Dr Cesare Tronci


Phone: Work: 01483 68 3356
Room no: 16 AA 04

Further information


I obtained a Laurea in Nuclear Engineering in May 2004 at the Politecnico di Torino (Italy). Then, after spending two years (06/2003 – 05/2005) at CERN (Switzerland) working on microwave electronics under the direction of Ugo Amaldi (also at TU München and TERA Foundation), I moved to the Theoretical Division (in the former Plasma Theory Group) of the Los Alamos National Lab (LANL, USA), where I visited Giovanni Lapenta (now at KU Leuven, Belgium) for several months. In 10/2005, I entered a PhD program at Imperial College, under the direction of Darryl Holm. In my thesis, I worked on geometric analogies between kinetic theory and porous media equations to model the aggregation of ferromagnetic nanoparticles. Between 2006 and 2007, I also spent two summers at LANL, working with Bruce Carlsten in the former International, Space & Response Division (High Power Electrodynamics Group). In 09/2008, I joined the Mathematics Section of EPF Lausanne (Switzerland) as a research assistant in Tudor Ratiu’s group (Geometric Analysis). Since 01/2012, I am Lecturer (Assistant Professor) in the Department of Mathematics of the University of Surrey and have visited several institutions in Europe and North America.

Research Interests

Over the years, I have worked with engineers, physicists and mathematicians and shared with them the excitement of doing research in each of the corresponding fields. I have developed an understanding of the needs and the challenges in these disciplines and this experience is for me a continuous source of inspiration. This diversified path has led me to the discovery of mathematical research and its interconnections with other pure and applied sciences. Then, applied mathematics emerges not only as a discipline that applies mathematical concepts to other fields, but also as an area in which other fields of science serve as a continuous inspiration to develop new exciting directions in mathematical research – this two-way vision is precisely where my research stands.

Specific interests include:
Momentum maps and reduction by symmetry; applications of symplectic and Poisson geometry; Hamiltonian and Lagrangian techniques in nonlinear dynamics; multi-physics modelling of nonlinear multiscale dynamics; nonlinear modelling of magnetized plasmas; liquid crystals and fluids with internal structure; nonlocal dynamics of aggregation and self-assembly; phase-space methods in classical and quantum mechanics; mixed classical-quantum dynamics and applications in chemistry.

Research Collaborations

International collaboration network:
Within a 4-year Leverhulme Research Project, I am leading an international collaboration composed of Emanuele Tassi at the Centre of Theoretical Physics in Marseille (France), Giovanni Lapenta at the Centre for Plasma Astrophysics of KU Leuven (Belgium), and Philip J. Morrison at the Institute of Fusion Studies at UT Austin (USA). Within the same project, I also collaborate with Alain J. Brizard (St. Michael College of Vermont, USA), Enrico Camporeale (CWI Amsterdam, The Netherlands), and Maria Elena Innocenti (KU Leuven, Belgium).

National collaboration network:
Within a London Mathematical Society Scheme 3 award, I am the coordinator of a national Network in Applied Geometric Mechanics involving three groups working on core topics in geometric mechanics: geometric quantum dynamics (Brunel University), geometric imaging science (Imperial College), and geometric fluid dynamics (University of Surrey).

Other collaborations:
Over the last 10 years, I have worked with several (mainly international) collaborators on different mathematical problems, with special emphasis on applications. Recent collaborators include: Joshua W. Burby (Courant Institute - NYU, USA), Bin Cheng (U. Surrey, UK), François Gay-Balmaz (ENS-CNRS Paris, France), Darryl D. Holm (Imperial College, UK), Tomoki Ohsawa (UT Dallas, USA), Tudor S. Ratiu (EPF Lausanne, Switzerland), Vakhtang Putkaradze (U. Alberta, Canada), Endre Süli (Oxford, UK), Cornelia Vizman (U. West Timisoara, Romania).


The Hamiltonian setting of Koopman-von Neumann theory and the dynamics of hybrid classical-quantum systems, F. Gay-Balmaz, C. Tronci (to be submitted)

A low-frequency variational model for energetic particle effects in the pressure-coupling scheme, A.R.D. Close, J.W. Burby, C. Tronci, J. Plasma Phys. (submitted)

Geometry and dynamics of Gaussian wave packets and their Wigner transforms, T. Ohsawa, C. Tronci, J. Math. Phys., 58 (2017), no. 1, 092105

Existence of global weak solutions to a hybrid Vlasov-MHD model for magnetized plasmas, B. Cheng, E. Süli, C. Tronci, Proc. London Math. Soc., 115 (2017), no. 4, 1-43

Electron inertia and quasi-neutrality in the Weibel instability, E. Camporeale, C. Tronci, J. Plasma Phys., 83 (2017), no. 3, 705830301

