Graduate Student Recruiting:
- I am continuously seeking highly motivated and well-prepared M.Sc. and Ph.D. candidates with an interest in pure and applied mathematics, especially in the general areas of sub-Riemannian geometry, stochastic analysis, and geometric equivalence.
- Interested candidates should contact me directly by e-mail.
- A link to our departmental page on graduate studies.
- A link to the online application.
Research Interests
- Hypoelliptic Operators and Heat Kernels
- Stochastic Analysis and the Malliavin Calculus
- Sub-Riemannian Geometry and Geometric Equivalence
- Topological Problems in Systems Theory
- Mathematical Problems in Imaging and Inverse Problems
Academic Experience
- Post-Doctoral Associate, Laboratory for Information and
Decision Systems, MIT.
- Ph.D. (Applied Mathematics), Harvard University.
- M. Sc. (Mathematics), McGill University.
- M.Eng (Electrical) McGill University.
- B.Eng (Electrical) McGill University.
Research Collaborators
- Professor Fabrice Baudoin, Department of Mathematics, University of Connecticut (Storrs). Research project: Subelliptic operators on semisimple Lie groups
- Professor Niky Kamran, Department of Mathematics and Statistics, Mc Gill University. Research project: Geometric study of singular partial differential equations
- Professor Frank Proske, Department of Mathematics (Stochastic Analysis group), University of Oslo. Research project: Regularization by noise and pathwise uniqueness of solutions of differential equations
Current Graduate Students and Postdoctoral Fellows
- Oussama Amine (Ph.D., 2017-), University of Oslo (Department of Mathematics, Stochastic Analysis Group) (co-supervision with Professor F. Proske, U. of Oslo)
Former Graduate Students and Post-Doctoral Fellows
- Graeme Baker (M.Sc., 2016-18) currently a Ph.D. student in Operational Research and Financial Engineering at Princeton University
- Alireza Samsamshariat (M.Sc., 2017-18, co-supervision with Professor B. Gharesifard)
- Jeremy Coulson (M.Sc., 2015-17, co-supervision with Professor B. Gharesifard) currently a Ph.D. student in Electrical and Computer Engineering at ETH (Zurich)
- Drew Steeves (M.Sc., 2015-17, co-supervision with Professor B. Gharesifard) currently a Ph.D. student in Mechanical and Aerospace Engineering at University of California, San Diego
- Tristan Milne (M.Sc., 2014-16), currently a Ph.D. student in Mathematics at University of Toronto
- Babak Beheshti Vadeqan (M.Sc., 2013-16, co-supervision with Profs. B. Gharesifard and T. Linder), currently a Ph.D. student in Mathematics at Western University
- Dr. Robert Kipka (PDF, 2014-16, co-supervision with Professors Bogoyavlenskij, Gharesifard, and Lewis), currently an Assistant Professor of Mathematics at Kent State University
- John Treilhard (M.Sc., 2012-14), M.Sc. in Biomedical Engineering at Yale University (2014-2016), currently a Technology Specialist at Fish and Richardson
- Dr. Shahla Molahajloo (PDF, 2011-13 , co-supervision with Prof. A. Lewis)
- Steven Wu (M.Sc., 2010-13 , co-supervision with Prof. T. Linder)
- Caroline Seguin (M.Sc., 2009-11)
- Ian Scriver (M.Sc., 2010-11), currently a M.Sc. student in Earth and Atmospheric Sciences at University of Alberta
- Andrew Brennan (M.Sc., 2010-11), currently a PhD student in Bioengineering at Harvard University
- Jeffrey Calder (M.Sc., 2008-10), currently an Assistant Professor of Mathematics at University of Minnesota
- Bahman Gharesifard (PhD, 2005 - 2009, co-supervision with Prof. A. Lewis), Assistant Professor of Mathematics and Statistics at Queen's University
- Thomas Norman (M.Sc. 2006-07), currently a PhD student in Systems Biology at Harvard University
- Michael Greene (M.Sc. 2006-07)
Selected Publications
- T. Milne, A. Mansouri, "Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation", Transactions of the American Mathematical Society (accepted for publication).
- M. Broucke, M. Ornik, A. Mansouri, "A Topological Obstruction in a Control Problem", Systems and Control Letters, Vol. 108 (2017), 71-79.
- J. Treilhard, A. Mansouri, "Concentration Inequalities via Malliavin Calculus with Applications", Electronic Communications in Probability, Vol. 20 (2015), no. 36, 1-14.
- A. Mansouri, "Topological Obstructions to Distributed Feedback Stabilization to a Submanifold", Proceedings of the 2015 SIAM Conference on Control and its Applications, July 2015.
- A. Mansouri, "Topological Obstructions to Distributed Feedback Stabilization", Proceedings of the 51st Allerton Conference on Communication, Control, and Computing, October 2013.
- C. Seguin, A. Mansouri, "Short-time asymptotics of heat kernels of hypoelliptic Laplacians on unimodular Lie groups", Journal of Functional Analysis Vol. 262 (9) 2012, 3891--3928.
- J. Calder, A. Mansouri, "Anisotropic image sharpening via well-posed Sobolev gradient flows",
SIAM Journal on Mathematical Analysis Vol. 43 (4), 2011, 1536--1556.
