Seminars in April 2015

  • Eric Vigoda, Computational Phase Transitions for the Potts Model
    Computational Phase Transitions for the Potts Model
    Eric Vigoda
    College of Computing, Georgia Institute of Technology, Atlanta, GA, USA
    2015/4/14 Tue 4PM-5PM
    This is a followup talk to my CS colloquium on March 2. In that talk I discussed the problems of counting independent sets and colorings. Those problems are examples of antiferromagnetic systems in which neighboring vertices prefer different assignments. In this talk we will look at ferromagnetic systems where neighboring vertices prefer the same assignment. We will focus on the ferromagnetic Potts model. We will look at the phase transitions in this model, and their connections to the complexity of associated counting/sampling problems and the performance of related Markov chains.
    The talk is based on joint works with Andreas Galanis, Daniel Stefankovic, and Linji Yang.
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  • [Colloquium] Jang Soo Kim, Combinatorics of orthogonal polynomials
    Combinatorics of orthogonal polynomials
    Jang Soo Kim (김장수)
    Department of Mathematics, Sungkyunkwan University, Suwon
    2015/4/9 Thu 4:30PM-5:30PM (E6, Room 1501)
    Orthogonal polynomials are a family of polynomials which are orthogonal with respect to certain inner product. The n-th moment of orthogonal polynomials is an important quantity, which is given as an integral. In 1983 Viennot found a combinatorial expression for moments using lattice paths. In this talk we will compute the moments of several important orthogonal polynomials using Viennot’s theory. We will also see their connections with continued fractions, matchings, set partitions, and permutations.
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  • Andreas Holmsen, Topological methods in matching theory
    Topological methods in matching theory
    Andreas Holmsen
    Department of Mathematical Sciences, KAIST
    2015/4/7 Tue 4PM-5PM
    Around 15 years ago, Aharoni and Haxell gave a wonderful generalization of Hall’s marriage theorem. Their proof introduced topological methods in matching theory which were further developed by Berger, Meshulam, and others. Recently, motivated by some geometric questions, we extended these methods further, and in this talk I’ll explain the ideas and some of our results.
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