Variational approach to low-frequency kinetic-MHD in the current-coupling scheme, J.W. Burby, C. Tronci, Plasma Phys. Control. Fusion, 59 (2017), no. 4, 045013

From liquid crystal models to the guiding-center theory of magnetized plasmas, C. Tronci, Ann. Phys., 371 (2016), 323-337

Variational formulations of guiding-center Vlasov-Maxwell theory, A.J. Brizard, C. Tronci, Phys. Plasmas, 23 (2016), no. 6, 062107

Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states, E. Bonet Luz, C. Tronci, Proc. R. Soc. Lond. Ser. A, 472 (2016), no. 2189, 20150777

Grid coupling mechanism in the semi-implicit adaptive Multi-Level Multi-Domain method, M.E. Innocenti, C. Tronci, S. Markidis, G. Lapenta, J. Phys.: Conf. Ser., 719 (2016), no. 1, 012019

Equivalent variational approaches to biaxial liquid crystal dynamics, A.R.D. Close, C. Tronci, Proc. R. Soc. Lond. Ser. A, 471 (2015), no. 2183, 20150308

Geometry and symmetry of quantum and classical-quantum variational principles, E. Bonet Luz, C. Tronci, J. Math. Phys., 56 (2015), no. 8, 082104

Neutral Vlasov kinetic theory of magnetized plasmas, C. Tronci, E. Camporeale, Phys. Plasmas, 22 (2015), no. 2, 020704

Energy-Casimir stability of hybrid Vlasov-MHD models, C. Tronci, E. Tassi, P.J. Morrison, J. Phys. A, 48 (2015), no. 18, 185501 (selected for interview as “Publisher’s pick”; also appeared in “J. Phys. A Highlights 2015”)

Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian, C. Tronci, E. Tassi, E. Camporeale, P.J. Morrison, Plasma Phys. Control. Fusion, 56 (2014), no. 9, 095008

Equivalent theories of liquid crystal dynamics, F. Gay-Balmaz, T.S. Ratiu, C. Tronci, Arch. Ration. Mech. Anal., 210 (2013), no. 3, 773-811

Energy stability analysis for a hybrid fluid-kinetic plasma model, P.J. Morrison, E. Tassi, C. Tronci, in Nonlinear Physical Systems (eds O.N.  Kirillov and D.E. Pelinovsky), John Wiley & Sons, Inc., Hoboken, USA, 2013.

Geometric dynamics on the automorphism group of principal bundles, F. Gay-Balmaz, C. Tronci, C. Vizman, J. Geom. Mech., 5 (2013), no. 1, 39–84

A Lagrangian kinetic model for collisionless magnetic reconnection, C. Tronci, Plasma Phys. Control. Fusion, 55 (2013), no. 3, 035001

Collisionless kinetic theory of rolling molecules, D.D. Holm, V. Putkaradze, C. Tronci, Kinet. Relat. Models, 6 (2013), no. 2, 429–458

Vlasov moment flows and geodesics on the Jacobi group, F. Gay-Balmaz, C. Tronci, J. Math. Phys., 43 (2012), no. 12, 123502

Hybrid models for perfect complex fluids with multipolar interactions, C. Tronci, J. Geom. Mech., 4 (2012), no. 3, 333–363

Multiscale turbulence models based on convected fluid microstructure, D.D. Holm, C. Tronci, J. Math. Phys., 53 (2012), no. 11, 115614

Euler-Poincaré approaches to nematodynamics, F. Gay-Balmaz, T.S. Ratiu, C. Tronci, Acta Appl. Math. 120 (2012), no. 1, 127–151

Euler-Poincaré formulation of hybrid plasma models, D.D. Holm, C. Tronci, Comm. Math. Sci. 10 (2012), no.1, 191–222

The helicity and vorticity of liquid-crystal flows, F. Gay-Balmaz, C. Tronci, Proc. R. Soc. Lond. Ser. A 467 (2011), no. 2128, 1197–1213

Reduction theory for symmetry breaking with applications to nematic systems, F. Gay-Balmaz, C. Tronci, Phys. D 239 (2010), no. 20-22, 1929-1947

Hamiltonian approach to hybrid plasma models, C. Tronci, J. Phys. A 43 (2010), no. 37, 375501

Double bracket dissipation in kinetic theory for particles with anisotropic interactions, D.D. Holm, V. Putkaradze, C. Tronci, Proc. R. Soc. Lond. Ser. A 466 (2010), no. 2122, 2991-3012

Geodesic Vlasov equations and their integrable moment closures, D.D. Holm, C. Tronci, J. Geom. Mech. 1 (2009), no. 2, 181-208

Singular solutions of a modified two-component Camassa-Holm equation, D.D. Holm, L. Ó Náraigh, C. Tronci, Phys. Rev. E 79 (2009), no. 1, 016601

Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions, D.D. Holm, C. Tronci, Proc. R. Soc. Lond. Ser. A 465 (2009), no. 2102, 457–476

Emergent singular solutions of nonlocal density-magnetization equations in one dimension, D.D. Holm, L. Ó Náraigh, C. Tronci, Phys. Rev. E 77 (2008), no. 3, 036211

Geometry of Vlasov kinetic moments: a bosonic Fock space for the Schouten concomitant, J. Gibbons, D.D. Holm, C. Tronci, Phys. Lett. A 40 8 (2008), no. 23, 4184-4196

Kinetic models of oriented self-assembly, D.D. Holm, V. Putkaradze, C. Tronci, J. Phys. A 41 (2008), no. 34,  344010

Geometric gradient-flow dynamics with singular solutions, D.D. Holm, V. Putkaradze, C. Tronci, Phys. D 237 (2008), no. 22, 2952-2965

Vlasov moments, integrable systems and singular solutions, J. Gibbons, D.D. Holm, C. Tronci, Phys. Lett. A 372 (2008), no. 7, 1024–1033

Singular solutions for geodesic flows of Vlasov moments, J. Gibbons, D.D. Holm, C. Tronci, Math. Sci. Res. Inst. Publ. 55 (2008) 199–220

Geometric dissipation in kinetic equations, D.D. Holm, V. Putkaradze, C. Tronci, C. R. Acad. Sci. Paris, Sér. I 345 (2007), no. 5, 297–302

Formulation of the relativistic moment implicit particle-in-cell method, K. Noguchi, C. Tronci, G. Zuccaro, G. Lapenta, Phys. Plasmas 14 (2007), no. 4, 042308

A high frequency H-mode coupled cavity linac for low and medium energies, U. Amaldi, A. Citterio, M. Crescenti, A. Giuliacci, C. Tronci, R. Zennaro, Nucl. Instr. Meth. A 579 (2007), no. 3, 924-936

Concept study and design of a low-medium β accelerating structure, U. Amaldi, A. Citterio, M. Crescenti, A. Giuliacci, C. Tronci, R. Zennaro, Nucl. Phys. B Proc. Supp. 172 (2007) 277-279


Teaching portfolio: Linear Algebra & Vector Calculus (MAT1037), Geometric Mechanics (MATM032), Geometric Mechanics (MAGIC080)

Since I joined the University of Surrey, I introduced a new 4th year module (thought 5 times) in Geometric Mechanics. The module introduces symmetry methods in mechanical problems for different applications, from rigid body dynamics to quantum mechanics. I introduced a new partial assessment method that requires students to give presentations to the rest of the class. Also, I have thought (4 times) an online mini-course (10 hours) in Geometric Mechanics (with more advanced content) to PhD students across the UK, within the Mathematics Access Grid group of universities. In 2016 (first semester), I have also thought a first-year module in Linear Algebra & Vector Calculus (including a small part on MATLAB).

Research Grants

Leverhulme Research Project Grant:
in 2014, I was awarded the Leverhulme Research Grant RPG2014-112 “From geometry to kinetic-fluid systems (and back)”. Total budget: £252K. Duration: 4 years (started 7/1/15). This grant involves two 2-years research assistants and three international collaborations in Europe and USA.

Small awards:
over the last five years, I have been awarded a series of small grants (<£3K) by the London Mathematical Society, the Institute of Mathematics and Applications and the internal Faculty Research Support Fund at the University of Surrey.

Selected invited talks

Symmetry methods for quantum variational principles and expectation value dynamics, PACM Colloquium, Princeton University, November 6 2017, Princeton NJ, USA

Variational formulations of low frequency kinetic-MHD in the current-coupling scheme, Mini-conference on "New Developments in Algorithms and Verification of Gyro Kinetic Simulations", 58th Annual Meeting of the APS Division of Plasma Physics, October 31 - November 4, 2016, San Jose CA, USA. (Solicited talk)

Modeling efforts in hybrid kinetic-MHD and fully kinetic theories, Princeton Plasma Physics Laboratory, October 27 2016, Princeton NJ, USA

Multiphysics models for hybrid kinetic-fluid systems, Courant Institute of Mathematical Sciences, New York University, April 7 2016, New York NY, USA

Classical-quantum variational principles, Classic and Stochastic Geometric Mechanics Workshop, June 8-11, 2015, École Polytechnique Fédérale de Lausanne, Switzerland

Relabeling symmetry in fluid dynamics, Geometry and Fluids, April 7-11 2014, Clay Mathematics Institute, Oxford, UK

Hydrodynamic vorticity and helicity of conservative liquid crystal flows, Isaac Newton Institute for Mathematical Sciences, June 11 2103, Cambridge, UK

Geometry and symmetry in multi-physics models for magnetized plasmas, Fields Institute for Research in Mathematical Sciences, July 9 2012, Toronto, Canada

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