Dr. silvia fernandez

Contact Information

Office. Santa Susana Hall (SN) 406

E-mail. silvia.fernandez@csun.edu

Phone. (818) 677-6445

Fax. (818) 677-3634

Address. Department of Mathematics
California State University, Northridge
18111 Nordhoff St. Northrige CA 91330-8313

Office Hours. Monday and Wednesday 4:20-5:20 pm..

Other Activities

• Coordinator of the Masters in Mathematics for Educational Careers (Option III).
• Cohost of the CSUN Problem of the Week.
• CSUN Math Club faculty advisor.
• Member of the American Mathematics Competitions 10-12 Committee (AMC10/12)

Research

Interests

My research interests are in Discrete Geometry, Combinatorics, and Graph Theory. I specially like Erdös type problems. I am currently working on Crossing Number problems.

Colaborators

Bernardo Ábrego, Jorge Arocha, Estie Arkin, Jozsef Balogh, Mario Cetina, György Elekes, Ferran Hurtado, Mikio Kano, Jesús Leaños, Bernardo Llano, Joseph Mitchell, Michael Neubauer, Víctor Neumann-Lara, Gelasio Salazar, Jorge Urrutia, and William Watkins.

Publications

• B. M. Ábrego, M. Cetina, S. Fernández-Merchant, J. Leaños, and G. Salazar. 3-symmetric and 3-decomposable drawings of Kn. Submitted (2008) arXiv:0805.0016.
• B. M. Ábrego, E. Arkin, S. Fernández-Merchant, F. Hurtado, M. Kano, J. Mitchell, J. Urrutia. Matching points with squares. To appear in Discrete and Computational Geometry (2008) Available online as article in press. doi:10.1007/s0045-008-9099-1.
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Sum of squares of degrees in a graph. Submitted (2008). arXiv:0808.2234
• B. M. Ábrego, S. Fernández-Merchant, and B. Llano. On the maximum number of translates in a point set. To appear in Discrete and Computational Geometry (2008) Available online as article in press. doi:10.1007/s00454-008-9111-9.
• B. M. Ábrego, S. Fernández-Merchant, and B. Llano. An inequality for Kruskal-Macaulay Functions. Submitted (2008) arXiv:0809.3549.
• B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. A central approach to bound the number of crossings in a generalized configuration. To appear in Electronic Notes in Discrete Mathematics 30 (2008) 273-278.
• B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. The maximum number of halving lines and the rectilinear crossing number of Kn for n<=27. To appear in Electronic Notes in Discrete Mathematics 30 (2008) 261-266.
• B. M. Ábrego, J. Balogh, S. Fernández-Merchant, J. Leaños, and G. Salazar. An extended lower bound on the number of (<=k)-edges to generalized configurations of points and the pseudolinear crossing number of Kn. To appear in Journal of Combinatorial Theory, Series A. (2008) Available online as article in press. doi:10.1016/j.jcta.2007.11.004.
• B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. Recent developments on the number of (<=k)-sets, halving-lines, and the rectilinear crossing number of Kn. Proceedings of XII Encuentros de Geometría Computacional, Universidad de Valladolid, Spain, June 25-27, (2007), ISBN 978-84-690-6900-4.
• B. M. Ábrego and S. Fernández-Merchant. Geometric drawings of Kn with few crossings. Journal of Combinatorial Theory, Series A 114 (2007) 373-379. (Article available online in 2006.)
• B. M. Ábrego, J. Balogh, S. Fernández-Merchant, J. Leaños, and G. Salazar. On (<=k)–pseudoedges in generalized configurations and the pseudolinear crossing number of Kn. Preprint (2006).
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Trace-minimal graphs and D-optimal weighing designs, Linear Algebra and its Applications 412 (2006), 161-221.
• B. M. Ábrego and S. Fernández-Merchant. A lower bound for the rectilinear crossing number. Graphs and Combinatorics, Springer-Verlag Tokyo Inc., Vol. 21, Num 3, (2005), p. 293 - 300.
• B. M. Ábrego, E. Arkin, S. Fernández-Merchant, F. Hurtado, M. Kano, J. Mitchell, J. Urrutia. Matching points with geometric objects: combinatorial results. Discrete and Computational Geometry Japanese Conference, JCDCG 2004, Tokyo, Japan, October 8-11, 2004. Springer-Verlag, Lecture Notes in Computer Science Series, Vol. 3742, Akiyama, Jin; Kano, Mikio; Tan, Xuehou (Eds.) 2005, VIII, p. 1-15, ISBN: 3-540-30467-3.
• B. M. Ábrego, S. Fernández-Merchant, and Gy. Elekes. Structural results for planar sets with many similar subsets. Combinatorica 24 (2004), no. 4, 541-554.
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. D-optimal weighing designs for n=-1 (mod 4) objects and a large number of weighings, Linear Algebra and its Applications 374 (2003), 175-218.
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Maximum volume simplices and trace-minimal graphs, Proceedings of X Encuentros de Geometria Computacional, University of Sevilla, Sevilla Spain, June 16-17, (2003), 51-56.
• B. M. Ábrego and S. Fernández-Merchant. The unit distance problem for centrally symmetric convex polygons. Discrete and computational geometry and graph drawing (Columbia, SC, 2001). Discrete and Computational Geometry 28 (2002), no 4, 467-473.
• B. M. Ábrego and S. Fernández-Merchant. Convex Polyhedra in R^3 Spanning W(n^(4/3)) Congruent Triangles, Journal of Combinatorial Theory, Series A 98, 406-409 (2002).
• B. M. Ábrego and S. Fernández-Merchant. On the Maximum Number of Equilateral Triangles II. DIMACS Technical Report 99-47, (1999).
• B. M. Ábrego and S. Fernández-Merchant. On the Maximum Number of Equilateral Triangles I. Discrete and Computational Geometry 23, (2000), no. 1, 129-115.
• B. M. Ábrego, J. L. Arocha, S. Fernández-Merchant, and V. Neumann-Lara. Tightness Problems in the Plane. Discrete Mathematics 194 (1999), no. 1-3, 1-11.