Publications and preprints
-Book: Geometric
inverse problems, with emphasis on two dimensions,
with Mikko Salo
and Gunther
Uhlmann, to appear in CUP.
-On some information-theoretic aspects of non-linear statistical inverse problems, with Richard Nickl, arXiv:2107.09488.
-The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds, with Mihajlo Cekić, Benjamin Delarue and Semyon Dyatlov, to appear in Invent. Math.
-Statistical guarantees for Bayesian uncertainty quantification in non-linear inverse problems with Gaussian process priors, with François Monard and Richard Nickl, Annals of Statistics 49 (2021) 3255--3298.
-The non-abelian X-ray transform on surfaces, with Mikko Salo, to appear in J. Differential Geom.
-Inverse Problem for the Yang-Mills equations, with Xi Chen, Matti Lassas and Lauri Oksanen, Comm. Math. Phys. 384 (2021) 1187--1225.
-Vortices over Riemann surfaces and dominated splittings, with Thomas Mettler, to appear in Ergodic Theory and Dynam. Systems.
-A sharp stability estimate for tensor tomography in non-positive curvature, with Mikko Salo, Math. Z. 298 (2021) 1323--1344.
-Resonant spaces for volume preserving Anosov flows, with Mihajlo Cekić, Pure and Applied Analysis 2 (2020) 795--840.
-Consistent Inversion of Noisy Non-Abelian X-Ray Transforms, with François Monard and Richard Nickl, Comm. Pure Appl. Math. 74 (2021) 1045--1099.
-Detection of Hermitian connections in wave equations with cubic non-linearity, with Xi Chen, Matti Lassas and Lauri Oksanen, to appear in JEMS.
-Functions of constant geodesic X-ray transform, with Joonas Ilmavirta, Inverse Problems 35 (2019) 065002.
-Broken ray tensor tomography with one reflecting obstacle, with Joonas Ilmavirta, to appear in Comm. Anal. Geom.
-Carleman estimates for geodesic X-ray transforms, with Mikko Salo, to appear in Ann. Sci. Éc. Norm. Supér.
-Convex projective surfaces with compatible Weyl connection are hyperbolic, with Thomas Mettler, Analysis & PDE 13 (2020) 1073--1097.
-Lens rigidity for a particle in a Yang-Mills field, with Gunther Uhlmann and Hanming Zhou, Comm. Math. Phys. 366 (2019) 681--707.
-Efficient nonparametric Bayesian inference for X-ray transforms , with François Monard and Richard Nickl, Annals of Statistics 47 (2019) 1113--1147.
-Holomorphic differentials, thermostats and Anosov flows, with Thomas Mettler, Math. Ann. 373 (2019) 553--580.
-The geodesic X-ray transform with a GL(n,C)-connection, with François Monard, J. Geom. Anal. 30 (2020) 2515--2557.
-The geodesic X-ray transform with matrix weights, with Mikko Salo, Gunther Uhlmann and Hanming Zhou, Amer. J. Math. 141 (2019) 1707--1750.
-Invariant distributions and the geodesic ray transform, with Hanming Zhou, Analysis & PDE. 9 (2016) 1903--1930.
-Inverse problems for the connection Laplacian, with Yaroslav Kurylev and Lauri Oksanen, J. Differential Geom. 110 (2018) 457--494.
-The X-ray transform for connections in negative curvature, with Colin Guillarmou, Mikko Salo and Gunther Uhlmann, Comm. Math. Phys. 343 (2016) 83–-127.
-Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level, with Alberto Abbondandolo, Leonardo Macarini and Marco Mazzucchelli, J. Eur. Math. Soc. 19 (2017) 551--579.
-Invariant distributions, Beurling transforms and tensor tomography in higher dimensions, with Mikko Salo and Gunther Uhlmann, Math. Ann. 363 (2015) 305--362.
-Symplectic and contact properties of the Mañé critical value of the universal cover, with Alfonso Sorrentino, NoDEA 21 (2014) 679--708.
-Conformal great circle flows on the three-sphere, with Adam Harris, Proc. Amer. Math. Soc. 144 (2016) 1725–1734.
-Floer homology for non-resonant magnetic fields on flat tori , with Urs Frauenfelder and Will J. Merry, Nonlinearity 28 (2015) 1351--1370.
-On the existence of three closed magnetic geodesics for subcritical energies, with Alberto Abbondandolo and Leonardo Macarini, Comment. Math. Helv. 90 (2015) 155--193.
-Tensor tomography: progress and challenges, with Mikko Salo and Gunther Uhlmann, Chinese Ann. Math. Ser. B. 35 (2014) 399--849.
-On the range of the attenuated ray transform for unitary connections, with Mikko Salo and Gunther Uhlmann, Int. Math. Res. Notices 4 (2015) 873--897.
-Spectral rigidity and invariant distributions on Anosov surfaces, with Mikko Salo and Gunther Uhlmann, J. of Differential Geom. 98 (2014) 147--181.
-Equivariant symplectic homology of Anosov contact structures, with Leonardo Macarini, Bull. Braz. Math. Soc. 43 (2012) 513--527.
-Inverse problems for connections, survey article, Inverse problems and applications: inside out. II, 369--409, Math. Sci. Res. Inst. Publ., 60, Cambridge Univ. Press, Cambridge, 2013.
-Tensor tomography on surfaces, with Mikko Salo and Gunther Uhlmann, Invent. Math. 193 (2013) 229--247.
