## Afternoons on Algebra, Combinatorics and Optimization

The Department of Mathematics, Cinvestav-IPN invites you to the Afternoons on Algebra, Combinatorics and Optimization. This symposium is held on the second Wednesday of each month at 4:00 p.m. at the Auditorium José Adem, Cinvestav-IPN.

Organizing Committee:

Ruy Fabila Monroy
ruyfabila [@] math.cinvestav.edu.mx

March 13, 2013 CANCELED
Dra. María de Luz Gasca Soto
Faculty of Science, UNAM
Variants of the Hypercube: Topological and algorithmic properties

October 17, 2012
Dra. Amanda Montejano
Multidisciplinary Research and Education Department of the Faculty of Science, UNAM-Juriquilla
How to use additive number theory to solve problems in anti-Ramsey theory?

July 25, 2012
Dr. Clemens Huemer
Departament of Applied Mathematics IV, BarcelonaTech
Dimensions for Fiedler parameter for planar graphs. A geometric problem

May 23, 2012
Dra. Mucuy-kak Guevara
Faculty of Science, UNAM
When a digraph has kernel?

August 10, 2011
Dr. Rafael Villarroel Flores
Academic Area of Mathematics and Physics, UAEH
Iterated Clique Graphs and Topology

Abstract: Given a simple graph G, the clique graph K (G) is defined as the intersection graph of maximal complete subgraphs of G, are defined then iterated clique graphs of G for n > = 1 as: K^n(G)=K(G) if n=1 and K^n(G)=K^{n-1}(K(G)) if n>1.

On the other hand, the whole graph G is associated with a simplicial complex \Delta(G) (and therefore a topological space) whose faces complete subgraphs G. It is said that the graphs G_1 and G_2 are homotopic if their respective complex \Delta(G_1), \Delta(G_2) are.

The study of the effect of the operator of clans in the topology of the graphs began with the demonstration of Prisner, published in 1992 that if the graph G is clique-Helly, then G and K (G) are homotopic. This talk will review several results relating the clique-behavior of G with the topology as well as several conjectures about.

June 8, 2011
Dr. David Flores-Peñaloza
Faculty of Sciences, UNAM
Number of quasi-heterochromatic spanning trees in convex position flat

Abstract: This talk will discuss the solution of the following anti-Ramsey problem geometry. Given a rectilinear drawing of a complete graph whose vertices are n points in convex position, what is the minimum number of colors that should color their edges, so that any color for that number of colors, there is always a plane spanning tree has at most two edges of the same color?

Show
1 - The exact solution of the problem.
2 .- The whole structure of color using a color less and to avoid a plane spanning tree "near-heterochromatic".
3.-The solution of the general case which calls for the existence of a plane spanning tree with at most k edges of the same color.

Working together with J.J Montellano, E. Campo and R. Rivera Zuazua.

May 11, 2011
Dolores Lara
UAM-Azcapotzalco
Minimum weight matching of moving dots

Abstract: The problem of Euclidean minimum weight matching is a classic problem in the area of ​​graph theory and optimization. Given a complete geometric graph K, a perfect matching M is generating a subgraph K in which the degree of each vertex is exactly one. We say that two points are paired if there is an edge between them. The weight of M is defined as the sum of the Euclidean distances between the points matched. Given K, the problem of Euclidean minimum weight matching is to find a matching whose weight is minimized.

There are many variations to this problem, however, this talk will present the first variant in which motion is introduced. That is, study the problem when the points all move with constant speed, each on a different beam. Clearly, under this scenario, the minimum weight matching is a function of time. Using linear programming techniques have achieved some results for this variant kinetic problem.

### March-December 2010

December 7, 2010
Edgar Possani Espinoza
Department of Mathematics, ITAM
Applications of data envelopment analysis for assessing eco-efficiency

Abstract: This talk will give a brief introduction to the technique of data envelopment analysis. Data envelopment analysis is a technique for evaluating the efficiency based on linear programming. There will be a model for project evaluation, considering environmental impacts with concrete examples of its application.

November 16, 2010
Luis Verde Star
Department of Mathematics, UAM-Iztapalapa
Generalized rational functions and functional equations

Abstract: From a cyclic group P isomorphic to the integers with addition operation, we build a field of functions, generalized rational, which is a subfield of formal Laurent series generated by the group P. In this context, abstract algebra, we study linear equations associated with a modified shift operator L and resolve in full the equations of the form w (L) f = g. Taking concrete realizations of the elements of P, these equations become differential equations, difference equations, fractional equations, and many other types of functional equations of interest in various areas. It uses only basic linear algebra.

