Special geometries and related structures

CNCS grant PN-III-P4-ID-PCE-2016-0019 contract no. 117/ 2017

Abstract: The project will bring his contribution in modern differential geometry and its interplay with complex geometry, theoretical physics and algebraic geometry.

Project coordinator

�         Dr. Liana David , Scientific Researcher I at Institute of Mathematics " Simion Stoilow " of the Romanian Academy

Research team (in alphabetical order)

�         Dr. Monica Aprodu

�         Dr. Gabriel Badiţoiu

�         Master student Mircea Andrei Florea

�         Master student Ionut-Alexandru Hurjui

�         Dr. Radu Pantilie

�         Dr. Costin Vîlcu

 

Phase one of the project (12.07-2017-30.12.2017)

Expected results in: generalized complex geometry, meromorphic connections, harmonic maps.

Scientific report: link

Scientific paper

�          V. Cortes, L. David : Twist, elementary deformation, and the KK correspondence in generalized complex geometry, Int. J. Math. to appear; arXiv:1706.05516v2 [math.DG]

 

Presentations as Invited Speakers

�         Monica Aprodu: Workshop "Mathematics, Computer Science and Applications", Galaţi, Romania, December 2017.

�         Costin Vîlcu: International Symposium on Discrete and Convex Geometry, Shijiazhuang, China, December 2017.

 

Research Visits Abroad

�         Monica Aprodu: University of Genoa (Italy), (5 days) September 2017.

�         Liana David: University of Mannheim (Germany), (18 days) October - November 2017.

�         Radu Pantilie: Université de Brest (France), (13 days) December 2017.

 

Phase two of the project

Expected results in: quaternionic and quaternionic-Kahler geometry, special Kahler geometry, harmonic maps, meromorphic connections.

Scientific report: link

Scientific papers

�          M. A. Aprodu : Harmonic non-holomorphic maps from S² to Hirzebruch surfaces, sent for publication

�          L. David, C. Hertling : (T)-structures over 2-dimensional F-manifolds: formal classification , Annali di Matematica Pura ed Applicata, to appear; arXiv:1811.03406 [math.DG]

�          R. Pantilie : Projective structures and ρ-connections, J. Inst. Math. Jussieu 19 (2020), 571-579

�          R. Pantilie : Harmonic morphisms and the Penrose-Ward transform, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 30 (1), 2019, 175-194

�          A. Rivière, J. Rouyer, C. Vîlcu, T. Zamfirescu : Double normals of most convex bodies, Adv. in Math. 343 (2019), 245-272; arXiv:1804.07015 [math.MG]

 

Presentations as Invited Speakers

�         Liana David: Workshop "Special Metrics and Symmetries on Complex Manifolds", Universitaty of Regensburg, Germany, 10-15 September, 2018.

�         Radu Pantilie: The Differential Geometry Workshop 2018, Università di Cagliari, Italy, 12-14 September, 2018.

�         Monica Aprodu: Workshop "Mathematics, Computer Science and Applications", University "Dunărea de Jos" of Galaţi, Romania, December 2018.

 

Research Visits Abroad

�         Liana David: University of Hamburg (Germany), (6 days) September 2018.

 

Phase three of the project

Expected results in: quaternionic and quaternionic-Kahler geometry, harmonic maps, singular spaces.

Scientific report: link

Scientific papers

�          R. Pantilie : On the embeddings of the Riemann sphere with nonnegative normal bundles, Electron. Res. Announc. Math. Sci. 25 (2018) 87–95; arXiv:1307.1993v3 [math.DG]

�          G. Deschamps, E. Loubeau, R. Pantilie : Harmonic maps and twistorial structures, Mathematika 66 (2020) 112–124; arXiv:1804.05423 [math.DG]

�          V. Cortés, L. David : Generalized connections, spinors, and integrability of generalized structures on Courant algebroids, sent for publication; arXiv:1905.01977v2 [math.DG]

�          L. David, C. Hertling: (TE)-structures over the irreducible 2-dimensional globally nilpotent F-manifold germ, Rev. Roum. Math. Pure Appl., to appear; arxiv:2001.01063 [math.DG], 53 pages

�          J. Itoh, C. Vîlcu, T. Zamfirescu : With respect to whom are you critical?, Adv. in Math. 369 (2020) 107187; arXiv:1903.10908 [math.GT]

�          Several papers are still in progress. Details about them are presented in the scientific report for the period 2017 - September 2019.

 

Presentations as Invited Speakers

�         Liana David: Workshop on Riemannian and Kähler Geometry, Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Romania, 15-19 April, 2019.

�         Liana David: The Ninth Congress of Romanian Mathematicians, University "Dunărea de Jos" of Galaţi, Romania, June 28 - July 3, 2019.

�         Costin Vîlcu: The Ninth Congress of Romanian Mathematicians, University "Dunărea de Jos" of Galaţi, Romania, June 28 - July 3, 2019.

�         Costin Vîlcu: International Symposium on Convexity and Discrete Geometry, Hebei Normal University, China, 25 - 30 August, 2019.

�         Monica Aprodu was a member in the organizing committee of the "Ninth Congress of Romanian Mathematicians", University "Dunărea de Jos" of Galaţi, Romania, June 28 - July 3, 2019.

 

Research Visits of Foreign Mathematicians

�         Prof. Vicente Cortés from University of Hamburg (Germany) visited IMAR during September 2 -8, 2019, in order to participate at the workshop "Geometry and Physics" organized at IMAR during this period, and to collaborate with Liana David on topics of the project (about generalized geometry).