Schedule ECCO 2016 : Programa/Schedule

1 | Lunes 13 | Martes 14 | Miercoles 15 | Jueves 16 | Viernes 17 | Domingo 19 | ||
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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 | |||||||

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 | 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 | |||||||

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 | Alejandro Soto | ||||||

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 | ||||

37 | 3:00-3:30 | DESCANSO/BREAK | ||||||

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 | |||||||

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. |