October 27

 O'Donnell Hall 111

Speaker:  Agnès Beaudry, University of Colorado

Title:  TBA

Abstract:  TBA

 October 27

 O'Donnell Hall 111

 2:30PM - 3:30PM

Speaker:  Katherine Poirier, New York City College of Technology

Title:  TBA

Abstract:  TBA

 October 27

 O'Donnell Hall 111

 4:00PM - 5:00PM

Speaker:  Zhouli Xu, University of California at San Diego

Title:  TBA

Abstract:  TBA

 August 25

Speaker:  Michael DiPasquale, NMSU

Title:  Two Perspectives on Affine Semigroup

Abstract:  A numerical semigroup is the set of all integers which can be written as a non-negative integer combination of a fixed set of positive integers which are relatively prime.  The non-negative integers which are not in the numerical semigroup is called the set of holes of the semigroup.  In 1978, Herbert Wilf posed a question about the density of this set of holes which is still widely open and has become known as Wilf's conjecture.  In the first portion of this talk we will discuss Wilf's conjecture and an extension of it to higher dimensions, where a numerical semigroup is replaced by a certain type of affine semigroup.  An affine semigroup is the set of non-negative integer combinations of a fixed set of vectors with integer entries.

In the remainder of the talk we will focus on the representation of an affine semigroup as a quotient of a polynomial ring by a so-called toric ideal. A Gr\"obner basis for the toric ideal possesses a wealth of information about the semigroup, and it is of particular interest both in pure and applied algebraic geometry to find a Gr\"obner basis of low degree. Time permitting we will touch on two projects where we find a Gr\"obner basis of quadrics for combinatorially meaningful classes of toric ideals.

 September 1

Speaker:  Yang Hu, NMSU

Title:  A Calculus Approach to Vector Bundle Enumerations

Abstract:  In the unstable range, topological vector bundles over finite CW complexes are difficult to classify in general. Over complex projective spaces, such bundles are far from being fully classified, or even enumerated, except for a few small dimensional cases studied in the 1970’s using classical tools from homotopy theory, and more recently using the modern tool of chromatic homotopy theory. We apply another modern tool, Weiss calculus, to enumerate topological complex vector bundles over complex projective spaces with trivial Chern class data, in the first two cases of the metastable range.

 April 28

Speaker:  Samuel Scarpino, Northeastern University

Title:  Behavior-induced Phase Transitions in Contagion Models on Networks

Abstract:  Seemingly trivial modifications to the classical model of contagion spreading can dramatically alter its phenomenology.  For example, discontinuous phase transitions can occur due to complex or interacting contagions, accelerating transmission and hysteresis loops can occur when individuals modify their behavior after becoming infectious, and double phase transitions can emerge in the presence of asymmetric percolation. In this talk, I will present theoretical work on the effects of behavior on contagion spreading and discuss empirical support for these new models. Our findings demonstrate the inherent complexity of biological contagion, and we anticipate that our methods will advance the emerging field of disease forecasting.

 April 21

Speaker:  Boris Choy, University of Sydney Business School

Title:  Non-elliptical Student-t Distributions with Computations and Applications

Abstract:  In this talk, an extension from the elliptical to non-elliptical Student-t distribution is proposed to improve modelling capability. This extension is based on the mean-variance structure of the t and skew-t distributions. Although the probability density distributions of these non-elliptical distributions do not have a close form, the MCMC and EM algorithms have proven to be very efficient to handle these distributions. Financial data and insurance loss data are used for illustration purposes.

 April 14

Speaker:  Stephen Brazil, Actuary, USA

Title:  What's an Actuary?

Joint with the Actuarial Seminar Business College, New Mexico State University

 March 24

Speaker:  Marco Aiello, University of Stuttgart, Germany

Title:  Data is Nothing Without Control: On Building IoT Architectures for a Sustainable Society

Abstract:  The availability of data in digital form is at unprecedented levels and is enabling a new way of building systems that are transforming our society. But data by itself is not enough to provide useful systems. In this talk, I will overview recent and current research efforts at the Service Computing Department of the Institute of Architecture of Application Systems of the University of Stuttgart. The research efforts revolve around the design of architectures that go beyond the mere collection of data and can support humans in smart ways. The applications of these systems are in the field of energy and sustainability, in particular: Smart Buildings, Smart Grids, and Smart Data Centers.

 March 3

Speaker:  Eugene Bilokopytov from University of Alberta, Canada

Title:  Locally Solid Convergences on a Vector Lattice

Abstract:  In this talk we will discuss convergences on a vector lattice which are not necessarily induced by a topology, but are compatible with the order and algebraic structure of the vector lattice. An example of such convergence is the convergence almost everywhere on the spaces of measurable functions. The word "convergence" will be given a precise meaning. We will also look at some canonical convergences associated with a vector lattice and characterize certain completeness-like properties of vector lattices in terms of the completeness of the corresponding convergence.

