# 2015-16 Colloquia talks

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

Tuesday, April 19, 2016 | Van C. Nguyen, Northeastern University |
Abstract: We visit one of the problems arising in homological algebra, dealing with a theory called "Tate cohomology," which carries some algebraic information of the object it is defined on. Let that object be any finite dimensional Hopf algebra A over a field k. The aim of this talk is to extend a known relation of the ordinary cohomology and Hochschild cohomology of A to negative degrees. In particular, we prove that the Tate cohomology of A is an algebra direct summand of its Tate-Hochschild cohomology. Some terminologies will come from a semester of abstract algebra, but all necessary definitions and background will be given and no prior knowledge is expected. |

Thursday, April 14, 2016 | Yuri Bahturin, Vanderbilt University & Memorial University of Newfoundland, Canada |
Abstract: A graded algebra A over a field F is an algebra written as the direct sum
of subspaces called graded components such that for any two components U and V there
is a component W such that UV is a subset of W. If graded components can be labeled
by elements of a group G, U by g, V by h, and W by gh, then we say that A is a G-graded
algebra. For example, the algebra A of polynomials in several variable is graded by
the group |

Friday, March 25, 2016 | Drew Lewis, University of Alabama |
Abstract: The group of automorphisms of affine space, called the general automorphism group, is a fundamental object of study in algebraic geometry. There are several ways of studying this group. First, one can consider some natural subgroups, and try to describe the subgroup lattice. Another approach is to try and describe the structure of this group as an infinite dimensional algebraic variety. We will describe some recent work on both of these approaches to understanding the group, including a potential application to the Jacobian conjecture. |

Thursday, March 10, 2016 | Paul Sobaje, University of Georgia |
Abstract: Let G be a semisimple algebraic group over an algebraically closed field
k (for example, SL |

Tuesday, March 8, 2016 | Eduardo Dueñez, University of Texas at San Antonio |
Abstract: The classical Mean Ergodic Theorem of von Neumann proves the existence of
pointwise limits of averages for any cyclic group K={U |

Thursday, March 3, 2016 | Steven Clontz, University of North Carolina at Charlotte |
Abstract: For the metric arc I=[0,1] and continuum-valued bonding relation f closed
in I |

Tuesday, March 1, 2016 | Eric Rowland, Université de Liège, Belgium |
Abstract: Given a sequence of integers that counts a family of combinatorial objects, it is natural to ask about its long-term behavior. Traditionally researchers have been interested in asymptotic growth rates. However, one can also ask about number theoretic properties, such as the density of attained residues modulo a prime power and p-adic asymptotics. Such questions can be answered by partial interpolations of a sequence to the p-adic integers. |

Thursday, February 18, 2016 | Dan Silver, University of South Alabama This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
Abstract: Augustus De Morgan coined the term "mathematical induction" in 1838. It was an accident. "An intuitive truth" is how Felix Klein described this important method of proof, one that "carries us over the boundary where sense perception fails." We survey the history of mathematical induction from Euclid to Bertrand Russell. Along the way we will prove that all ponies are red. |

Thursday, February 11, 2016 | Elizabeth Jurisich, College of Charleston |
Abstract: Examples of Lie algebras with coefficients in polynomial rings, and quotient rings will be presented. In particular, Lie algebras formed as tensor products of simple Lie algebras and rings, where the rings are polynomial rings, or quotients of polynomial rings. Several examples will be described, such as affine Lie algebras, elliptic algebras, and n-point algebras. The three-point algebra is perhaps the simplest nontrivial example of a Krichever–Novikov algebra beyond an affine Kac–Moody algebra. |

Thursday, January 21, 2016 | Abhijit Champanerkar, College of Staten Island & The Graduate Center, CUNY |
Abstract: Knot theory has a fascinating history of using techniques from diverse fields of mathematics. In this talk we will explore the interactions between knot theory, graph theory and hyperbolic geometry. After giving some background in knots and geometry, we will focus on two natural knot invariants, a geometric quantity called the volume density, and a diagrammatic quantity called the determinant density. We will talk about recently discovered interesting relationships between the spectra of volume and determinant densities, and explore natural questions and conjectures motivated by this study. This is joint work with Ilya Kofman and Jessica Purcell. |

Thursday, December 3, 2015 | Dan Silver, University of South Alabama |
Abstract: The year 2015 was the 75th anniversary of the appearance of G.H. Hardy’s "A Mathematician's Apology." When its second edition appeared in 1967, one well-known critic added to his praise a warning: "it won’t make a nickel for anyone." In this talk, intended for a general audience, we explore the history of the book as well as the controversy that continues to surround it. |

Thursday, November 19, 2015 | Bhramar Mukherjee, University of Michigan |
Abstract: We consider predicting an outcome Y using a large number of covariates Our work is motivated by the rapid development of genomic assay technologies. In our
application, mRNA expression of a selected number of genes is measured by both quantitative
real-time polymerase chain reaction (qRT-PCR, The high-dimensionality of the problem, the large fraction of missing covariate information,
and the fact that we are interested in a prediction model for Y| |