October 5, 2010
Javier Cano Vila
IIMAS, UNAM
Guarding curvilinear art galleries

Abstract: One of the classic problems of combinatorial geometry is to determine the number of guards sufficient and sometimes necessary to guard an art gallery with n walls. We model the gallery is modeled as a simple polygon (with it). We call edges walls. We say that a point p in an art gallery A, sees another point q in A, if the segment pq is completely contained in A. Chvàtal proved that $\lfloor \frac{n}{3}\rfloor$ guards are always sufficient and sometimes necessary to monitor any gallery with n walls. Karavelas and Tsigaridas recently proposed a variant of this problem, in which the walls rather than just line segments can also be arcs of convex curves. This presentation will give fair levels for the number of guards sufficient and necessary in these galleries.

September 14, 2010 CANCELED
Carlos Renteria
TBA

June 8, 2010
Fuensanta Aroca
Institute of Mathematics, Campus Cuernavaca, UNAM
Arbitrary Range Tropical Geometry

Abstract: Tropical Classical Geometry studies the tropical half-ring: the real numbers with maximum and sum. These operations are defined for a totally ordered abelian group. We will see some results that are still maintained and some not.

May 11, 2010
Enrique Reyes
Cinvestav-IPN
Toric ideals of graphs and their minimal generators

Abstract: Let G = (V, E) a graph with V = {x 1,. . . , X n} and E = {y1,. . . , ym} the sets of vertices and edges respectively. The toric ideal PG associated to G is the kernel of a morphism of k-algebras. This talk will give a characterization of primitive pairs, minimum, essential and fundamental ideal of PG. Also characterize the graphs whose toric ideals are complete intersections and analyze the graphs that are complete intersections for any guidance.

April 13, 2010
Rodolfo San Agustín Chi
Faculty of Sciences, UNAM
Salmon points and sicigetic beams

Abstract: The Papus is a recurring figure in finite and combinatorial geometries. We will consider, this time from the following: Although Pascal (ca. 1640) gave the condition that six points were in a conic, according to George Salmon; Jacob Steiner was the first that directed the attention of geometers to the entire figure that is obtained by combining six points in a conic, in every way possible. Related work, as well as Pascal Steiner, Kirkman also include, Plucker, Cayley, Salmon, Veronese, Cremona, Richmond, Ladd and some other mathematicians in the second half of the nineteenth and early twentieth centuries. This figure basically consists of 95 points and 95 lines distributed in different subsets of the most diverse interests. Their study has been retrieved from the late twentieth century, along with the resurgence of the settings. The case of a conical reduced but reducible (ie two different lines) in a field of characteristic different from 2 and 3 can be studied from the generic case majoring in fiber. This meeting will raise the problem from the standpoint of the settings for both the generic case (Pascal) to that of Papus and study specialization mentioned above.

March 9, 2010
Ruy Fabila
Cinvestav-IPN
Lighting problems with k-modems

Abstract: The general question of lighting problems is to ask how many "lamps" are necessary and sufficient to "light up" a region of the plane in the presence of obstacles. The work on problems of lighting is classic. In this talk we talk about a new variant that we have introduced which now instead of lamps, use radio signals emitting devices (called k-modems) capable of crossing a predetermined number k of walls. You might think that these modems are points of access to a wireless network where you want to have access to the network from any point of a region in the presence of obstacles. We show progress to date in this new family of problems.

### February-July 2009

July 14, 2009
Itnuit Janovitz Freireich
Cinvestav-IPN
Advances in methods of polynomial resolution using tropical tools

June 9, 2009
Pablo Suárez-Serrato
CIMAT
Kaehler Decompositions for finitely presented groups

May 12, 2009 CANCELED
Rodolfo San Agustín Chi
Faculty of Sciences, UNAM
Diagrams in partially linear space categories of order two

April 14, 2009
Javier Elizondo Huerta
Institute of Mathematics, UNAM
Real structures in toric varieties

March 10, 2009
Ernesto Vallejo
Institute of Mathematics, Campus Morelia, UNAM
The bi-algebra of permutations

February 10, 2009
Gelasio Salazar
Institute of Physics, Universidad Autónoma de San Luis Potosí
Turán's brick factory problem