Schedule ECCO 2016


1			Lunes 13	Martes 14	Miercoles 15	Jueves 16	Viernes 17	Domingo 19
2		8:00-9:00	Inscripción/Registration					EXCURSIÓN
3		9:00-9:30	Michelle Wachs	Michelle Wachs	Plenary Talk Matt Beck	Michelle Wachs	Michelle Wachs
4		9:30-10:00	Michelle Wachs	Michelle Wachs	Plenary Talk Matt Beck	Michelle Wachs	Michelle Wachs
5		10:00-10:30	DESCANSO/BREAK	DESCANSO/BREAK	DESCANSO/BREAK	DESCANSO/BREAK	DESCANSO/BREAK
6		10:30-11:00	Nicole Yamzon	Mehdi Garrousian	SAGE	DESCANSO/BREAK	Monica Blanco
7		11:00-11:30	Taller (M. Wachs)	Taller (M. Wachs)		Taller (M. Wachs)	Taller (M. Wachs)
8		11:30-12:00
9		12:00-12:30
10		12:30-1:00	ALMUERZO / LUNCH	ALMUERZO / LUNCH	ALMUERZO / LUNCH	ALMUERZO / LUNCH	ALMUERZO / LUNCH
11		1:00-1:30
12		1:30-2:00
13		2:00-2:30	Manuela Cerdeiro	Andres Felipe Saldaña	Problemas abiertos / Open problems	Jesús Leaños	Cesar Cuenca
14		2:30-3:00	Sylvie Corteel	Sylvie Corteel		Sylvie Corteel	Sylvie Corteel
15		3:00-3:30	Sylvie Corteel	Sylvie Corteel		Sylvie Corteel	Sylvie Corteel
16		3:30-4:00	DESCANSO/BREAK	DESCANSO/BREAK		DESCANSO/BREAK	DESCANSO/BREAK
17		4:00-4:30	Taller (S.Corteel)	Taller (S.Corteel)		Taller (S.Corteel)	Taller (S.Corteel)
18		4:30-5:00
19		5:00-5:30
20
21
22
23
24			Lunes 20	Martes 21	Miercoles 22	Jueves 23	Viernes 24
25		9:00-9:30	Marcelo Aguiar	Marcelo Aguiar	Pedro Fernández	Marcelo Aguiar	Marcelo Aguiar
26		9:30-10:00	Marcelo Aguiar	Marcelo Aguiar	Alejandro Soto	Marcelo Aguiar	Marcelo Aguiar
27		10:00-10:30	DESCANSO/BREAK	DESCANSO/BREAK	DESCANSO/BREAK	DESCANSO/BREAK	DESCANSO/BREAK
28		10:30-11:00	Laura Colmenarejo	Ana María Botero	SAGE	Cameron Marcott	Federico Castillo
29		11:00-11:30	Taller (M. Aguiar)	Taller (M. Aguiar)		Taller (M. Aguiar)	Taller (M. Aguiar)
30		11:30-12:00
31		12:00-12:30
32		12:30-1:00	ALMUERZO / LUNCH	ALMUERZO / LUNCH	ALMUERZO / LUNCH	ALMUERZO / LUNCH	ALMUERZO / LUNCH
33		1:00-1:30
34		1:30-2:00
35		2:00-2:30	Jerson Borja	Wilson Martinez	Problemas abiertos / Open problems	Francisco Santos	Jean-Philippe Labbé
36		2:30-3:00	Francisco Santos	Francisco Santos		Francisco Santos	Francisco Santos
37		3:00-3:30	Francisco Santos	Francisco Santos		DESCANSO/BREAK	Francisco Santos
38		3:30-4:00	DESCANSO/BREAK	DESCANSO/BREAK	DESCANSO/BREAK	Taller (F. Santos)	DESCANSO/BREAK
39		4:00-5:30	Taller (F. Santos)	Taller (F. Santos)	PANEL		Taller (F. Santos)
40		4:30-5:00
41		5:00-5:30
42		5:30-6:00
43		6:00-6:30
44		6:30-7:00				Charla Pública / Public lecture
45		7:00-7:30				Charla Pública / Public lecture
46
47
48
49		Charlas contribuidas/ Contributed talks
50
51		Author	Mónica Blanco Gómez
52		Affiliation	Universidad de Cantabria
53		Title	On the enumeration of lattice 3-polytopes
54		Abstract	A lattice 3-polytope is a polytope P with integer vertices. We call size of P the number of lattice points it contains, and width of P the minimum, over all integer linear functionals f, of the length of the interval f(P). In a previous paper we have shown that all but finitely many lattice 3-polytopes of a given size have width one, which opens the possibility of enumerating those of width larger than one. There is none of size 4 (White, 1964) and those of sizes five and six were classified in our previous papers. In this paper we prove that every lattice 3-polytope P of width larger than one and size at least seven falls into one of the following three categories: - It projects in a very specific manner to one of a list of seven particular 2-polytopes. We call 3-polytopes of this type spiked, and we describe them explicitly. - All except three of the lattice points in P are contained in a rational parallelepiped of width one with respect to every facet. We call these polytopes boxed. They have size at most 11 and we have completely enumerated them. - P has (at least) two vertices u and v such that, when removing each of them, the width is still larger than one. Polytopes of this type can be all obtained ``gluing'' smaller polytopes of width larger than one. This allows for a computational enumeration of all lattice 3-polytopes of width larger than one up to any given size. We have completely enumerated 3-polytopes of width larger than one and size up to eleven.
