Liana David

Position

Senior Researcher grade I at Institute of Mathematics "Simion Stoilow" of the Romanian Academy (I.M.A.R.)

Languages

Romanian (mother tongue), English (advanced), Italian (advanced), French (advanced), German (level B2)

Education

1995 West University of Timisoara, Diploma in Mathematics
1996 West University of Timisoara, Master Degree in Mathematics
1997 University of Cambridge (UK), Certificate of Advanced Study in Mathematics (graduated with Distinction)
2001 University of Edinburgh, Ph.D in Mathematics

Post-Doctoral and Visiting Positions

2001 - 2002 Ecole Polytechnique (Palaiseau), EDGE Post-doctoral Fellow
2002 - 2003 University of Hull, EPSRC Post-doctoral Research Assistant
2003 - 2004 University of Glasgow, EPSRC Post-doctoral Research Assistant
2005 (3 months) Ecole Polytechnique (Palaiseau), CNRS researcher
2006 - 2008 Centro di Ricerca Matematica "Ennio de Giorgi" (Scuola Normale Superiore di Pisa), Cari-Luca SNS Junior Visiting Fellow
2008 (2 months) The "Abdus Salam" International Center for Theoretical Physics, Visiting Researcher
2010 (6 weeks) University of Glasgow, Senior Research Fellow
2012 (2 months) Institut des Hautes Etudes Scientifiques (Bures sur Yvette), Visiting Scientist.
2013-2016 (18 months) University of Mannheim and University of Hamburg, Humboldt Research Fellow

Habilitation

Thesis title: Geometric structures on manifolds; Thesis defence at IMAR, on 19th of June 2013.

Research Interests

Kahler and CR geometry, quaternionic geometry, generalized complex geometry, Frobenius manifolds and meromorphic connections, Penrose transforms.

Director of national research projects won by competition: Geometric structures on manifolds (CNCS grant, code 1187/2008), during 2009-2011; Hermitian and quaternionic structures on manifolds and applications (PN-II-ID-PCE-2011-3-0362), during 2012-2016; Special geometries and related structures (PN-III-ID-P4-PCE-2016-0019), during 2017-2019.

Publications and Preprints

- Generalized connections, spinors and integrability of generalized structures on Courant algebroids, arxiv:1905.01977 (62 pages), sent for publication (joint with V. Cortes)

- Twist, elementary deformation, and the KK-correspondence in generalized complex geometry, arxiv:1706.05516 (57 pages), sent for publication (joint with V. Cortes)

--(T)-structures over 2-dimensional F-manifolds: formal classification, accepted at Ann Mat. Pura Applic (joint with C. Hertling)

