About:
This annual lecture commemorates the outstanding achievements of the late Professor Jack Carr FRSE, formerly Head of Department of Mathematics at Heriot-Watt University. He was not only an international authority in his field of differential equations and dynamical systems, but was also widely recognised for a selfless commitment to the University, Scottish, and international communities. He had a special interest in fostering mathematics in African and other developing countries. His links with colleagues at Edinburgh University helped establish the ICMS and also the Maxwell Institute.
About the speaker:
Duvan Henao, Universidad de O'Higgins in Chile
The Jack Carr Lecture this year will be delivered by Duvan Henao, Professor at Universidad de O'Higgins in Chile. Originally from Colombia, he arrived in Santiago in 2000, where he pursued undergraduate and Master studies in Mathematics at Pontificia Universidad Católica. He is awarded his D. Phil. in 2009 at University of Oxford, guided by Sir John M. Ball. After his postdoctoral position with Sylvia Serfaty at Université Pierre et Marie Curie, he worked at Pontificia Universidad Católica de Chile from 2011, before finally taking his current position at O'Higgins in 2022. Having specialized in the formation of singularities in nonconvex variational problems in soft matter (fracture initiation under large deformations in elastic and ductile materials; biaxiality of defects in liquid crystals; harmonic dipoles in neoHookean materials; debonding of polymer gels), he has been invited speaker at various international conferences and events, including the Variational and PDE Methods in Nonlinear Science C.I.M.E. Course (Cetraro, 2023).
Talk Title: Synergies between analysis, geometry, mechanics, and topology in nonlinear elasticity theory
Abstract: This lecture presents various examples of the rich interactions in the analysis of the response of an elastic body to external loading, following the common thread of distributional determinants. These fascinating objects play a crucial role in physical systems where the energy concentrates in topologically charged lower-dimensional structures, such as the U(1)-Yang-Mills-Higgs model in gauge theory, the formation of vortex filaments in superconductivity, or the motion of dislocations in crystal plasticity. Here the focus will be on their part in the existence of solutions to the equilibrium equations in elasticity, in the preservation of orientation, and in the injectivity of deformations for the non-interpenetration of matter, profiting from the familiar notions of the Brouwer degree and the winding number, the stereographic projection, and a variant of the inverse function theorem for maps that are only weakly differentiable.