55
56		Author	Jerson Borja
57		Affiliation	Universidad de los Andes
58		Title	Evasiveness of graph properties
59		Abstract	A property of graphs on n vertices is said to be evasive if its query complexity is the maximum n(n-1)/2. The evasiveness conjecture for graph properties asserts that every non-trivial monotone graph property is evasive. An important advance in the conjecture was achieved when Kahn, Saks and Sturtevant in the paper ``A topological approach to evasiveness'' showed a connection between this complexity problem and topology. To each monotone graph property, there is an associated simplicial complex and it is proved that monotone non-evasive graph properties have a collapsible associated simplicial complex. With the help of results from Smith theory, they prove that the conjecture is true when the number of vertices n is a prime power. They also prove the 6 vertices case. Since then, much of the work on the evasiveness conjecture is based on this topological approach. In this talk, we review the topological approach to evasivenes , then specialize to graphs on 2p vertices, where p is prime, to show the following results: flower bounds for the dimension of the simplicial complex associated to non-evasive monotone graph properties, and estimations of the Euler characteristic of simplicial complexes associated to non-evasive monotone graph properties by studying the size of the automorphism group of graphs. Finally we test our estimations in the cases of 6 and 10 vertices.
60
61		Author	Ana María Botero
62		Affiliation	HU Berlin
63		Title	Singular metrics, lattice points in convex bodies and multiple zeta values
64		Abstract	We introduce toric b-divisors on complete smooth toric varieties and a notion of integrability of such divisors. We see that under some positivity assumptions, toric b-divisors are integrable and that their degree is given as the volume of a convex set. Moreover, the dimension of the space of global sections of a nef toric b-divisor corresponds to the number of lattice points in this convex set and we give an asymptotic Riemann-Roch type formula describing its growth. This generalizes classical results for classical toric divisors on toric varieties. We further extend some of these results to arbitrary toroidal varieties. Examples in which such b-divisors naturally appear are invariant metrics on line bundles over toroidal compactifications of mixed Shimura varieties. Indeed, the singularity type which the metric acquires along the boundary can be encoded using toroidal b-divisors. Interestingly, the arithmetic degree of such a compactified metrized line bundle is expected to be a multiple zeta value. This in turn is connected with a (to my knowledge) open combinatorial problem. We will see a very clear example in dimension 2 illustrating this theory. All of this is expected to be published as a PhD thesis in 2016.
65
66	Author	Marcott Cameron
67	Affiliation	University of Waterloo
68	Title	Matroids and stratifications of flag manifolds
69	Abstract	Any point in the Grassmannian naturally defines a matroid. Any generic point inside a Schubert variety defines the same matroid; these matroids are known as shifted matroids. Likewise, generic points in Richardson varieties define lattice path matroids and generic points in positroid varieties define positroids. One may play the same game with other flag manifolds, defining matriodal objects associated to points in the flag manifold and special classes of these objects corresponding to common stratifications of the flag manifold. After discussing these various flavors of matroids and matriodal objects, we explain how to use recent geometric results of Knutson, Lam, and Speyer to expand known results about lattice path matroids to positroids.
70
71	Author	Federico Castillo
72	Affiliation	UC Davis
73	Title	The multidegree polytope of an irreducible subvariety of product of projective spaces.
74	Abstract	Recently June Huh classified, up to a multiple, all possible classes in the Chow ring of a product of two projective spaces that can be represented by an irreducible variety. As a first step to generalize this result to any number of copies of projective spaces, we focus only on the support of these classes. It turns out that the support of any irreducible variety can be described naturally as the integer points in a polytope, more precisely a generalized permutohedron.