Thursday, November 12, 2015 | Hung Ngoc Nguyen, University of Akron |
Abstract: A representation of degree n of a group G over a field F is a way to represent elements in G by n x n invertible matrices with entries in F in such a way that the rule of group operation corresponds to matrix multiplication. Perhaps the best way to describe representations is through characters. The character afforded by a representation is a function on the group which associates to each group element the trace of the corresponding matrix. In the representation theory and character theory of finite groups, one of the main problem is to study the influence of the degrees of irreducible representations/characters on the structure of groups. We will present some recent results on the average degree of irreducible representations of finite groups. In particular, we show that there is a tight connection between the average degree and important global characteristics of finite groups such as solvability, nilpotency, and commutativity, as well as p-local characteristics such as p-solvability, p-nilpotency, and the normality of Sylow p-subgroups. These are joint works with Lewis, Maroti, Moreto, and Tiep. |

Friday, November 6, 2015 | Karen Kohl, The University of Southern Mississippi - Gulf Coast |
Abstract: The method of brackets is a collection of a few heuristic rules for symbolic evaluation of definite integrals. The method is useful for a large class of single and multiple integrals, including many involving special functions. One of the computational challenges of this method is the simplification of the resulting output, especially when consisting of multi-sum series. This talk will show how to tackle some of these double- and triple-sums using a recurrence-finding approach. Adding more power to the method of brackets, this approach produces multi-sum identities for special function expressions. |

Tuesday, November 3, 2015 | Xiaofeng Wang, Department of Quantitative Health Sciences, Cleveland Clinic Lerner Research Institute |
Abstract: Clinical research studies commonly acquire complementary multi-modal and multi-source data for each patient in order to obtain a more accurate and rigorous assessment of the disease status and likelihood of progression. Multi-modal feature learning and prediction are challenging when integrating these kind of large-scale biomedical data. Motivated from a study of lung cancer detection, we present a novel integrative learning framework for the joint analysis of multi-modal data. The method is a statistical ensemble built on several modern statistical learning techniques, including feature extraction on functional data, random forests, and supervised multidimensional scaling. We also discuss a fast unsupervised clustering method for big data using an adaptive density peak detection procedure. The proposed framework is evaluated by application to high-dimensional chemical sensor array data from the Cleveland Clinic lung cancer early detection project. |

Thursday, October 29, 2015 | Alexander Hulpke, Colorado State University |
Abstract: Given a number of invertible matrices over a finite field, an obvious question is to find out more about the group they generate. Answering this question is the main object of Matrix Group Recognition and recently started to make steps from purely theoretical analysis to concrete calculations. I will describe how a divide-and-conquer approach is used to reduce the problem to that of simple groups, how identity relations can be used to verify calculations based on random elements, and how the resulting information can be used for practical calculation on the computer, e.g. in the system GAP. |

Thursday, October 22, 2015 | Akim Adekpedjou, Missouri University of Science and Technology |
Abstract: Recurrent event data are often observed in a wide variety of disciplines
including the biomedical, public health, engineering, economic, actuarial science,
and social science settings. Consider |

Thursday, October 15, 2015 | Narayanaswamy Balakrishnan, McMaster University, Canada |
Abstract: In this talk, I shall first give a historical account of cure rate models and present an introduction to the problems and the models used. I shall then present a flexible family of cure rate models and discuss likelihood inference for this family of models. I shall elaborate on the use of EM-algorithm for this purpose, and also present some results on model fitting and model discrimination between some of the well-known cure rate models. Finally, I will use the developed methods on a cutaneous melanoma data and illustrate all the results. |

Wednesday, October 14, 2015This talk is aimed at a general audience! |
Narayanaswamy Balakrishnan, McMaster University, CanadaSecond Satya Mishra Memorial Lecture |
Abstract: I will first give a brief account of how the field of Statistics developed over history, and also mention in the process some major advancements that took place in the growth of the field. Next, I will give a concise review of various aspects/topics of the field. Finally, I will then highlight some key applications of statistical methods to a wide range of problems arising from Science, Engineering, Medicine and Business. |

Thursday, October 1, 2015 | Jarrod Cunningham, University of South Alabama This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
Abstract: In this talk, I will discuss my experiences as a summer 2015 intern at the U.S. Department of Energy, as well as the projects I worked on over the summer. I will also discuss the things I did to obtain the internship, give advice on how to get accepted, and explore other internship, summer research, and job opportunities offered for undergraduate and graduate students in the STEM (Science, Technology, Engineering, and Math) disciplines. |

Thursday, September 24, 2015 | Susan Williams, University of South Alabama This talk is part of the Student Symposium Series, organized and conducted by the
graduate students. |
Abstract: Checkerboard doodling leads to a connection between knot theory and graph theory. The Laplacian matrix of a graph can be used to compute the number of components of the graph's medial link. |