Saturday, February 9, 2019, Florida Atlantic University
February 15 & 16, 2019, Florida Atlantic University, Science and Engineering Complex
March 4-8, 2019, Florida Atlantic University, Student Union
May 19-24, 2019, Bahia Mar Fort Lauderdale Beach
April 6, 2019, Florida Atlantic University
Need to improve your mathematical skills? Check out the Math Boot Camp! New sessions open throughout the semester!
January 19, 2019, Florida Atlantic University, Davie Campus.
January 26, 2019, Florida Atlantic University, 8:00 a.m. - 3:30 p.m.
Friday, January 11, 2019, SE-43, Rm. 215, 4:00 p.m.
Speaker: Ilya M. Spitkovsky, New York University, Abu Dhabi
Title: Factorization of almost periodic matrix functions: some recent results and open problems
Abstract: The set AP of (Bohr) almost periodic functions is the closed sub- algebra of L∞(R) generated by all the exponents eλ(x) := eiλx, λ ∈ R. An AP factorization of an n-by-n matrix function G is its representation as a product
G = G+diag[eλ1,...,eλn]G−,
where G±1 and G±1 have all entries in AP with non-negative (resp., non-positive) Bohr-Fourier coefficients. This is a natural generalization of the classical Wiener-Hopf factorization of continuous matrix-functions on the unit circle, arising in particular when considering convolution type equation on finite intervals, Toeplitz operators with matrix symbols on Hardy or Bezikovitch spaces, etc. The talk will be devoted to the current state of AP factorization theory. Time permitting, problems still open will also be described.
Tuesday, January 15, 2019, SE-43, Rm 215, 2:00-3:20 p.m.
Speaker: Professor M. Golumbic, University of Haifa, Israel
Title: Graph sandwich Problems
Abstract: Graph sandwich problems are a prototypical example of checking consistency when faced with only partial data. A sandwich problem for a graph with respect to a graph property $\Pi$ is a partially specified graph, i.e., only some of the edges and non-edges are given, and the question to be answered is, can this graph be completed to a graph which has the property $\Pi$? The graph sandwich problem was investigated for a large number of families of graphs in a 1995 paper by Golumbic, Kaplan and Shamir, and over 200 subsequent papers by many researchers have been published since. In some cases, the problem is NP-complete such as for interval graphs, comparability graphs, chordal graphs and others. In other cases, the sandwich problem can be solved in polynomial time such as for threshold graphs, cographs, and split graphs. There are also interesting special cases of the sandwich problem, most notably the probe graph problem where the unspecified edges are confined to be within a subset of the vertices. Similar sandwich problems can also be defined for hypergraphs, matrices, posets and Boolean functions, namely, completing partially specified structures such that the result satisfies a desirable property. In this talk, we will present a survey of results that we and others have obtained in this area during the past decade.