75
76	Author	Manuela Cerdeiro
77	Affiliation	Universidad de Buenos Aires - CONICET
78	Title	Aplicaciones de espacios fintos al estudio de asfericidad de complejos LOT
79	Abstract	En este trabajo se estudia el problema de la asfericidad de los complejos LOT (Labeled Oriented Tree). Esta clase de CW-complejos de dimensión 2 aparece en el estudio de ciertas variedades que surgen como complementos de los llamados ribbon discs, en una generalización de la teoría de nudos clásica. Un espacio topológico arcoconexo se dice asférico si sus grupos de homotopía π_n(X) son triviales para todo n ≥ 2. En el caso de los complejos de dimensión 2, esta condición es equivalente a que π_2(X) = 0. Durante mucho tiempo estuvo abierta la conjetura sobre la asfericidad de los complementos de nudos, que fue finalmente probada por Papakyriakopoulos [8] usando métodos de 3-variedades. Actualmente se conjetura que, al igual que en el caso de los nudos, los complementos de ribbon discs también son asféricos. Este problema está fuertemente relacionado con otros problemas de la topología algebraica, la teoría de grupos y la topología diferencial. Si bien se han alcanzado algunos resultados parciales [5, 6, 4, 7], aún se sabe muy poco sobre la asfericidad de los complejos LOT. En este trabajo le damos un nuevo enfoque al problema al llevarlo al contexto de los espacios topológicos finitos, donde podemos aplicar técnicas nuevas que aprovechan la naturaleza geométrica y combinatoria de los espacios finitos. Utilizando resultados recientes de Barmak y Minian sobre G-coloreos de espacios finitos [1, 2], obtenemos una descripción eficiente del segundo grupo de homotopía de un complejo LOT, como un submódulo de un módulo libre, con generadores indexados por las aristas, y ecuaciones indexadas por los vértices. A partir de esta descripción, hallamos un método para el análisis de la asfericidad de estos complejos. Con este nuevo método obtenemos resultados sobre la asfericidad de importantes familias de LOTs. Estos resultados son parte de mi tesis doctoral [3].
80
81	Author	Laura Colmenarejo
82	Affiliation	Universidad de Sevilla
83	Title	Some families of reduced Kronecker coefficients, plane partitions and quasipolynomials
84	Abstract	In this talk we present a complete study of several families of reduced Kronecker coefficients, which are particular instances of Kronecker coefficients that contain enough information to recover them. Using the Kronecker tableaux defined by C. Ballantine and R. Orellana, we can give the generating functions of our families of reduces Kronecker coefficients. The generating functions give us also their relation with plane partitions and a description of them in terms of quasi polynomials, specifying their period and degree. Finally, we show the consequences of this study with respect to the rate of growth of the Kronecker coefficients.
85
86	Author	Cesar Cuenca
87	Affiliation	MIT
88	Title	Asymptotics of Jack polynomials
89	Abstract	We derive explicit formulas for Jack polynomials that are suitable for various asymptotics regimes as the number of variables tends to infinity. We discuss an application to asymptotic representation theory.
90
91	Author	Pedro Fernando Fernández Espinosa (Joint with Agustín Moreno Cañadas)
92	Affiliation	Universidad Nacional de Colombia
93	Title	Categorification of some integer sequences
94	Abstract	The term categorification of an integer sequence was introduced by Fahr and Ringel to the process which consists of considering numbers in the sequence as invariants of objects of a given category in such a way that identities between numbers in the sequence can be considered as functional relations between objects of the category. Ringel and Fahr gave a a categorification of Fibonacci numbers by using preproyective and regular components of the $3$-Kronecker. In this talk we describe how Kronecker modules, tiled orders or semimaximal rings (introduced by Zavadskij and Kirichenko) and indecomposable representations of equipped graphs (introduced by Gelfand and Ponomarev) can be used to categorize Catalan numbers and the integer sequences A052558 and A016269 in the OEIS. We recall that such sequences count the number of ways of connecting $n+1$ equally spaced points on a circle with a path of $n$ line segments ignoring reflections, and the number of two-point antichains in the powerset of an $n$-element set ordered by inclusion respectively .
95
96	Author	Mehdi Garrousian
97	Affiliation	Universidad de los Andes
98	Title	A combinatorial-algebraic approach to the generalized Hamming weights of a linear code
99	Abstract	The Hamming distance of a linear code is a measure of the number of bits in a linear code that can be error corrected. This is the first distance in a sequence of Hamming weights that one can associate with a linear code. The higher Hamming weights are important in cryptography. One can naturally associate a matroid as well a sequence of ideals that are generated by products of linear forms to the given linear code. We show that the Hamming weights are determined by the homological properties of these ideals. Among other results, we show that the leading coefficients of the Hilbert polynomials of these ideals are determined by the Tutte polynomial. This is a joint work with Ben Anzis and Stefan Tohaneanu.
