Filip Rindler Professor of Mathematics   Office: B1.26  Phone: +44 (0) 2476 5 28328  Email: F dot Rindler at warwick dot ac dot uk

 

Research

My research sits at the intersection between Applied and Theoretical Mathematics. In particular, I am interested in oscillation and concentration phenomena and what can be rigorously proved about their "shape". Many of the questions I work originate in Material Science, in particular thetheories of elasto-plasticity and dislocations, and I investigate them with methods of Mathematical Analysis (PDEs, Calculus of Variations, Geometric Measure Theory),

My research has been funded by the European Research Council (ERC) through an ERC Starting Grant SINGULARITY, an ERC Consolidator Grant CONCENTRATE (selected by the ERC, funded by UKRI under the ERC guarantee scheme), and other grants from EPSRC, the Royal Society, and the Lloyds Register Foundation.

 

Selected recent publications

• Energetic solutions to rate-independent large-strain elasto-plastic evolutions driven by discrete dislocation flow, to appear in J. Eur. Math. Soc. arXiv:2109.14416Link opens in a new window.
• Transport of currents and geometric Rademacher-type theorems (with P. Bonicatto, G. Del Nin), to appear in Trans. Amer. Math. Soc., arXiv:2207.03922Link opens in a new window.
• Existence and uniqueness for the transport of currents by Lipschitz vector fields (with P. Bonicatto, G. Del Nin), J. Func. Anal. 286 (2024) 110315. Online versionLink opens in a new window.
• Shape optimization of light structures and the vanishing mass conjecture (with J.-F. Babadjian, F. Iurlano), Duke Math. J. 172 (2023), 43-103. Online versionLink opens in a new window.
• Space-time integral currents of bounded variation, Calc. Var. Partial Differential Equations 62 (2023), Paper No. 54. Online versionLink opens in a new window.
• Elasto-plastic evolution of crystal materials driven by dislocation flow (with T. Hudson), Math. Models Methods Appl. Sci. (M3AS) 32 (2022), 851-910. Online versionLink opens in a new window.
• Concentration versus oscillation effects in brittle damage (with J.-F. Babadjian, F. Iurlano), Comm. Pure Appl. Math. 74 (2021), 1803-1854. Online versionLink opens in a new window.
• Dimensional estimates and rectifiability for measures satisfying linear PDE constraints (with A. Arroyo-Rabasa, G. De Philippis, J. Hirsch), Geom. Funct. Anal. 29 (2019), pp 639-658. Online versionLink opens in a new window.
• Liftings, Young measures, and lower semicontinuity (with G. Shaw), Arch. Ration. Mech. Anal. 232 (2019), 1227-1328. Online versionLink opens in a new window.
• On the structure of A-free measures and applications (with G. De Philippis), Ann. of Math. 184 (2016), 1017-1039. Online versionLink opens in a new window.

 

Curriculum Vitae

 

Editorial activities

I am an editor for Mathematical Models and Methods in Applied Sciences (M3AS)Link opens in a new window, Revista Matemática Iberoamericana (RMI)Link opens in a new window, and Proceedings of the Royal Society of Edinburgh Section A: Mathematics (PRSE/A)Link opens in a new window. Please consider submitting papers to these journals!

 

Calculus of Variations book

The book Calculus of Variations is based on my lectures at the University of Warwick and appeared with Springer in 2018:

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See www.calculusofvariations.comLink opens in a new window for details.