Anthony Bloch

Anthony M. Bloch is an American mathematician and the Alexander Ziwet Collegiate Professor of Mathematics at the University of Michigan.

He is known for his contributions to Hamiltonian and Lagrangian mechanics, geometric control theory, integrable systems, and nonholonomic mechanics. He has held editorial positions and served three terms as Chair of the University of Michigan Department of Mathematics.

In 2012 he was named a Fellow of Society for Industrial and Applied Mathematics and a Fellow of the American Mathematical Society.

He was named a Fellow of the Institute of Electrical and Electronics Engineers in 2003. He is also a Guggenheim fellow and Simons Fellows in Mathematics.

Education Bloch earned a B.Sc. and B.Sc. (Hons.) in Applied Mathematics and Physics from the University of the Witwatersrand in 1977 and 1978, respectively. He completed an M.S. in Physics at the California Institute of Technology in 1979 and an M.Phil. in Control Engineering and Operations Research at the University of Cambridge in 1981.

Bloch is also a Fellow of the American Mathematical Society (AMS), and a Corresponding Member of the National Academy of Artificial Intelligence.

Research Bloch's research spans Hamiltonian and Lagrangian mechanics, symplectic geometry, geometric control theory, gradient flows on manifolds, integrable systems, stability theory, nonholonomic mechanics, quantum control and astrophysics.

He has worked extensively on the geometric formulation and control of nonholonomic systems, with influential papers on symmetry reduction and stabilization, and is one of the original developers of the method of controlled Lagrangians.

His research in control theory includes widely cited results with M. Reyhanoglu and N. H. McClamroch on the control of nonholonomic mechanical systems.

In integrable systems, Bloch is well known for showing that the Toda lattice flow is gradient on adjoint orbit and for his work with Roger Brockett and Tudor Rațiu generalizing this to general Lie algebras as well for his related work on gradient and double bracket flows.

He also known for work on the symmetric representation of the generalized rigid body equations with Crouch, Marsden, and Rațiu and his work with Iserles, Marsden, and Rațiu on integrable flows on symmetric matrices.

Bloch is the author of Nonholonomic Mechanics and Control (now in its second edition), which has been cited over 2,000 times and is regarded as a standard reference in the field.

His recent work also involves data-guided control, network dynamics, and applications to biological systems. He maintains active collaborations across mathematics, physics, engineering, and applied sciences.

Selected publications