Many knot invariants are defined from features of knot projections such as arcs or crossings. Gauss diagrams provide an alternative combinatorial scheme for representing knots. In this talk we will use Gauss diagrams to enhance the biquandle counting invariant for classical and virual knots using biquandle arrow weights, a new algebraic structure without a clear […]
Title: Building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City Speaker: Joan Ponce, Department of Mathematics, Arizona State University Abstract: Epidemiological models can provide the dynamic evolution of a pandemic but they are based on many assumptions and parameters that have to be adjusted over the time the pandemic lasts. […]
There are two different measures of how far a given Euclidean lattice is from being orthogonal -- the orthogonality defect and the average coherence. The first of these comes from the study of sphere packing while the second is motivated by frame theory, but both of them have applications in digital communications, especially in coding […]
Title: The mathematics of neural networks: recent advances, thoughts, and the path forward Speaker: Prof. Mikhail Belkin, Department of Mathematics, University of California San Diego Abstract: The recent remarkable practical achievements of neural networks have far outpaced our theoretical understanding of their properties. Yet, it is hard to imagine that progress can continue indefinitely, without […]
We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) to include both linear multifractional Brownian sheets and linear multifractional stable sheets. The purpose of the framework is to study the existence and joint continuity of the local times of LMSS, and also the local Holder condition of the local times […]
Title: Quantum chromatic numbers of products of quantum graphs Speaker: Rolando De Santiago, Department of Mathematics, Purdue University Abstract: Quantum graphs are an operator space generalization of classical graphs that have emerged in different branches of mathematics including operator theory, non-commutative topology and quantum information theory. We provide a brief introduction to quantum graphs and […]
Graph products of groups were introduced in E. Green’s thesis in the 90’s as generalizations of Right-Angled Artin Groups. These have become objects of intense study due to their key roles in topology and group theory. Recently, Caspers and Fima introduced graph products of von Neumann algebras. Since their inception, several structural aspects such as […]
Consider rational polynomials in multiple variables that are linear with respect to some of the variables. In this talk we discuss the problem of finding a zero of such polynomials that are bounded with respect to a height function. For a system of such polynomials satisfying certain technical conditions we prove the existence of a […]
Title: Mathematical model for HIV-1 infection with stem cell and immune-therapy Speaker: Noufe Aljahdaly, Department of Mathematics, King Abdulaziz University / CGU Abstract: The AIDS is a chronic disease. Its most common treatment is the antiretroviral therapy (cART) and the virus can be more effected if the patients stop using cART. The other problem is […]
Title:Geometric Scattering on Measure Spaces Abstract: Geometric Deep Learning is an emerging field of research that aims to extend the success of convolutional neural networks (CNNs) to data with non-Euclidean geometric structure. Despitebeing in its relative infancy, this field has already found great success in many applications such as recommender systems, computer graphics, and traffic […]
Title: Watch your step: Modeling on Time Scales Speaker: Raegan Higgins, Department of Mathematics & Statistics, Texas Tech University Abstract: Generally, differential and difference equations are used in the mathematical modeling of physical systems. Our modeling approach uses dynamic equations on time scales. A time scale T is an arbitrary, nonempty, closed subset of the […]
Given a unital AF (approximately finite-dimensional) algebra A equipped with a faithful tracial state, we equip each (norm-closed two-sided) ideal of A with a metrized quantum vector bundle structure, when canonically viewed as a module over A, in the sense of Latrémolière using previous work of Aguilar and Latrémolière. Moreover, we show that convergence of […]