100
101	Author	Jean-Philippe Labbé
102	Affiliation	Hebrew University Jerusalem
103	Title	Problems with Subword Complexes
104	Abstract	In this talk, I would like to introduce subword complexes of Coxeter groups, some of their connections to various areas in discrete geometry, tropical geometry, cluster algebras and finish by displaying some of their still mysterious facets. No prior knowledge of Coxeter groups will be necessary, although some basic algebraic topology, discrete geometry and group theory is desirable (simplicial complexes, fans, polytopes, finitely generated groups, etc.).
105
106	Author	Jesús Leaños Macías
107	Affiliation	Universidad Autónoma de Zacatecas
108	Title	Gauss paragraphs of pseudolinear arrangements
109	Abstract	Gauss has given necessary but not sufficient conditions for a sequence of letters to represent the sequence of self-crossings of some closed planar curve. Such sequences of letters were called Gaussian words and recently generalized to Gaussian paragraphs (aka. Gaussian multi-words), sets of words that arise from sequences of crossings of several curves. In the paper, we apply Gaussian approach to study pseudolinear arrangements. We introduce the graph of a pseudolinear arrangement and show that the degrees of its vertices are completely described by specifying the number of degree-two vertices. The graph of the arrangement, which can be constructed from its Gaussian paragraph description, is 3-connected and planar with an additional property. We use these elementary characterizations to improve a previous algorithm recognizing realizable combinatorial descriptions of pseudolinear arrangements with a novel linear algorithm.
110
111	Author	Wilson Arley Martinez Flor
112	Affiliation	Universidad del Cauca
113	Title	Construction of Rota^m-Algebras and Ballot^m-Algebras from associative algebras with a Rota-Baxter morphism and a Rota-Baxter operator of weights three and two
114	Abstract	We give a generalization of Rota-Baxter Operators and introduce the notion of a Ballot^m-algebra. We introduce the concepts of a Rota-Baxter Morphism, Dyck^m-algebra and Rota^m-algebra. An element u is said to be idempotent with respect to product . in the algebra if: u . u = u; and it is a left identity if x . u = x for all element x in the algebra. Associative algebras with a left identity that simultaneously is a element idempotent, permit us to present examples of a Rota-Baxter Morphism and so we can construct a Rota^m-algebra.
115
116	Author	Andrés Felipe Saldaña Torres
117	Affiliation	Universidad del Valle
118	Title	On Tutte polynomials, medial graphs and knots
119	Abstract	It will be introduced a two variable polynomial defined over the set of the eulerian partitions of a medial graph obtained from a connected graph, generalizing some results already known about the Tutte polynomial, also show that such polynomial is in fact a Tutte-Grothendieck invariant and is given an expression for the Tutte polynomial in terms of this. Also is shown a relationship between the Jones polynomial of a link diagram related with initial connected graph and again obtain an expression for this in terms of our polynomial. Therefore, it's generalizate the well known relationship between Jones and Tutte polynomial.
120
121	Author	Alejandro Soto
122	Affiliation	Goethe Universität - Frankfurt am Main
123	Title	Tropical theta functions and applications
124	Abstract	The theory of theta functions has been always an important subject for the study of abelian varieties. In tropical geometry, they have been introduced in 2008 by Mikhalkin and Zarkov in a purely combinatorial setting. In this talk, we will present its combinatorics and show that they are intimately related with the classical theory, i.e. we show that the tropicalization of a theta function is a tropical theta function. We will also see how this give rise to an application in the framework of faithful tropicalization of abelian varieties defined over a rank one valued field. This is a joint work with T. Foster, J. Rabinoff and F. Shokrieh.
125
126	Author	Nicole Yamzon
127	Affiliation	San Francisco State University
128	Title	The Dehn--Sommerville Relations and the Catalan matroid
129	Abstract	The $f$-vector of a $d$-dimensional polytope $P$ stores the number of faces of each dimension. When $P$ is simplicial the Dehn--Sommerville relations imply that to determine the $f$-vector of $P$, we only need to know approximately half of its entries. This raises the question: Which $(\lceil{\frac{d+1}{2}}\rceil)$-subsets of the $f$-vector of a general simplicial polytope are sufficient to determine the whole $f$-vector? We prove that the answer is given by the bases of the Catalan matroid.