# 2014-15 Colloquia talks

Date | Speaker | Talk |
---|---|---|

Thursday, April 23, 2015 | Guillermo López Lagomasino, Universidad Carlos III de Madrid, Spain |
Abstract: In the recent past multiple orthogonal polynomials have attracted great attention. They appear in simultaneous rational approximation, simultaneous quadrature rules, number theory, and more recently in the study of certain random matrix models. These are sequences of polynomials which share orthogonality conditions with respect to a system of measures. A central role in the development of this theory is played by the so called Nikishin systems of measures for which many results of the standard theory of orthogonal polynomials have been extended. In this regard, we present some results on the convergence of type I and type II Hermite-Padé approximation for a class of meromorphic functions obtained by adding vector rational functions with real coefficients to a Nikishin system of functions (the Cauchy transforms of a Nikishin system of measures). |

Thursday, April 9, 2015 | Iain Moffatt, Royal Holloway, University of London, UK |
Abstract: A matroid is a mathematical structure that generalises the notion of linear independence in vector spaces. There is a natural way to associate a matroid with a graph, and this results in a very close connection between graph theory and matroid theory. This is beneficial in two ways: graph theory can serve as an excellent guide for studying matroids; and matroid theory can lead to new, and more general, results about graphs. In fact, matroid theory may be best thought of as a generalisation of graph theory. In many applications of graph theory, graphs come equipped with a drawing on a surface. However, the (graphic) matroid associated with such a graph records absolutely no information about how it is drawn. Thus matroids do not appear to provide a 'correct' generalisation of graphs in surfaces. This leads to the question if matroids don't, what do? In this talk, after giving a gentle introduction to matroids, I will propose an answer to this question. This is joint work with Carolyn Chun, Steven Noble and Ralf Rueckriemen. |

Tuesday, March 17, 2015 | Shibasish Dasgupta, Miami University |
Abstract: Finding efficient biomarker is critically important for disease detection. Furthermore, rigorous evaluation of biomarkers is essential to guarantee that the tests that are developed are sufficiently accurate and beneficial to the patient. Here we propose a Bayesian predictive approach for determining sample size to compare efficiencies of two binary biomarkers. The operational criteria include classification accuracy, sensitivity, and specificity. In the frequentist approach, one usually estimates the operational criterion from the training data for each marker and using the estimate as the 'true' value to select the sample size corresponding to a desirable power, say 80%. However, due to uncertainty to the training data estimates, the designed study could be under powered when the estimates are treated as true. This may result in a substantially underpowered study while the sample size for the training data is small. In the Bayesian predictive approach the sample size is determined taking into account the uncertainty of the training data estimates. Through simulation studies we show the effectiveness of the proposed approach. We can also extend this approach in case of continuous biomarkers. |

Thursday, March 12, 2015 | Elena Pavelescu, Oklahoma State University |
Abstract: A contact structure on a 3-dimensional manifold is an everywhere non-integrable
plane field. In this talk, we look at Legendrian graphs in the standard contact structure
of the 3-dimensional Euclidian space. A Legendrian graph is a graph embedded in such
a way that its edges are everywhere tangent to the contact planes. We extend classical
invariants of Legendrian knots like the Thurston-Bennequin number and the rotation
number to Legendrian graphs. We look at various questions which arise in this context.
In particular, we show that a graph G can be Legendrian realized with all cycles unknots
of maximal Thurston-Bennequin number if and only if G doesn't contain K |

Tuesday, March 10, 2015 | Andrei Bogdan Pavelescu, Oklahoma State University |
Abstract: The study of the fixed points of permutations is a common topic in Probability Theory, Number Theory and Algebraic Geometry. In this talk we shall focus on the Group Theory machinery that lurks behind the curtains. We shall introduce the audience to basic combinatorial techniques and notions needed to tackle the following question: Let A be a primitive permutation group and G a normal subgroup of A such that A/G is cyclic. Let xG be a generating coset for A/G. Motivated by questions arising in connection to coverings of smooth connected projective curves, we study the proportion of derangements in the coset xG. We use the Aschbacher-O'Nan-Scott theorem for primitive groups to partition the problem and provide answers in several cases. |

Thursday, February 26, 2015 | Armin Straub, University of Illinois at Urbana-Champaign |
Abstract: Apéry-like numbers are special integer sequences, going back to Beukers and Zagier, which are modeled after and share many of the properties of the numbers that underly Apéry's proof of the irrationality of ζ(3). Among their remarkable properties are connections with modular forms and so-called supercongruences, some of which remain conjectural. In the course of several examples, we demonstrate how these numbers and their connection with modular forms feature in various, apparently unrelated, problems. The examples are taken from personal research of the speaker and include the theories of short random walks, binomial congruences, series for 1/π, and positivity of rational functions. Finally, we return to the discussion of supercongruences and report on new perspectives and recent progress. |

