Seminars in September 2011

  • Mihyun Kang (강미현), Phase transitions in random graphs
    Phase transitions in random graphs
    Mihyun Kang (강미현)
    Institut für Mathematik, Freie Universität Berlin, Germany
    2011/09/30 Fri 4PM-5PM
    The phase transition deals with sudden global changes and is observed in many fundamental problems from statistical physics, mathematics and theoretical computer science, for example, Potts models, graph colourings and random k-SAT. The phase transition in random graphs refers to a phenomenon that there is a critical edge density, to which adding a small amount a drastic change in the size of the largest component occurs. In Erdös-Renyi random graph, which begins with an empty graph on n vertices and edges are added randomly one at a time to a graph, a phase transition takes place when the number of edges reaches n/2 and a giant component emerges. Since this seminal work of Erdös and Renyi, various random graph models have been introduced and studied. In this talk we discuss phase transitions in several random graph models, including Erdös-Renyi random graph, random graphs with a given degree sequence, random graph processes and random planar graphs.
    Tags:

  • Shishuo Fu, A conjecture on the (q,t)-binomial coefficients
    A conjecture on the (q,t)-binomial coefficients
    Shishuo Fu
    Department of Mathematical Sciences, KAIST
    2011/09/23 Fri 4PM-5PM
    In one of their joint papers, Victor Reiner and Dennis Stanton introduced a (q,t)-generalization of the binomial coefficient. There was an interesting conjecture for the cases when q≤-2 is a negative integer. In this talk, I will prove this conjecture and try to give some combinatorial sense using integer partitions.
    Tags:

  • Andreas Holmsen, Convex representations of Oriented Matroids
    Convex representations of Oriented Matroids
    Andreas Holmsen
    Department of Mathematical Sciences, KAIST
    2011/09/16 Fri 4PM-5PM
    Many combinatorial problems and arguments concerning finite point sets in the Euclidean plane (or higher dimensions) often do not use the linear structure. A more general concept is that of an Oriented Matroid (OM). It is well-known that every OM can realized by pseudolines, and in fact most oriented matroids can not be realized by straight lines.
    Recently, Alfreod Hubard (Courant Institute) and myself have found a new way to represent an OM by convex sets which retains much more of the “straightness” of the Euclidean plane. Interestingly, in our model the isotopy conjecture holds in a very strong sense, and it unifies several aspects of pseudoline arrangements.
    Tags:

Monthly Archives