Directeur de Recherche CNRS of first class (DR1),

equipe INRIA Paris CAGE.

Laboratoire Jacques-Louis Lions

Sorbonne Université (Paris VI)

Boite courrier 187

75252 Paris Cedex 05

ugo.boscain -AT- upmc.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 processes on sub-Riemannian manifolds
- Applications to
**geometry of vision and image processing** - Applications to
**sound processing**.

[72] D. Barilari, U. Boscain, D. Cannarsa, On the induced geometry on surfaces in 3D contact sub-Riemannian manifolds. ESAIM Control Optim. Calc. Var. 28 (2022), Paper No. 9, 28 pp.

[69] I. Beschastnyi, U. Boscain, E. Pozzoli. Quantum Confinement for the Curvature Laplacian -Delta + cK on 2D-Almost- Riemannian Manifolds. Potential Analysis 2021. [67] U. Boscain, D. Prandi, L. Sacchelli, G.Turco. A bio-inspired geometric model for sound reconstruction. Journal of Mathematical Neuroscience. Volume 11, Article number: 2 (2021).

[66] D. Barilari, U. Boscain, D. Cannarsa, K. Habermann. Stochastic processes on surfaces in three-dimensional contact sub-Riemannian manifolds. Ann. Inst. Henri Poincare Probab. Stat. 57 (2021), no. 3, 1388-1410.

[64] R. Adami, U. Boscain, V. Franceschi, D. Prandi. Point interactions for 3D sub-Laplacians. Ann. Inst. H. Poincare Anal. Non Lineaire 38 (2021), no. 4, 1095-1113.

[62] U. Boscain, R. Neel, Extensions of Brownian motion to a family of Grushin-type singularities. Electron. Commun. Probab. 25 (2020), Paper No. 29, 12 pp.

[60] D. Barilari, U. Boscain, R. Neel, Heat kernel asymptotics on sub-Riemannian manifolds with symmetries and applications to the bi-Heisenberg group Ann. Fac. Sci. Toulouse Math. (6) 28 (2019), no. 4, 707-732.

[58] U. Boscain, R. Chertovskih, J.P. Gauthier, D. Prandi, A. Remizov. Highly corrupted image inpainting through hypoelliptic diffusion. Journal of Mathematical Imaging and Vision. October 2018, Volume 60, Issue 8, pp 1231-1245.

[56] A. Agrachev, U. Boscain, R. Neel, L. Rizzi. Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling. ESAIM COCV. 24 (2018) n. 3. pp. 1075-1105.

[55] U. Boscain, R. Neel, L. Rizzi Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry. Adv. Math. 314 (2017), 124-184.

[54] U. Boscain, L. Sacchelli, M. Sigalotti, Generic singularities of line fields on 2D manifolds. Differential Geom. Appl. 49 (2016), 326-350.

[53] D. Barilari, U. Boscain, E. Le Donne, M. Sigalotti, Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions. J. Dyn. Control Syst. 23 (2017), no. 3, 547-575.

[51] D. Barilari, U. Boscain, G. Charlot, R.W. Neel On the heat diffusion for generic Riemannian and sub-Riemannian structures Int. Math. Res. Not. IMRN 2017, no. 15, 4639-4672.

[49] U. Boscain, D. Prandi, M. Seri, Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds. Comm. Partial Differential Equations 41 (2016), no. 1, 32-50.

[48] U. Boscain, D. Prandi, The heat and Schrdinger equations on conic and anticonic-type surfaces J. Differential Equations 260 (2016) 3234-3269

[47] U. Boscain, G. Charlot, M. Gaye, P. Mason, Local properties of almost-Riemannian structures in dimension 3. Discrete and Continuous Dynamical Systems Volume 35, Issue 9, 2015. Pages 4115-4147

[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

[76] C. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbru ̈ggen, D. Sugny, F. Wilhelm Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe. EPJ Quantum Technology volume 9, Article number: 19 (2022)

[75] M. Leibscher, E. Pozzoli, C. P ́erez, M. Schnell, M. Sigalotti, U. Boscain, C. Koch, Complete Controllability Despite Degeneracy: Quantum Control of Enantiomer-Specific State Transfer in Chiral Molecules. Communications Physics 5, 110 (2022).

[74] E. Pozzoli, M. Leibscher, M. Sigalotti, U. Boscain, C. Koch, Lie algebra for rotational subsystems of a driven asymmetric top. J. Phys. A 55 (2022), no. 21, Paper No. 215301, 16 pp.

[73] R. Robin, N. Augier, U. Boscain, M. Sigalotti. Ensemble qubit controllability with a single control via adiabatic and rotating wave approximations. J. Differential Equations 318 (2022), 414–442.

[71] U. Boscain, M. Sigalotti, D. Sugny, Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control PRX Quantum 2, 030203 (2021).

[70] N. Augier, U. Boscain, M. Sigalotti. Effective adiabatic control of a decoupled Hamiltonian obtained by rotating wave approximation. Automatica J. IFAC 136 (2022), Paper No. 110034, 9 pp.

[68] I. Beschastnyi, U. Boscain, M. Sigalotti. An obstruction to small-time controllability of the bilinear Schroedinger equation. J. Math. Phys. 62 (2021), no. 3, Paper No. 032103, 14 pp..

[65] U. Boscain, E. Pozzoli, M. Sigalotti. Classical and quantum controllability of a rotating 3D symmetric molecule 2019. SIAM J. Control Optim. 59 (2021), no. 1, 156–184.

[63] N. Augier, U. Boscain, M. Sigalotti. Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems. MCRF doi: 10.3934/mcrf.2020023 (2020).

[59] N. Augier, U. Boscain, M. Sigalotti. Adiabatic ensemble control of a continuum of quantum systems. SIAM J. Control Optim. 56 (2018), no 6. pp. 4045-4068.

[52] S. Glaser, U. Boscain, T. Calarco, C. Koch, W. Kckenberger, R. Kosloff, I. Kuprov, B. Luy, S.Schirmer, T. Schulte-Herbrggen, D. Sugny, F. Wilhelm Training Schrdinger's cat: quantum optimal control. Eur. Phys. J. D (2015) 69: 279.

[50] U. Boscain, P. Mason, G. Panati, M. Sigalotti, On the control of spin-boson systems. J. Math. Phys. 56 (2015), no. 9, 092101, 15 pp.

[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 Comm. Math. Phys. 333 (2015), no. 3, 1225-1239.:w

[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

IHP Trimester ``Geometry, analysis, and dynamics on sub-Riemannian manifolds'' Paris Sep.-Dec. 2014

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.