Thursday, February 19, 2015 | Saeid Amiri, University of Nebraska-Lincoln |
Abstract: Here, we propose a clustering technique for general clustering problems including those that have non-convex clusters. For a given desired number of clusters K, we use three stages to find a clustering. The first stage uses a hybrid clustering technique to produce a series of clusterings of various sizes (randomly selected). They key steps are to find a K-means clustering using K2-clusters where K2 ≫ K and then joins these small clusters by using single linkage clustering. The second stage stabilizes the result of stage one by reclustering via the 'membership matrix' under Hamming distance to generate a dendrogram. The third stage is to cut the dendrogram to get K3 clusters where K3 ≥ K and then prune back to K to give a final clustering. A variant on our technique also gives a reasonable estimate for KT, the true number of clusters. We provide a series of arguments to justify the steps in the stages of our methods and we provide numerous examples involving real and simulated data to compare our technique with other related techniques. |

Thursday, February 12, 2015This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
Sytske Kimball, Department of Earth Sciences, University of South Alabama |
Abstract: We all experience wind in our daily lives, but we never think about it as a mathematical quantity. Establishing a climatology of any meteorological property, requires the calculation of means, standard deviations, extremes, and other statically properties. Wind is no different. But because wind has both speed and direction, it has to be quantified as a vector. Wind speed can easily be averaged the normal arithmetic way, but wind direction presents a problem due to its circular nature (a northerly wind is direction 0, easterly is 90, southerly 180, and so forth back to 360 degrees for a northerly wind). In this seminar, several ways of calculating wind speed and direction averages will be presented. Wind speed measurements from South Alabama Mesonet weather stations (http://chiliweb.southalabama.edu/) will be used to statistically investigate the differences between these methods. |

Thursday, February 5, 2015 | Thomas Brüstle, Université de Sherbrooke & Bishop's University, Canada |
Abstract: Cluster algebras were invented in 2000 by S. Fomin and A. Zelevinsky as constructively defined commutative algebras with a distinguished set of generators (cluster variables) grouped into overlapping subsets (clusters) of fixed cardinality. Both the generators and the relations among them are not given from the outset, but are produced by an iterative process of successive mutations. Although this procedure appears murky at first, it turns out to encode a surprisingly widespread range of phenomena. We illustrate in this talk one particularly nice example of how certain cluster algebras are related to classical objects in mathematics, and we hope this helps explaining the explosive development of the subject in recent years. |

Thursday, January 29, 2015 | Moshe Cohen, Technion - Israel Institute of Technology, Israel |
Abstract: Zariski gave a pair of sextics with the same types of singularities but whose complements have different fundamental groups. This motivates the search for a similar "Zariski pair" of line arrangements: two with the same combinatorial intersection data but whose (complex projective) complements have different fundamental groups. Only one minimal case has been found so far: Rybnikov produced one with thirteen lines in 1998 by gluing two smaller arrangements together. No such pair exists on nine or fewer lines. Together with Amram, Sun, Teicher, Ye, and Zarkh, we investigate arrangements of ten lines. This talk is accessible to those without backgrounds in combinatorics, topology, or algebraic geometry. |

Tuesday, November 25, 2014 | Erwin Miña-Díaz, University of Mississippi |
Abstract: Generally speaking, orthogonal polynomials refers to a sequence of polynomials
p |

Thursday, November 20, 2014This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
Nemanja Kosovalić, University of South Alabama |
Abstract: We introduce and give a survey of a functional analytic approach to solving problems in bifurcation theory and nonlinear analysis called the Lyapunov-Schmidt reduction. We illustrate how this method works in the context of a Hopf bifurcation in a system of ordinary differential equations, and indicate how it applies to other problems in nonlinear analysis. If time permits, we discuss some limitations of the method in the context of partial differential equations. The talk is aimed to be accessible to students and outsiders of the field. |

Thursday, November 13, 2014This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
Frazier Bindele, University of South Alabama |
Abstract: In this talk, we will start by introducing some asymptotic results on nonparametric kernel estimation. Next we will show how kernel estimation can be used in the study of the signed-rank estimator of the regression coefficients under the assumption that some responses are missing at random in the regression model. Strong consistency and asymptotic normality of the proposed estimator will be established under mild conditions. To demonstrate the performance of the signed-rank estimator, a simulation study under different settings of errors’ distributions will show that the proposed estimator is more efficient than the least squares estimator whenever the error distribution is heavy tailed or contaminated. When the errors follow a normal distribution, the simulation experiment also will show that the signed-rank estimator is more efficient than its least squares counterpart whenever a large proportion of the responses are missing. |

