Anthony M. Bloch

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Anthony Bloch
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Alma mater University of the Witwatersrand ( B.Sc. and B.Sc. (Hons.) , California Institute of Technology (M.S), University of Cambridge(M.Phil.), Harvard University (Ph.D.)
Known for Hamiltonian and Lagrangian mechanics
Awards Fellow of the Institute of Electrical and Electronics Engineers
Guggenheim fellow
Fellow of the American Mathematical Society
Scientific career
Fields Mathematics
Institutions University of Michigan

Anthony M. Bloch is an American mathematician and the Alexander Ziwet Collegiate Professor of Mathematics at the University of Michigan. [1]

Contents

He is known for his contributions to Hamiltonian and Lagrangian mechanics, geometric control theory, integrable systems, and nonholonomic mechanics. [2] He has held editorial positions and served three terms as Chair of the University of Michigan Department of Mathematics. [3]

In 2012 he was named a Fellow of Society for Industrial and Applied Mathematics [4] and a Fellow of the American Mathematical Society. [5]

He was named a Fellow of the Institute of Electrical and Electronics Engineers in 2003. [6] He is also a Guggenheim fellow [7] and Simons Fellows in Mathematics. [8]

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. [9] 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. [6] In 1985, he received his Ph.D. in Applied Mathematics from Harvard University. [9]

Career

Bloch joined the University of Michigan faculty in 1985, becoming Alexander Ziwet Collegiate Professor of Mathematics in 2005. He served as Graduate Chair of the Department of Mathematics from 2001 to 2004 and as Department Chair from 2005 to 2008 and again from 2017 to 2023. [3]

He has been a Guggenheim Fellow, Simons Fellow, Senior Fellow of the Michigan Society of Fellows, and is a Life Fellow of the Institute of Electrical and Electronics Engineers (IEEE). [10]

Bloch is also a Fellow of the American Mathematical Society (AMS), [5] the Society for Industrial and Applied Mathematics (SIAM), [4] the International Core Academy of Sciences and Humanities, [11] and a Corresponding Member of the National Academy of Artificial Intelligence. [9]

Bloch has served as Editor-in-Chief of the SIAM Journal on Control and Optimization (2012–2018), Co-Editor-in-Chief of the Journal of Nonlinear Science (2018–present), and Book Series Editor for Springer's Applied Mathematical Sciences series (2018–present). [9]

He was a member of the Institute for Advanced Study in 1997. In 2023 he was a Distinguished Visiting Professor at the Instituto de Ciencias Matemáticas (ICMAT) in Spain and delivered the 30th Annual Owens Lecture at Wayne State University. [12]

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. [13]

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. [14]

His research in control theory includes widely cited results with M. Reyhanoglu and N. H. McClamroch on the control of nonholonomic mechanical systems. [15]

In integrable systems, Bloch is well known for showing that the Toda lattice flow is gradient on adjoint orbit [16] 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. [17]

He also known for work on the symmetric representation of the generalized rigid body equations with Crouch, Marsden, and Rațiu [18] and his work with Iserles, Marsden, and Rațiu on  integrable flows on symmetric matrices. [19]

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. [1] His most recent book, co-authored with A. Rojo, is The Principle of Least Action: History and Physics, which examines the development and applications of variational principles in mechanics. [20]

His recent work also involves data-guided control, network dynamics, and applications to biological systems. [21] He maintains active collaborations across mathematics, physics, engineering, and applied sciences. [22]