-Floer homology for magnetic fields with at most linear growth on the universal cover, with Urs Frauenfelder and Will J. Merry, J. Funct. Anal. 262 (2012) 1070--1083
-The attenuated ray transform for connections and Higgs fields, with Mikko Salo and Gunther Uhlmann, Geom.Funct. Anal. 22 (2012) 1460--1489.
-On the growth rate of leaf-wise intersections, with Leonardo Macarini and Will J. Merry, J. Symplectic Geom. 10 (2012) 601--653
-Transparent pairs, J. Geom. Anal. 22 (2012) 1211--1235.
-The contact geometry of the restricted 3-body problem, with Peter Albers, Urs Frauenfelder and Otto van Koert, Comm. Pure Appl. Math. 65 (2012) 229--263.
-Index computations in Rabinowitz Floer homology, with Will J. Merry, J. Fixed Point Theory Appl. 10 (2011) 88--111.
-On the stability of Mañé critical hypersurfaces, with Leonardo Macarini, Calc. Var. Partial Differential Equations 39 (2010) 579--591.
-Stability is not open, with Kai Cieliebak and Urs Frauenfelder, Ann. Inst. Fourier 60 (2010) 2449--2459 (Volume in honour of P. Berard and S. Gallot 60th birthday).
-Bäcklund transformations for transparent connections, J. Reine Angew. Math. 658 (2011) 27--37.
-Stability of Anosov Hamiltonian structures, with Will J. Merry, J. Topol. Anal. 2 (2010) 419--451.
-Symplectic topology of Mañé's critical values, with Kai Cieliebak and Urs Frauenfelder, Geometry & Topology 14 (2010) 1765--1870.
-Helicity and the Mañé critical value, Algebraic & Geometric Topology 9 (2009) 1413--1422.
-Transparent connections over negatively curved surfaces, J. Modern Dynamics 3 (2009) 311--333.
-On the cohomological equation of magnetic flows, with Nurlan Dairbekov, Matemática Contemporânea 34 (2008) 155--193 (Volume in honour of Manfredo DoCarmo's 80th birthday).
-Magnetic flows on Sol-manifolds: dynamical and symplectic aspects, with Leo Butler, Comm. Math. Phys. 284 (2008) 187--202.
-On the injectivity of the X-ray transform for Anosov thermostats, with Dan Jane, Discrete Contin. Dyn. Syst. 24 (2009) 471--487.
-Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders, with Adam Harris, Ann. Global Anal. Geom. 34 (2008) 115--134.
-The boundary rigidity problem in the presence of a magnetic field, with Nurlan Dairbekov, Plamen Stefanov and Gunther Uhlmann, Adv. Math. 216 (2007) 535--609.
-Entropy production in thermostats II, with Nurlan Dairbekov, J. Statist. Phys. 127 (2007) 887--914.
-Regularity of weak foliations for thermostats, Nonlinearity 20 (2007) 87--104.
-Entropy production in Gaussian thermostats, with Nurlan Dairbekov, Comm. Math. Phys. 269 (2007) 533--543.
-Rigidity properties of Anosov optical hypersurfaces, with Nurlan Dairbekov, Ergodic Theory and Dynam. Systems 28 (2008) 707--737.
-Collapsing manifolds obtained by Kummer-type constructions, with Jimmy Petean, Trans. Amer. Math. Soc. 361 (2009) 4077--4090.
-Longitudinal KAM-cocycles and action spectra of magnetic flows, with Nurlan Dairbekov, Math. Res. Lett. 12 (2005) 719--729.
-Magnetic rigidity of horocycle flows, Pacific J. Math. 225 (2006) 301--323.
-Zero entropy and bounded topology, with Jimmy Petean, Comment. Math. Helv. 81 (2006) 287--304.
-The longitudinal KAM-cocycle of a magnetic flow, Math. Proc. Cambridge Philos. Soc. 139 (2005) 307--316.
-On the growth rate of contractible closed geodesics on reducible manifolds, with Jimmy Petean, Proceedings of the AlbertoFest, Geometry and dynamics, 191--196, Contemp. Math., 389, Amer. Math. Soc., Providence, RI, 2005.
-Entropy and collapsing of compact complex surfaces, with Jimmy Petean, Proceedings of the London Math. Soc. 89 (2004) 763--786.
-Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory, with L. Polterovich and K.F. Siburg, Moscow Mathematical Journal 3 (2003) 593--619.
-Periodic orbits for magnetic flows on surfaces, with Gonzalo Contreras and Leonardo Macarini, IMRN 8 (2004) 361--387.
-Collective geodesic flows, with Leo Butler, Annales de l'Institut Fourier 53 (2003) 265--308.
-The pressure of Ricci curvature, with Jimmy Petean, Geom. Dedicata 100 (2003) 93--102.
-The minimal entropy problem for 3-manifolds with zero simplicial volume, with James W. Anderson, Geometric methods in Dynamics I, Asterisque 286 (2003) 63--79.
-The asymptotic Maslov index and its applications with Gonzalo Contreras, Jean-Marc Gambaudo and Renato Iturriaga, Ergodic Theory and Dynam. Systems 23 (2003) 1415--1443. (Erratum)
-Minimal entropy and collapsing with curvature bounded from below, with Jimmy Petean, Inventiones 151 (2003) 415--450.
-Genericity of geodesic flows with positive topological entropy on the 2-sphere, with Gonzalo Contreras, J. Differential Geometry 61 (2002) 1--49.
-Anosov magnetic flows, critical values and topological entropy, with Keith Burns, Nonlinearity 15 (2002) 281--314.
-Connecting orbits between static classes for generic Lagrangian systems with Gonzalo Contreras, Topology 41 (2002) 645--666.