Monday 24
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3:10 pm, room 1431. Graph Theory and Combinatorics Seminar. Peter Hamburger, Western Kentucky University. On the Kneser index of graphs. The Kneser graph $K_{n:k}$ for positive integers $n\ge k$ has as its
vertex set the $k$-element subsets of some $n$-set, with disjoint sets
being adjacent. Every finite simple graph can be found as an induced
subgraph of some Kneser graph; this article explores some questions
arising from that fact. This is joint work with Attila Por, Western Kentucky University, and
Matt Walsh, Indiana University Purdue University Fort Wayne, IPFW.
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Tuesday 25
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Wednesday 26
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4:10 pm, room 1310.
Topology
& Group Theory Seminar. Iva Kozakova, Vanderbilt University. TBA.
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Thursday 27
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4:10-5 pm, room 5211. Colloquium. Petar Markovic, University of Novi Sad, Serbia. Computational complexity of the constraint satisfaction problem. I will give an overview of the current state of knowledge on the following conjecture: Given the class of all constraint satisfaction problems with a fixed template, the complexity of deciding if there is a solution of an instance of such a constraint satisfaction problem is either polynomial-time solvable, or NP-complete (depending on the template). In the first part of the talk I will provide all definitions needed for understanding the problem. In the second part I will overview the best partial results known so far using the approaches of logic, complexity theory, universal algebra and graph theory. In the third part I will concentrate on a subcase of the problem when the template is a directed graph, as the dichotomy conjecture for computational complexity is equivalent to the restricted conjecture for this subcase. I will present the most recent results which prove the conjecture in the case that the template has no sources and no sinks, and some extensions of this obtained in collaboration with R. McKenzie this Fall. This approach uses a combination of graph-theoretic and universal algebraic methods, and we feel that it is the most promising one of all that have been attempted so far. Tea at 3:30 pm in SC 1425.
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Friday 28
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1:10-2:30 pm, room 1310. Universal
Algebra
and Logic Seminar. Petar Markovic, University of Novi Sad, Serbia. TBA.
4:10-5:00 pm, room 1307. Partial Differential Equations Seminar. Boris Belinskiy, University of Tennessee at Chattanooga. Stochastic Wave Equation Driven by a Fractional Brownian Motion. We consider a linear stochastic wave eq-n driven by fractional-in-time noise. We prove the existence and uniqueness of the weak solution.We also study the expected energy associated with wave eq-n and improve our previous results on that matter. Specifically, we find the iff condition of the convergence of the series representing the expected energy using physically natural objects. We discuss the smoothness of the solution. We consider both cases H > 1/2 and H < 1/2 for the Hurst parameter.
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