Selected publications

References

  1. 1 2 Leonardo, Colombo; Manuel, de León; Tomoki, Ohsawa (2021-03-01). "Preface to the special issue dedicated to Anthony Bloch". Journal of Geometric Mechanics. 13 (1): i–iii. doi:10.3934/jgm.2021004. ISSN   1941-4889.
  2. ↑ "Anthony Bloch". Institute of Mathematical Sciences (Spain) .
  3. 1 2 https://lsa.umich.edu/content/dam/math-assets/math-document/continuum/summer2005.pdf Anthony Bloch Named Chair
  4. 1 2 "Anthony Bloch named a Fellow of the Society of Industrial and Applied Mathematics (SIAM) | U-M LSA Mathematics". lsa.umich.edu. Retrieved 2025-09-27.
  5. 1 2 "AMS :: List of Fellows of the American Mathematical Society". www.ams.org. Retrieved 2025-09-27.
  6. 1 2 "Fellow of IEEE Anthony Bloch". ieeexplore.ieee.org. Retrieved 2025-09-27.
  7. ↑ "Anthony M. Bloch Guggenheim Fellowships: Supporting Artists, Scholars, & Scientists". www.gf.org. Retrieved 2025-09-27.
  8. ↑ "Simons Fellows in Mathematics". Simons Foundation. 2012-06-20. Retrieved 2025-09-27.
  9. 1 2 3 4 Baillieul, John. "CISE Seminar: Anthony Bloch, University of Michigan | Center for Information & Systems Engineering". Boston University . Retrieved 2025-09-27.
  10. ↑ "Anthony Bloch, the Alexander Ziwet Professor and Head of the Mathematics Department at the University of Michigan, has been elected as a Corresponding Member of NAAI!". thenaai.org. Retrieved 2025-09-27.
  11. ↑ "Fellows-CORE Academy". coreacad.org. Retrieved 2025-09-27.
  12. ↑ "Anthony Bloch". ICMAT.
  13. ↑ Richter, Ingrid. "Anthony Bloch Integrable Hamiltonian and gradient flows and total positivity". University of Washington . Retrieved 2025-09-27.
  14. ↑ Bloch, Anthony M. (2015), Bloch, A.M.; Krishnaprasad, P. S.; Murray, R.M. (eds.), "Basic Concepts in Geometric Mechanics", Nonholonomic Mechanics and Control, Interdisciplinary Applied Mathematics, vol. 24, New York, NY: Springer, pp. 125–198, doi:10.1007/978-1-4939-3017-3_3, ISBN   978-1-4939-3017-3
  15. ↑ Reyhanoglu, Mahmut; Bloch, Anthony M.; Harris Mcclamroch, N. (1995). "Control of nonholonomic systems with extended base space dynamics". International Journal of Robust and Nonlinear Control. 5 (4): 325–330. doi:10.1002/rnc.4590050408. ISSN   1099-1239.
  16. ↑ https://community.ams.org/journals/bull/1990-23-02/S0273-0979-1990-15960-9/S0273-0979-1990-15960-9.pdf A new formulation of the generalized toda lattice equations and their fixed point analysis via the momentum map  
  17. ↑ Bloch, Anthony M.; Brockett, Roger W.; Rațiu, Tudor S. (1992-06-01). "Completely integrable gradient flows". Communications in Mathematical Physics. 147 (1): 57–74. Bibcode:1992CMaPh.147...57B. doi:10.1007/BF02099528. ISSN   1432-0916.
  18. ↑ Bloch, Anthony M.; Crouch, Peter E.; Marsden, Jerrold E.; Rațiu, Tudor S. (2002). "The symmetric representation of the rigid body equations and their discretization". Nonlinearity. 4 (15). hdl:2027.42/49076. ISSN   0951-7715.
  19. ↑ A Class of Integrable Flows on the Space of Symmetric Matrices https://sites.lsa.umich.edu/abloch/wp-content/uploads/sites/1327/2024/08/BlBrIsMaRa5309_new.pdf
  20. ↑ Rojo, Alberto; Bloch, Anthony (2018). The Principle of Least Action: History and Physics. Cambridge: Cambridge University Press. doi:10.1017/9781139021029. ISBN   978-0-521-86902-7.
  21. ↑ "Baillieul Distinguished Lecture Series : Department of Mathematics and Statistics: UMass Amherst". www.umass.edu. Retrieved 2025-09-27.
  22. ↑ Rand, Stephen. "New research program to investigate optical energy conversion". Electrical and Computer Engineering. Retrieved 2025-09-27.
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