Directeur de Recherche CNRS of first class (DR1),

Part time professor ``charge de cours'' at Ecole Polytechnique

CMAP, Ecole Polytechnique

Route de Saclay

91128 Palaiseau Cedex

Tel. 0033 1 69 33 46 36

Fax. 0033 1 69 33 4646

boscain -AT- cmap.polytechnique.fr

- Properties of the distance function, cut, conjugate loci
- Intrinsic volumes: Hausdorff, spherical Hausdorff, Popp
- Degenerate diffusion on manifolds and hypoelliptic operators
- Intrinsic Random walks
- Spectral theory and self-adjointness of the intrinsic Laplacian
- Stochastic completeness
- Applications to Geometry of Vision and image processing

[Pre3] U. Boscain, D. Prandi, M. Seri, Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds.

[Pre2] U. Boscain, D. Prandi, The heat and Schrdinger equations on conic and anticonic-type surfaces

[Pre1] D. Barilari, U. Boscain, G. Charlot, R.W. Neel On the heat diffusion for generic Riemannian and sub-Riemannian structures

[43] U. Boscain, R. Chertovskih, J.P. Gauthier, A. Remizov. Hypoelliptic diffusion and human vision: a semi-discrete new twist. SIAM Journal on Imaging Sciences 2014, Vol. 7, No. 2, pp. 669-695

[38] D. Barilari, U. Boscain, R. Neel, Small time heat kernel asymptotics at the sub-Riemannian cut locus. JDG Vol 92, No.3, 2012, pp. 373-416.

[36] U. Boscain, C. Laurent, The Laplace-Beltrami operator in almost-Riemannian Geometry. Ann. Inst. Fourier (Grenoble) 63 (2013), no. 5, 1739-1770.

[32] U. Boscain, J. Duplaix, J.P. Gauthier, F. Rossi, Anthropomorphic image reconstruction via hypoelliptic diffusion. SIAM J. CONTROL OPTIM.Vol. 50, No. 3, pp. 1309--1336

[31] A. Agrachev, D. Barilari, U. Boscain, On the Hausdorff volume in sub-Riemannian geometry. Calculus of Variations and PDE's Volume 43, Numbers 3-4 March 2012.

[24] A. Agrachev, U. Boscain, J.P. Gauthier, F. Rossi, ``The intrinsic hypoelliptic Laplacian $ corresponding heat kernel on unimodular Lie groups'' Journal of Functional Analysis, Volume 256, Issue 8, 15 April 2009, Pages 2621-2655.

- Optimal control on finite dimensional quantum systems
- Controllability of the Schrodinger Equation via Galerkin Approximation
- Controllability of the Schrodinger Equation via Intersections of the Eigenvalues

[46] U. Boscain, J.P. Gauthier, F. Rossi M. Sigalotti, Approximate controllability, exact controllability, and conical eigenvalue intersections for quantum mechanical systems.. Communications in Mathematical Physics November 2014.

[40] U. Boscain, M.Caponigro, Mario Sigalotti Multi-input Schrdinger equation: controllability, tracking, and application to the quantum angular momentum. Journal of Differential Equations 256 (2014), no. 11, 3524-3551.

[35] U. Boscain, F. Chittaro, P. Mason, M. Sigalotti, Adiabatic control of the Schroedinger equation via conical intersections of the eigenvalues. IEEE Transactions on Automatic Control, Volume: 57, Issue: 8, pp. 1970 - 1983, 2012. [34] U. Boscain, M. Caponigro, T. Chambrion, and M. Sigalotti, A weak spectral condition for the controllability of the bilinear Schrdinger equation with application to the control of a rotating planar molecule. Commun. Math. Phys. 311, 423-455 (2012).

[23] T. Chambrion, P. Mason, M. Sigalotti and U. Boscain, Controllability of the discrete-spectrum Schroedinger equation driven by an external field, Annales de l'Institut Henri Poincare (C) Non Linear Analysis Volume 26, Issue 1, January-February 2009, Pages 329-349.

- Time optimal Syntheses on 2-D Manifolds
- Optimal Control on Lie Groups

- Stability of switching systems for arbitrary switchings
- Existence of common polynomial Lyapunov functions

Workshop on ``Conical intersections in Mathematical Physics'' Istitute Henri Poincar?? Paris - May 29-31, 2013

INDAM meeting on Geometric Control and sub-Riemannian Geometry Cortona, Italy, May 21 - 25, 2012

Session on Analytic and Geometric Optimal Control IFIP September 12-16-2011, Berlin.

Workshop on Control and Topology Topolo' (Udine, Italy), May 30th-31th, 2011.

Workshop on Quantum Control IHP, Paris Dec. 8-10, 2010.

Workshop on Nonlinear Control and Singularities Porquerolles (83400 HYERES LES PALMIERS, France), October 24th-28th, 2010.

Franco-Brazilian Workshop on Sub-Riemannian Geometry Belem, August 23-27, 2010.