General
Information
| Office.
SN 406 (SN
= Santa Susana Hall) |
| E-mail.
silvia.fernandez@csun.edu
|
| Telephone.
(818) 677-6445 |
| Fax.
(818) 677-3634 |
| Address.
|
California
State University, Northridge |
| Department
of Mathematics |
| 18111
Nordhoff St |
| Northridge,
CA 91330-8313 |
|
| Office
hours. On sabbatical Fall 2007 and Spring 2008. |
Other.
- Coordinator of the Masters in Mathematics for Educational Careers
(Option III).
- Cohost of the CSUN Problem of the Week (back in Spring 2008, www.csun.edu/math/probweek). |
|
Research
My
research interests are in Discrete Mathematics, particularly Combinatorial
Geometry, Computational Geometry 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, 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, S. Fernández-Merchant, and B. Llano. On the maximum number of translates. Submitted to Discrete and Computational Geometry (2008).
- B. M. Ábrego, S. Fernández-Merchant, and B. Llano. An inequality for Kruskal-Macaulay Functions. Submitted to European Journal of Combinatorics (2007).
- 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 (2007).
- 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 (2007).
- 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.
- 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.
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