Thursday, November 6, 2014 | David Sprehn, University of Washington |
Abstract: I will introduce the theory of characteristic classes for permutation representations
of groups, and illustrate the technique by playing around with the natural representation
of S |

Thursday, October 30, 2014 | Masaaki Suzuki, Meiji University, Tokyo, Japan |
Abstract: We will consider epimorphisms between knot groups. Especially, we will focus on the image of a meridian under such an epimorphism. A homomorphism between knot groups is called meridional if it preserves their meridians. The existence of a meridional epimorphism introduces a partial order on the set of prime knots. We will determine the pairs of prime knots with up to 11 crossings which admit meridional epimorphisms between their knot groups. Moreover, we will describe some examples of non-meridional epimorphisms explicitly. |

Thursday, October 23, 2014 | Nutan Mishra, University of South Alabama |
Abstract: An undirected graph without loops, is strongly regular when each vertex is of equal degree with any two vertices with an edge are joined with exactly m common vertices and any two vertices without an edge are joined to n common vertices. R.C. Bose, in his 1963 paper, has shown that a two class association scheme can be expressed as a strongly regular graph. And thus strongly regular graphs has close connections with two classes of partially balanced incomplete block designs (PBIBD). Basic concepts, definitions, interrelationships of graph theory and design theory will be discussed along with a few construction theorems for partially balanced incomplete block designs. |

Thursday, October 16, 2014 | Nutan Mishra, University of South Alabama |
Abstract: It is well known that for a proper block design the combinatorial property of pairwise balance is sufficient to ensure the statistical property of variance balance. The variance balance property of a block design implies the complete symmetry of the information matrix. Using these facts we discuss the optimality in a class of proper variance balanced designs with unequal replications. Further unequal replications force the variance balanced designs to be non-binary designs. Hence instead of using the usual optimality criteria given by J. Keifer, we compare the designs with respect to the functions based on efficiency factors of the design, namely eigenvalues of the matrix (RinverseC). |

Thursday, October 9, 2014 | Ash Abebe, Auburn University |
Abstract: In this talk, I will discuss some nonparametric max-central classifiers as well as methods for selecting features that are relevant for discrimination. The feature selection method rewards features for information towards discrimination but penalizes them for their similarity to already selected features. Monte Carlo simulation studies demonstrate that there are several situations where the proposed procedures provide lower misclassification error rates than classical methods. Finally, I will discuss results of application of the proposed procedures on food safety and gene expression data. |

Thursday, October 2, 2014 This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
David Mullens, University of South Alabama |
Abstract: We will define what it means to be Scissors Congruent for polygons and polyhedra. We'll see a scissors congruence proof of the Pythagorean Theorem and show that scissors congruence is an invariant of area. Next, we'll understand scissors congruence in terms of the distributive law and various other properties. We will define the Dehn Invariant. Noting that volume is an invariant of scissors congruence we'll recall Hilbert's Third Problem and see a simple proof that the converse is not true. We will explore a scissors congruence proof of Heron's Formula. Finally, if we have time, we will define scissors congruence in terms of the group of isometries and explore this notion in a group theoretic context. |

Thursday, September 25, 2014 This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
David Benko, University of South Alabama |
Abstract: We give a brief introduction to potential theory. Then we explain how to use balayage to get beautiful fractalicious images such as dogs. |

Thursday, September 18, 2014 This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
Scott Carter, University of South Alabama |
Abstract: It is well-known among mathematicians that the result of the Chaos Game on 3 equidistant vertices yields a figure that approximates the Sierpinski triangle. It is also known that the binomial coefficients when read modulo 2 resemble this figure. In this talk, I want to show you some interesting n-dimensional generalizations of these phenomena. |

Thursday, September 11, 2014 This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
Cornelius Pillen, University of South Alabama |
Abstract: During our last summer camp some Mobile County six graders were given a rectangular prism of size 5 by 2 by 2. They were asked to calculate its surface area and then find another rectangular prism with integer dimensions and identical surface area. While daydreaming in the back of the class I started thinking about these rectangular “integer prisms”. Are there any such prisms whose surface area equals their volume? Can every (large) even number be realized as the surface area of some rectangular prism with integer dimension? The answer to these questions leads to some heavy-duty mathematics. Even the Riemann Hypothesis appears. |

Thursday, September 4, 2014 This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
Dan Silver, University of South Alabama |
Abstract: A dimer covering (also called a perfect matching) of a graph is a collection of edges that covers each vertex exactly once. The term “dimer” comes from chemistry: a dimer is a polymer with only two atoms. If we think of vertices as univalent atoms, then dimer coverings provide simple models for studying certain phase transitions. We explain how dimer coverings arise in both topology and algebraic dynamical systems. |