# Prof Bertram Düring

## Career

**2018-:**Visitor, DAMTP, University of Cambridge**2018-:**Professor of Mathematics, University of Sussex**2010-2018:**Senior Lecturer, then Reader in Mathematics, University of Sussex**2007-2010:**Postdoctoral research fellow, then Privatdozent, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria**2002-2007:**Research associate, then postdoctoral research fellow, Institute for Mathematics, Johannes Gutenberg University Mainz, Germany**1999-2002:**Research associate, Institute for Mathematics, University of Konstanz, Germany

## Research

Bertram is a member of the Department of Applied Mathematics and Theoretical Physics, Cambridge Image Analysis research group. His current research interests are in appliead and computational partial differential equations, including modelling, analysis and numerics. More specifically, he is interested in

- Kinetic and mean-field models for many-agent systems in socio-economics, e.g. wealth distribution and opinion formation in human societies
- Structure-preserving variational discretisations of nonlinear partial differential equations with a Wasserstein gradient flow structure
- High-order compact finite difference methods
- Dimensional splitting methods for nonlinear partial differential equations
- Higher-order nonlinear partial differential equations
- Computational finance
- Optimal control of partial differential equations

## Selected Publications

- B. Düring, M. Torregrossa and M.-T. Wolfram. Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects. To appear in
*J. Nonlinear Sci.*, 2019. - B. Düring, L. Pareschi and G. Toscani. Kinetic models for optimal control of wealth inequalities.
*Eur. Phys. J. B*91(10) (2018), 265. - J.A. Carrillo, B. Düring, D. Matthes and D.S. McCormick. A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes.
*J. Sci. Comput.*75(3) (2018), 1463-1499. - M. Burger, B. Düring, L.M. Kreusser, P.A. Markowich and C.-B. Schönlieb. Pattern formation of a nonlocal, anisotropic interaction model.
*Math. Models Methods Appl. Sci.*28(3) (2018), 409-451. - B. Düring and J. Miles. High-order ADI scheme for option pricing in stochastic volatility models.
*J. Comput. Appl. Math.*316 (2017), 109-121. - B. Düring, A. Jüngel and L. Trussardi. A kinetic equation for economic value estimation with irrationality and herding.
*Kinet. Relat. Models*10(1) (2017), 239-261. - B. Düring and M.-T. Wolfram. Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation.
*Proc. R. Soc. Lond. A*471 (2015), 20150345. - B. Düring and C. Heuer. High-order compact schemes for parabolic problems with mixed derivatives in multiple space dimensions.
*SIAM J. Numer. Anal.*53(5) (2015), 2113-2134. - L. Calatroni, B. Düring and C.-B. Schönlieb. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing.
*Discrete Contin. Dyn. Syst. Ser. A*34(3) (2014), 931-957. - B. Düring and M. Fournié. High-order compact finite difference scheme for option pricing in stochastic volatility models.
*J. Comput. Appl. Math.*236(17) (2012), 4462-4473. - B. Düring, D. Matthes and J.-P. Milisic. A gradient flow scheme for nonlinear fourth order equations.
*Discrete Contin. Dyn. Syst. Ser. B*14(3) (2010), 935-959. - B. Düring, P.A. Markowich, J.-F. Pietschmann and M.-T. Wolfram. Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders.
*Proc. R. Soc. Lond. A*465(2112) (2009), 3687-3708. - B. Düring, D. Matthes and G. Toscani. A Boltzmann-type approach to the formation of wealth distribution curves.
*Riv. Mat. Univ. Parma (8)*1 (2009), 199-261. - B. Düring. Asset pricing under information with stochastic volatility.
*Rev. Deriv. Res.*12(2) (2009), 141-167. - B. Düring and G. Toscani. International and domestic trading and wealth distribution.
*Comm. Math. Sci.*6(4) (2008), 1043-1058. - B. Düring, A. Jüngel and S. Volkwein. Sequential quadratic programming method for volatility estimation in option pricing.
*J. Optim. Theory Appl.*139(3) (2008), 515-540. - B. Düring, D. Matthes and G. Toscani. Kinetic equations modelling wealth redistribution: a comparison of approaches.
*Phys. Rev. E*78(5) (2008), 056103. - B. Düring and G. Toscani. Hydrodynamics from kinetic models of conservative economies.

*Physica A*384(2) (2007), 493-506. - B. Düring and E. Lüders. Option prices under generalized pricing kernels.
*Rev. Deriv. Res.*8(2) (2005), 97-123. - B. Düring and A. Jüngel. Existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets.
*Nonl. Anal. TMA*62(3) (2005), 519-544. - B. Düring, M. Fournié and A. Jüngel. Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation.
*Math. Mod. Num. Anal.*38(2) (2004), 359-369. - B. Düring, M. Fournié and A. Jüngel. High-order compact finite difference schemes for a nonlinear Black-Scholes equation.
*Intern. J. Theor. Appl. Finance*6(7) (2003), 767-789.