcritical case” as a Project Leader (2003-2005).  Total: £10.000. He was also supported by The Royal Society Grant (2003), REF 14782. Total: £4.100

Financial modelling

The research is concerned with the stochastic volatility models with long memory effects, stochastic optimisation approach for option pricing in incomplete market and credit risk modelling. Together with Professor Emmanuel Haven (PI), Dr. Fethi and Professors Phil Molyneux, John Wilson, an ESRC grant has been awarded on the topic “Financial Modelling Post 2008: Where Next?” (2012-2013). Total: £18,000.