Robert Kotiuga, from Boston University, will give a seminar entitled “Synthesis of Near Force-Free Magnetic Fields as a Geometric Inverse Problem” for our “Electromagnetic Modeling” Theme on Thursday June 25th 2026 at 09:30 a.m. in Pierre Cotton room.
Abstract : The Giroux correspondence helps characterizes the topological structure of near force-free magnetic fields with a deceptively simple intuitive “toy inverse problem” involving currents in wires and their magnetic fields [1]. This 1-1 correspondence involves the equivalence relations of isotopy and homotopy. One consequently has a level of nonrigidity which suggests a geometric inverse problem. The present talk constructs a conformally-invariant nonlinear Euclidean Dirac operator which bridges the geometric and topological perspectives with a free-boundary geometric inverse problem [2]. The role of natural differential operations on the deRham complex is key aspect to problem formulation and FEM discretization [3].
Biography : Prof. Kotiuga received his B.Eng., M. Eng., and Ph.D. from McGill University in 1981, 1982, and 1985 respectively. After a post-doc at MIT, he joined Boston University in 1987 where he is still researching and teaching a wide variety of topics. Over the years he has held visiting appointments at MIT (Cambridge MA), ETH (Zurich), U. Pau (France), TUT (Tampere, Finland), Univ of Trento (Italy), and other shorter appointments.
Prof. Kotiuga’s research focuses on topological aspects of 3-dimensional problems in computational electromagnetics, the use of Whitney forms and simplicial data structures in the context of the finite element method. His earlier work on cuts for magnetic scalar potentials and helicity functionals has, in recent years, led to a topological characterization of near force-free magnetic fields. His early topological work in the context of vertical Bloch line memories now informs topological considerations in nanoscale MRAM devices. More recently, informed by psychoacoustics, he is revisiting issues of transient modeling in electroacoustics.
He has presented his research on four continents and is a life member of both the AMS and IEEE, as well as a member of SIAM.
Two books tied to this research are:
• Gross, P.W., Kotiuga, P.R., Electromagnetic Theory and Computation: A Topological Approach. Cambridge U. Press, 2004; reissued in 2011, and there’s an e-book version.
• Kotiuga, P. R., (editor), A Celebration of the Mathematical Legacy of Raoul Bott, CRM Proceedings & Lecture Notes, Vol.: 50, Amer. Math. Soc., 2010.
References :
[1] Kotiuga, P. R., On the Topological Characterization of Near Force-Free Magnetic Fields and the Work of Late-onset Visually-impaired Topologists. pp 215-234 of Discrete and Continuous Dynamical Systems, Series S, Vol. 9 No. 1
[2] Kotiuga, P.R., Discretization of conformally-invariant Dirac-like operators in 3D via natural differential operations, and applications to geometric inverse problems. Short Communications ICM 2026.
[3] Kotiuga P.R., Lahtinen V., “An electrical engineering perspective on naturality in computational physics”. Advances in Computational Mathematics. Sept.2024.
Invitation : Electromagnetic Modeling Theme, contact Guillaume Demesy or Boris Grakak