--Regular F-manifolds: initial conditions and Frobenius metrics, Ann. Sc. Norm. Sup. Pisa, (5) 17 (2017), p. 1121-1152 (joint with C. Hertling)
- Prolongation of Tanaka structures: an alternative approach, Ann. Mat. Pura Applic. (3) 196 (2017), p. 1137-1164 (joint with D. Alekseevsky) --On cotangent manifolds, complex structures and generalized geometry, Ann. Inst. Fourier, 66 (2016), p. 1-28.
- Hermitian metrics on F-manifolds, J. Geom. Physics 107 (2016), p. 60-78 (joint with C. Hertling) --Tanaka structures (non-holonomic G-structures) and Cartan connections, J. Geom. Physics, (Conformal and Complex geometry in Honor of Paul Gauduchon), vol. 91 (2015), p. 88-100 (joint with D. V. Alekseevsky)
--The tt* geometry on the big phase space, Comm. Math. Physics , vol. 329 (2014), p. 295-323 (joint with I. A. B. Strachan).
-- Symmetries of F-manifolds with eventual identities and special families of connections , Ann. Sc. Norm. Sup. Pisa, vol. XIII (2014), p. 641-674 (joint with I. A. B. Strachan)
--On adding a variable to a Frobenius manifold and generalizations, Geom. Dedicata, vol. 167, (2013), p. 189-214
--Invariant generalized complex structures on Lie groups, Proc. London Math. Soc. , (4), vol. 105 (2012) (joint with D. V. Alekseevsky).
-- A note about invariant SKT-structures and generalized Kahler structures on flag manifolds, Proc. Edinb. Math. Soc., (3) vol. 55 (2012) (joint with D.V. Alekseevsky).
-- A prolongation of the conformal-Killing operator on quaternionic-Kahler manifolds, Ann. Mat. Pura Applic. (4) vol. 191 (2012).
-- The conformal-Killing equation on G2 and Spin7 structures, J. Geom. Physics, (6), vol. 61, (2011).
-- Dubrovin's duality for F-manifolds with eventual identities, Adv. Math., (5), vol. 266, (2011) (joint with I. A. B. Strachan).
-- A report on the geometry of Bochner-flat Kahler manifolds, (volume in the honour of Dan I. Papuc), A.U.T., XLVIII,1,2 (2010), p. 147-156.
-- The fundamental form of almost-quaternionic Hermitian manifolds, J. Geom. Physics, (4) 60 (2010), p. 574-580
-- A characterization of quaternionic projective space by the conformal-Killing equation, J. London Math. Soc. (2) 80 (2009), p. 326-340 (joint with M. Pontecorvo)
-- About the geometry of almost para-quaternionic manifolds, Diff. Geom. Applic. 27 (2009), p. 575-588.
-- Quaternionic connections, induced holomorphic structures and a vanishing theorem, Internat. J. Math., 19 (2008), no. 10, p.1167-1185
-- The Bochner-flat cone of a CR manifold, Compositio Math., 114 (2008), p. 747-777
-- The Bochner-flat geometry of Weighted Projective spaces,Perspectives in Riemannian Geometry, C.R.M. Proceed. Lecture Notes, AMS (2006), p. 109-156 (joint with P. Gauduchon)
-- Sasaki-Weyl connections on CR manifolds, Diff. Geom. Applic., 24 (2006), no. 5, p. 542-553.
-- Conformally-flat pencils of metrics, Frobenius structures and a modified Saito construction, J. Geom. Physics 56 (2006), no. 9, p. 1561-1575 (joint with I. A. B. Strachan)
-- A note on the multi-Eguchi-Hanson metric, Modern Trends in Geometry and Topology, (2006), no. 3-4, p. 179-184.
-- Weyl connections and curvature properties on CR manifolds, Ann. Global Anal. Geom., 26 (2004), no. 1 (2004), p. 59-72
-- Compatible metrics on a manifold and non-local bi-hamiltonian structures, Internat. Math. Res. Notices, 66 (2004), p.3433-3557 (joint with I. A. B. Strachan)
-- The X-ray transform for currents, Diff. Geom. Applic., vol. 18 no. 1 (2003) p. 113-117
-- The Penrose transform for compactly supported cohomology, J. London Math. Soc., vol. 66, no. 2 (2002) p. 131-141 (joint with T. N. Bailey)
-- The Atiyah-Ward Ansatz in 3-dimensions, Rendiconti di Matemematica, vol. 22 no. 7 (2002) p. 343-358
-- The Guillemin formula and Kaehler metrics on toric symplectic manifolds, J. Symplectic Geom., vol. 1, no. 4 (2002) p. 767-784 (joint with D. M. J. Calderbank and P. Gauduchon)
-- The Penrose transform for currents, Rivista Mat. Univ. Parma, vol. 7, no. 1 (2002) 1-7
-- Relative involutive cohomology and applications, An. Univ. Timisoara, Seria Matematica-Informatica, XXXIX (2001), p. 23-34
-- Several extensions of the smooth Penrose transform, An. Univ. Timisoara, Seria Mat.-Inf., vol. 39 (2001), p. 163-173
-- About positive operators on vector bundles, Rivista Mat. Univ. Parma vol. 5, no. 5 (1996) p. 55-64 (joint with D. Papuc)
On the composition of positive operators on vector bundles, Scripta Scient. Math., vol. 1 fasc. 2 (MCMXCIX), (joint with D. I. Papuc)
-- Spectral properties of positive operators defined on a vector bundle endowed with a field of cones, An. Univ. Timisoara, Seria Matematica-Informatica, vol. 33 no. 1 (1995) p. 55-65

Contact

Postal Address: I.M.A.R., Bucharest, RO-014700, ROMANIA
E-Mail: Liana dot David at imar dot ro