Institute of Mathematics "Simion Stoilow" of the Romanian Academy

Phone: (+40) 21 319 6506. Fax: (+40) 21 31 96505

IMAR, P.O.Box 1-764, RO-014700 Bucharest, Romania

e-mail: CostindotVilcuatimardot REMOVE.MEro

- Ph.D. in Mathematics, Dortmund University, 2003, with the thesis "
Farthest points on convex surfaces".- DEA Algorithmique, EDITE de Paris, 2004.
- Master of Science in Geometry, University of Bucharest, 1996.
- University Degree in Mathematics, University of Bucharest, 1995.

Critical points for distance functions; cut loci and (quasi)geodesics on convex surfaces and, more generally,on Alexandrov surfaces with curvature bounded below.Unfoldings of polyhedral convex surfaces.

12th International Conference on Discrete Mathematics: Discrete Geometry and Alexandrov surfaces, Bucharest, September 2013.Anniversary Conference Faculty of Sciences - 150 years, Bucharest, August-September 2013.Experimental and Theoretical Methods in Algebra, Geometry and Topology, Eforie Nord, June 2013.Colloque de géométries, Mulhouse, September 2012.The 10th International Workshop on Differential Geometry and its Applications, Constanta, August 2011.7th Congress of Romanian Mathematicians, Brasov, June-July 2011.11th International Conference on Discrete Mathematics: Covexity and Discrete Geometry, Dortmund, July 2009.10th International Conference on Covexity and Discrete Mathematics, Dortmund, August 2007.6th Congress of Romanian Mathematicians, Bucharest, June 2007.Mathematical Society of Japan, 2005 Autumn Meeting, Okayama, September 2005.The 52nd Geometry Symposium of The Mathematical Society of Japan, Fukuoka, August 2005.9th International Conference on Discrete Mathematics and Embedded Structures, Dortmund, August 2004.Convexity and Discrete Mathematics, Budapest, July 2004.8th International Conference on Discrete Mathematics, Dortmund, June 2000.7th International Conference on Covexity and Discrete Mathematics, Dortmund, June 1996.First Balkan Conference on Geometry, Bucharest, September 1996.

- Alicante (2011), Naha (2005), Nagoya (2005), Okayama (2005), Sapporo (2005), Nara (2005), Kumamoto (2004, 2005), Timisoara (2004), Dortmund (2002), Bucharest (1997, 2011).

Prize Gheorghe Titeica of the Romanian Academy, 2008 (awarded 2010).

- Research Grant PN-II-ID-PCE-2011-3-0533, team member (Grant Director : Acad. T. Zamfirescu).
- Research Grant PN II Idei-1187/2009, team member (Grant Director : S.R. II Dr. L. David).
- Research Grant 2-CEx 06-11-22/25.07.2006, team member (IMAR Responsible: S.R. II Dr. R. Pantilie).
- JSPS Post-doctoral Fellowship, 2004-2006.
- Doctoral Fellowship from the land North-Rhine Westfalia, 2000-2002.
- Research Grant ANSTI 4116/30.11.1998, team member (Grant Director: Prof. Dr. S. Ianus).

Simple closed geodesics on most Alexandrov surfaces, (with J. Rouyer).The connected components of the space of Alexandrov surfaces, (with J. Rouyer).On the Theorem of the Three Perpendiculars, (with J. Itoh and J. Rouyer).Moderate smoothness of most Alexandrov surfaces, (with J. Itoh and J. Rouyer).Conical existence of closed curves on convex polyhedra, Comput. Geom. Theory Appl., to appear (with J. O'Rourke).On the number of cut locus structures on graphs, (with J. Itoh).Orientable cut locus structures on graphs, (with J. Itoh).Every graph is a cut locus, (with J. Itoh).Every point is critical, Adv. Math. 235 (2013), 390-397, (with I. Bárány, J. Itoh, and T. Zamfirescu).Continuous Flattening of Convex Polyhedra, inComputational Geometry, Lecture Notes in Computer Science 7579 (2012), 85-97; (with J. Itoh, and C. Nara).Sets of tetrahedra, defined by maxima of distance functions, An. Stiint. Univ. ``Ovidius'' Constanta Ser. Mat. 20 (2012), 197-212; (with J. Rouyer).Cut locus structures on graphs, Discrete Math. 312 (2012), 524-531. (with J. Itoh); preliminary version here.Quasigeodesics and farthest points on convex surfaces, Adv. Geom. 11 (2011), 571-584 (with K. Ieiri and J. Itoh).Source unfoldings of convex polyhedra with respect to certain closed polygonal curves, Proc. 25th European Workshop Comput. Geom. (EuroCG) 61-64, March 2009. Full version submitted for publication, May 2009. (with J. Itoh and J. O'Rourke).Star unfolding convex polyhedra via quasigeodesic loops, Discrete Comput. Geom. 44 (2010), 35-54, (with J. Itoh and J. O'Rourke); arXiv:0812.2257v1 [cs.CG]. See also the preliminary version "Unfolding Convex Polyhedra via Quasigeodesics" below.What do cylinders look like?, J. Geom. 95 (2009), 41-48 (with J. Itoh).Criteria for farthest points on convex surfaces, Math. Nachr. 282 (2009), 1537-1547 (with J. Itoh).Antipodal convex hypersurfaces, Indag. Math. 19 (2008), 411-426 (with J. Itoh and J. Rouyer).On typical degenerate convex surfaces, Math. Ann. 340 (2008), 543-567.Common maxima of distance functions on orientable Alexandrov surfaces, J. Math. Soc. Japan 60 (2008), 51-64.Unfolding convex polyhedra via quasigeodesics, arXiv:0707.4258v3 [cs.CG]; 2-page abstract in Fall Workshop on Computational Geometry, Nov. 2007, pp. 79-80 (with J. Itoh and J. O'Rourke).Multiple farthest points on Alexandrov surfaces, Adv. Geom. 7 (2007), 83-100 (with T. Zamfirescu).On the length of simple closed quasigeodesics on convex surfaces, C. R. Math. Acad. Sci. Paris Ser. I. 343 (2006), 259-264 (with J. Itoh).Properties of the farthest point mapping on convex surfaces, Rev. Roum. Math. Pures Appl. 51 (2006), 125-134. Also published in the volume "Papers on Convexity and Discrete Geometry and other nice fields - Dedicated to Tudor Zamfirescu on the occasion of his 60th birthday", Ed. Academiei Romane, 2006.Symmetry and the farthest point mapping on convex surfaces, Adv. Geom. 6 (2006), 379-387 (with T. Zamfirescu).Farthest points and cut loci on some degenerate convex surfaces, J. Geom. 80 (2004), 106-120 (with J. Itoh).On Two Conjectures of Steinhaus, Geom. Dedicata 79 (2000), 267-275.Tangent Bundles and Submanifolds, Bull. Math. Soc. Sci. Math. Roum. 40 (1997), 43-48.On Some Submanifolds of Bochner Flat Indefinite Kaehler Manifolds, in the volume of the "Annual Conference of The Romanian Society of Mathematical Sciences", Bucharest 1997, 311-315.An idea from convex geometry(in Romanian), Gazeta Matematica Seria A Vol. XV 3 (1997), 193-196.