 February 24

Speaker:  Alexander Shen, University of Montpellier 2, France

Title:  Information Inequalities

Abstract:  The intuitive notion of "amount of information" can be formalized in may ways. The algorithmic information (Kolmogorov complexity) theory says that the amount of information in a finite object x is the minimal length of a program that produces x. Some intuitive properties of information (say, the amount of information in pair (x,y) is bounded by the sum of the amounts of information in x and y) can be proven. Another way to measure information is suggested by Shannon information theory. It turns out that the "laws of information theory" (understood as linear inequalities) are the same for both cases (Romashchenko), and the same class of inequalities appears in group theory, database theory, geometric dimension theory. A survey of these results will be given.

 January 25

Speaker:  Yairon Cid-Ruiz, KU Leuven, Belgium

Title:  Rees algebras of determinantal ideals

Abstract:  We will give an introduction to SAGBI basis theory and its application to the Rees algebra. We then present a couple of recent results using SAGBI basis theory to find the presentation equations of Rees algebras of determinantal ideals and their properties.

 January 23

Speaker:  Boyu Li, University of Waterloo

Title:  Analysis on Semigroups Through the Lens of Dilation Theory

Abstract:  The analysis of algebraic structures using bounded linear operators on Hilbert spaces traces back to the pioneering work of Murray and von Neumann. For example, the abstract harmonic analysis of groups relates various properties of a group to its unitary representations. For semigroups, however, the lack of inverse leads to much richer classes of representations. These representations are often interrelated via dilation theorems. In this talk, I will briefly go over the history of the analysis of semigroups, with a focus on the role of dilation theory. I will then explain how our recent dilation theorem on semigroup dynamical systems unifies many earlier results in dilation theory.

This is partly based on joint work with Marcelo Laca.

 January 20

Speaker:  Michael DiPasquale, University of South Alabama

Title:  A Bridge Between the Algebra and Geometry of Hyperplane Arrangements

Abstract:  A hyperplane arrangement is a union of codimension one linear spaces. These simple objects provide fertile ground for interactions between combinatorics, algebra, algebraic geometry, topology, and group actions. The combinatorics of an arrangement is encoded by the pattern of intersections among the hyperplanes, called its intersection lattice. On the other hand, a key algebraic object is the module of vector fields tangent to the arrangement, called the module of logarithmic derivations, which was introduced by Saito in 1980 to study the singularities of hypersurfaces. An enduring mystery in the theory of hyperplane arrangements is which algebraic properties of the module of logarithmic derivations can be determined from the intersection lattice, and which properties depend fundamentally on the geometry (i.e. the exact hyperplanes). At the center of this mystery is Terao's conjecture, which proposes that the algebraic property of freeness can be determined only from the intersection lattice. In this talk we explain how rigidity of planar frameworks (dating back to Maxwell) plays a key role in connecting the geometry and algebra of line arrangements in the projective plane.

This is joint work with Jessica Sidman and Will Traves.

 January 18

Speaker:  Timothy Rainone, Occidental College

Title:  Paradoxical decompositions, dichotomy, and Finite-Approximability in Operator Algebras

Abstract:  Notions of finiteness are prevalent in mathematics, not least in operator algebras. For instance, with matrix algebras we observe Dedekind-finiteness; that is every isometry is unitary. This also holds for large classes of C*-algebras as well as their stabilization. Such algebras are called stably finite. At the opposite end of the spectrum are the purely infinite C*-algebras whose internal structure admit paradoxical decompositions; especially when the algebras in question are crossed-product constructions. In this talk we will study the stably finite/purely infinite dichotomy for certain C*-algebras that arise from dynamical systems. We will then move our discussion to matricial field (MF) C*-algebras; a subclass of stably finite algebras that admit external matrix approximations. The C*-analogue of the Connes Embedding Conjecture proposes that every stably finite C*-algebra should admit such an approximation. We show that is is indeed the case for large classes of crossed products of nuclear algebras by free groups. This talk is aimed at a general math audience; we will carefully introduce the theory of C*-algebras as well as all the notions alluded to above.

January 16

Speaker:  Alessandra Costantini, Oklahoma State University

Title:  Rees Algebras: An Algebraic Tool to Study Singularities

Abstract:  How many tangent lines does a plane curve have at a given point? And how can we effectively solve polynomial equations with integral coefficients? These seemingly unrelated problems from algebraic geometry and number theory can be both solved using tools from abstract algebra, through the notion of Rees algebras.

In this talk, I will first discuss the fundamental role of Rees algebras in the study of commutative rings and singularities of algebraic varieties. I will then focus on the problem of describing Rees algebras in terms of generators and relations, presenting some of my recent results on this topic, which were obtained using techniques from algebraic combinatorics.

January 13

Speaker:  Sudan Xing, University of Alberta, Canada

Title:  Dual Orlicz-Minkowski Problem

Abstract:  The classical Minkowski problem is a central problem in convex geometry which asks that given a nonzero finite Borel measure, what are the necessary and sufficient conditions on this measure such that it equals to the surface area measure of a convex body. In this talk, I will present the general dual extension of the classical Minkowski problem—the generalized dual Orlicz-Minkowski problem.