Professeur des Universités
Directeur de l'UFR Mathématiques

IRMAR - Campus de Beaulieu

Université de Rennes 1
263 avenue du Général Leclerc
CS 74205
35042 Rennes Cedex, France

Director office : Building 23, room 35
Phone : + 33 (0)2 23 23 66 66 

Personal office : Building 22, room 211/1
Phone : + 33 (0)2 23 23 52 21 

karel.pravda-starov " at " univ-rennes1.fr

(Photo UR1/Dircom/Frédéric Obé)

I am Professor in the Research Group in Partial Differential Equations and Dean of the Faculty of Mathematics of the University of Rennes 1. The subject of my research deals with microlocal analysis. Here is my

Editorial activities

I am a member of the Editorial Board of the Journal of Pseudo-Differential Operators and Applications


38) Spectral inequalities for combinations of Hermite functions and null-controllability for evolution equations enjoying Gelfand-Shilov smoothing effects, (with Jérémy Martin), to appear in J. Inst. Math. Jussieu, pdf

37) Spectral inequality for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations, (with Karine Beauchard and Philippe Jaming), Studia Math. 260 (2021), no. 1, 1-43, pdf

36) Geometric conditions for the exact controllability of fractional free and harmonic Schrödinger equations, (with Jérémy Martin), J. Evol. Equ. 21 (2021), no. 1, 1059-1087, pdf

35) Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports, (with Karine Beauchard and Michela Egidi), C. R. Math. Acad. Sci. Paris, 358 (2020), n. 6, 651-700, pdf

34) Estimations de résolvante et localisation du spectre pour certaines classes d'opérateurs pseudo-différentiels semi-classiques non autoadjoints, d'après Dencker, Sjöstrand et Zworski, Séminaire Bourbaki, 72ème année, 2019-2020, Novembre 2019, Exposé no. 1169, pdf

33) Generalized Mehler formula for time-dependent non-selfadjoint quadratic operators and propagation of singularities, Math. Ann. 372 (2018), no. 3-4, 1335-1382, pdf

32) From semigroups to subelliptic estimates for quadratic operators, (with Michael Hitrik and Joe Viola), Trans. Amer. Math. Soc. 370 (2018), no. 10, 7391-7415, pdf

31) Null-controllability of hypoelliptic quadratic differential equations, (with Karine Beauchard), J. Éc. polytech. Math. 5 (2018), 1-43, pdf

30) Propagation of Gabor singularities for Schrödinger equations with quadratic Hamiltonians, (with Luigi Rodino and Patrik Wahlberg), Math. Nachr. 291 (2018), 128-159, pdf

29) Short-time asymptotics of the regularizing effect for semigroups generated by quadratic operators, (with Michael Hitrik and Joe Viola), Bull. Sci. Math. 141 (2017), no. 7, 615-675, pdf

28) Null-controllability of non-autonomous Ornstein-Uhlenbeck equations, (with Karine Beauchard), J. Math. Anal. Appl. 456 (2017), no. 1, 496-524, pdf

27) Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation, (with Nicolas Lerner, Yoshinori Morimoto and Chao-Jiang Xu), J. Funct. Anal., 269 (2015), no. 2, 459-535, pdf

26) Some remarks on degenerate hypoelliptic Ornstein-Uhlenbeck operators, (with Michela Ottobre and Grigorios Pavliotis), J. Math. Anal. Appl. 429 (2015), no. 2, 676-712, pdf

25) Semiclassical hypoelliptic estimates with a loss of many derivatives, (with Alberto Parmeggiani), Rev. Mat. Iberoam. 30 (2014), no. 4, 1439-1478, pdf

24) Gelfand-Shilov smoothing properties of the radially symmetric spatially homogeneous Boltzmann equation without angular cutoff, (with Nicolas Lerner, Yoshinori Morimoto and Chao-Jiang Xu), J. Differential Equations, 256 (2014), no. 2, 797-831, pdf

23) De l'analyse microlocale de quelques classes d'équations aux dérivées partielles, Habilitation dissertation, Université de Cergy-Pontoise, France (2013), pdf

22) A remark on the ultra-analytic smoothing properties of the spatially homogeneous Landau equation, (with Yoshinori Morimoto and Chao-Jiang Xu), Kinet. Relat. Models, 6 (2013), no. 4, 715-727, pdf

21) Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators, (with Nicolas Lerner, Yoshinori Morimoto and Chao-Jiang Xu), Kinet. Relat. Models, 6 (2013), no. 3, 625-648, pdf

20) Spectral and phase space analysis of the linearized non-cutoff Kac collision operator, (with Nicolas Lerner, Yoshinori Morimoto and Chao-Jiang Xu), J. Math. Pures Appl. 100, (2013), no. 6, 832-867, pdf

19) Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics, (with Michael Hitrik), Ann. Inst. Fourier, 63 (2013), no. 3, 985-1032, pdf

18) Exponential return to equilibrium for hypoelliptic quadratic systems, (with Michela Ottobre and Grigorios Pavliotis), J. Funct. Anal. 262 (2012), no. 9, 4000-4039, pdf

17) Subelliptic estimates for overdetermined systems of quadratic differential operators, Osaka J. Math. 49 (2012), no. 3, 563-611, pdf

16) Hypoelliptic estimates for a linear model of the Boltzmann equation without angular cutoff, (with Nicolas Lerner and Yoshinori Morimoto), Comm. Partial Differential Equations, 37 (2012), no. 2, 234-284, pdf

15) Hermite basis diagonalization for the non-cutoff radially symmetric linearized Boltzmann operator, (with Nicolas Lerner, Yoshinori Morimoto and Chao-Jiang Xu), Séminaire Laurent Schwartz - EDP et applications (2011-2012), Exp. No. 23, 10 pages, École Polytechnique, Palaiseau

14) Anisotropic hypoelliptic estimates for Landau-type operators, (with Frédéric Hérau), J. Math. Pures Appl. 95 (2011), 513-552, pdf

13) Sharp hypoelliptic estimates for some kinetic equations, (with Nicolas Lerner), (2011) Proceedings of the International Conference the 26th Matsuyama Camp, Ryukoku University, Kyoto, pdf

12) Subelliptic estimates for quadratic differential operators, Amer. J. Math. 133 (2011), no. 1, 39-89, pdf

11) Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics, (with Michael Hitrik), Comm. Partial Differential Equations, 35 (2010), no. 6, 988-1028, pdf

10) Spectra and semigroup smoothing for non-elliptic quadratic operators, (with Michael Hitrik), Math. Ann. 344 (2009), no. 4, 801-846, pdf

9) On the pseudospectrum of elliptic quadratic differential operators, Duke Math. J. 145 (2008), no. 2, 249-279

8) Pseudo-spectrum for a class of semi-classical operators, Bull. Soc. Math. France, 136 (2008), no. 3, 329-372

7) Contraction semigroups of elliptic quadratic differential operators, Math. Z. 259 (2008), no. 2, 363-391

6) Explicit examples of nonsolvable weakly hyperbolic operators with real coefficients, Bull. Braz. Math. Soc. 38 (2007), no. 3, 397-425

5) Sur le pseudo-spectre de certaines classes d'opérateurs pseudo-différentiels non auto-adjoints, Séminaire : Équations aux Dérivées Partielles, 2006-2007, Exp. No. XV, 33 p., École Polytechnique, Palaiseau

4) Boundary pseudospectral behaviour for semi-classical operators in one dimension, Int. Math. Res. Not. (2007) Vol. 2007, article ID rnm029, 31 pages

3) Étude du pseudo-spectre d'opérateurs non auto-adjoints, PhD Thesis, Université de Rennes 1, France (2006)

2) A complete study of the pseudo-spectrum for the rotated harmonic oscillator, J. London Math. Soc. 73 (2006), no. 2, 745-761

1) A general result about the pseudo-spectrum of Schrödinger operators, Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 460 (2004), 471-477

Analysis in Rennes

Séminaire d'équations aux dérivées partielles

Séminaire d'analyse numérique

Groupe de travail "applications des mathématiques"

Centre Henri Lebesgue

Analysis in Paris & London

Paris London Analysis Seminar

Séminaire: Problèmes Spectraux en Physique Mathématique, Institut Henri Poincaré

Vidéo-séminaire EDP Berkeley / Bonn / Zurich / Paris-Nord, Université de Paris-Nord