- J. Calder, A. Mansouri, A. Yezzi, "New Possibilities in Image Diffusion and Sharpening via High-Order Sobolev Gradient Flows", Journal of Mathematical Imaging and Vision
Vol. 40 (3), 2011, 248--258.
- J. Calder, A. Mansouri, A. Yezzi, "Image Sharpening via
Sobolev Gradient Flows", SIAM Journal on Imaging Sciences
Vol. 3 (4), 2010, 981--1014.
- A. Mansouri, "Topological Obstructions to Submanifold Stabilization",
IEEE Transactions on Automatic Control Vol. 55 (7) 2010, 1701--1703.
- A. Mansouri, "An Extension of Cartan's Method of Equivalence to Immersions: I. Necessary Conditions",
Differential Geometry and its Applications Vol. 27 (5) 2009, 635--646.
- R.W. Brockett, A. Mansouri, "Short-time asymptotics of heat kernels for a class of hypoelliptic
operators", American Journal of Mathematics Vol. 131 (6) 2009, 1795--1814.
- B. Gharesifard, A. Lewis, A. Mansouri, "A geometric framework for stabilization by energy shaping:
sufficient conditions for existence of solutions", Communications in Information and
Systems Vol. 8 (4) 2008, 353--398.
- A. Mansouri, "A topological obstruction to unit tangent
bundles", C.R. Math. Acad. Sci. Soc.
R. Can., Vol. 29 (3) 2007, 87--90.
- A. Mansouri, "Local asymptotic feedback
stabilization to a submanifold: topological conditions", Systems Control Lett., 56
(2007), no. 7-8, 525--528.
- A. Mansouri, "Topological obstructions to regular
non-integrable rank-2 distributions", C. R. Math. Acad. Sci. Paris
344 (2007), no. 7, 453--456.
- A. Mansouri, "Pattern generation,
topology, and non-holonomic systems", Systems Control Lett., 54
(2005), no. 10, 953--959.
- A. Mansouri, "On isotropic sub-Riemannian contact
manifolds", C. R. Math. Acad. Sci. Paris 339 (2004), no. 1,
39--42.
- A. Mansouri, D.P. Mukherjee, S.T. Acton, "Constraining active contour evolution via Lie groups of
transformation", IEEE Trans. Image
Proc., 13 (2004), no. 6, 853--863.
Teaching
- Winter 2018: MATH 923 Topics in Analysis: Stochastic Calculus and Analysis
- Winter 2018: APSC 174 (Introduction to Linear Algebra)
- Fall 2017: MATH 430/830 (Modern Control Theory)
- Winter 2017: MATH 923 Topics in Analysis: Stochastic Calculus and Analysis
- Winter 2017: APSC 174 (Introduction to Linear Algebra)
- Fall 2016: MATH 430/830 (Modern Control Theory)
- Winter 2016: MATH 844 (Differentiable Manifolds)
- Winter 2016: APSC 174 (Introduction to Linear Algebra)
- Fall 2015: MATH 430
- (On academic leave July 2014-June 2015)
- Winter 2014: MATH 332 (Introduction to Control)
- Winter 2014: MATH 393 (Engineering Design Project)
- Winter 2014: APSC 174
- Fall 2013: MATH 844
- Fall 2013: MATH 430/830
- Winter 2013: MATH 332
- Winter 2013: MATH 943 (seminar) -- Special Topics in Geometry and Topology: Heat Kernels and Index Theory
- Fall 2012: MATH 430/830
- Fall 2012: MATH 943 (seminar) -- Special Topics in Geometry and Topology: Heat Kernels and Index Theory
- Winter 2012: MATH 943 (seminar) -- Special Topics in Geometry and Topology: Sub-Riemannian Geometry
- Winter 2012: MATH 332
- Winter 2012: APSC 174
- Fall 2011: MATH 943 (seminar) -- Special Topics in Geometry and Topology: Sub-Riemannian Geometry
- Fall 2011: MATH 430/830
- Fall 2011: MATH 844
- Winter 2011: MATH 332
- Winter 2011: APSC 174
- Fall 2010: MATH 430/830
- Winter 2010: MATH 332
- Winter 2010: APSC 174
- Fall 2009: MATH 430/830
- Fall 2009: MATH 844
- Winter 2009: MATH 332
- Winter 2009: APSC 174
- Fall 2008: MATH 430/830
- Winter 2008: MATH 332
- Winter 2008: MATH 844
- Fall 2007: MATH 430/830
- Fall 2007: MATH 949 (seminar) -- Special Topics in Differential Geometry: Geometric Equivalence
- Winter 2007: MATH 332
- Winter 2007: MATH 844
- Winter 2007: MATH 891 (seminar) -- Special Topics in Applied Mathematics: Viscosity Solutions of Hamilton-Jacobi PDEs
- Fall 2006: MATH 430/830
- Winter 2006: MATH 844
- Winter 2006: MATH 335 (Mathematical Methods for Engineers)
- Fall 2005: MATH 430/830
Professional Memberships
- American Mathematical Society (AMS)
- Mathematical Association of America (MAA)
- Society for Industrial and Applied Mathematics (SIAM)
- Professional Engineers Ontario (PEO)
Contact
416 Jeffery Hall,
Queen's University,
Mathematics and Statistics,
Kingston, ON K7L 3N6, Canada
email: mansouri at queensu.ca |