2021-2022 Colloquia
to any semi-primitive root modulo 2k and present a generalized version of their algorithm to find the discrete logarithm modulo 2k.
Dr. Slavov is a Data Scientist with more than 15 years of experience in healthcare data analysis, medical research, and marketing analytics. He worked at the Department of Psychiatry at Columbia University and later at the Advanced Analytics Lab at UnitedHealth Group, Thompson Reuters and two startup companies. He will present a problem he encountered many times in his industry projects.
Title: Machine Learning in LiDAR 3D point clouds
Speaker: Dr. F. Patricia Medina (CS department in Yeshiva College-Yeshiva University)
Date: Wednesday, 02/16/2022
Time: 12:30pm – 1:30 pm
Room: Please contact L. Boyadzhiev for the Zoom link
Abstract
LiDAR point clouds contain measurements of complicated natural scenes and can be used to update digital elevation models, glacial monitoring, detecting faults and measuring uplift detecting, forest inventory, detect shoreline and beach volume changes, landslide risk analysis, habitat mapping, and urban development, among others. A very important application is the classification of the 3D cloud into elementary classes. For example, it can be used to differentiate between vegetation, man-made structures, and water. Our goal is to present a preliminary comparison study for classification of 3D point cloud LiDAR data that includes several types of feature engineering. In particular, we demonstrate that providing context by augmenting each point in the LiDAR point cloud with information about its neighboring points can improve the performance of downstream learning algorithms. We also experiment with several dimension reduction strategies, ranging from Principal Component Analysis (PCA) to neural network-based auto-encoders, and demonstrate how they affect classification performance in LiDAR point clouds. For instance, we observe that combining feature engineering with a dimension reduction method such as PCA, there is an improvement in the accuracy of the classification with respect to doing a straightforward classification with the raw data.
This is joint work with Prof. Randy Paffenroth, Worcester Polytechnic Institute.
Title: Dispersive hydrodynamics: convex to non-convex dispersion
Speaker: Dr. Saleh Baqer (Kuwait University)
Date: Wednesday, 12/15/2021
Time: 12:30pm – 1:30 pm
Room: Please contact L. Boyadzhiev for the Zoom link
Abstract
Dispersive hydrodynamics, mathematical models formulated by hyperbolic conservation laws with dispersive corrections, govern fluid or fluid-like phenomena that naturally emerge in media whose dissipative effect (e.g., viscosity) is negligible or non-existent relative to wave dispersion. Examples of such physical highly dispersive media are shallow water waves, internal oceanic waves, nonlinear optics (optical fibers and nematic liquid crystals) and quantum fluids (Bose-Einstein condensates). The framework of dispersive hydrodynamics possesses a plethora of nonlinear dispersive wave phenomena. This includes solitary waves (or solitons for integrable systems), produced by a nonlinear-dispersion balance, and dispersive shock waves (or undular bores as known in fluid mechanics), a multi-scale nonlinear wave generated by a rapid change of a physical quantity as time evolves. In this talk, we will overview some classical and more recent mathematical models in this growing field, discuss asymptotic and variational methods (mostly based on Whitham averaging theory) needed to analyze dispersive hydrodynamic solutions, and present some comparisons of theoretical solutions against numerical ones. In particular, the effects of non-convex dispersion will be considered that give rise to non-standard (resonant) wave structures.
Title: Using topos theory to make analogies precise
Speaker: Morgan Rogers (Università degli Studi dell’Insubria, Italy)
Date: Wednesday, December 1, 2021
Time: 12:30pm – 1:30 pm
Room: Please contact L. Boyadzhiev for the Zoom link
Abstract
Often in maths, insights from one area can provide inspiration in another. Formalizing analogies between different areas has resulted in the creation of whole new subfields and deep conjectures. A tool for this transfer process, which historically has been important in algebraic geometry, is topos theory, for the following very accessible reason: there are many ways to build toposes!
In this talk, we shall describe two ways of building toposes, or more precisely two classes of Grothendieck topos: toposes of sheaves on topological spaces, and toposes of actions of discrete monoids. These classes are as different as can be, in the sense that the only topos which is in both classes is the topos of sets (corresponding to the one-point space and the trivial monoid, respectively). In spite of this, we can translate ideas from topology to algebra through these toposes by considering the respective properties of spaces and monoids. We give some examples, some of them more intuitive than others, and then give some hints about future directions this work could go.
You won't need to know what a topos is ahead of time to follow this talk.
Title: The Yang-Mills equations and their geometry
Speaker: Dr. David Pham (Queensborough Community College)
Date: Wednesday, 11/24/2021
Time: 12:30pm – 1:30 pm
Room: Please contact L. Boyadzhiev for the Zoom link
Abstract
In 1954, C.N. Yang and R. Mills proposed a classical generalization of Maxwell's equations of electromagnetism. These equations (now called the Yang-Mills equations) have become the bedrock of the Standard Model of physics which describes three of the four forces of nature. The equations turn out to have a surprising geometric interpretation (which was not known to Yang and Mills until the 1970's) which ultimately had a big impact in the study of 4-manifolds. In this talk, we give an elementary introduction to the Yang-Mills equations and their geometry. The talk is essentially self-contained. The only prerequisite is a working knowledge of differential forms on R^n.
Title: The Richness of Models of Peano Arithmetic
Speaker: Dr. Erez Shochat (St. Francis College)
Date: Wednesday, 11/10/2021
Time: 12:30pm-1:30pm
Room: Please contact L. Boyadzhiev for the Zoom link
Power point slides: The-richness-of-models-of-Peano-Arithmetic.pptx
Abstract
In this talk we outline the axioms of Peano Arithmetic (PA) and show there are (countable) non-standard models of PA. We then discuss briefly Godel Incompleteness Theorem and show that it implies that there are uncountably many countable first order models of PA with different complete theories (that is, even though they all satisfy the same statements which are proven in PA, for every two such models there will be at least one statement that is satisfied by one but not by the other). We will show that for any of these uncountably many different theories, there are uncountably many non-isomorphic models. We will then discuss briefly well-known results in the field of models of arithmetic, for example, on the order type of models of arithmetic and on recursively saturated models (if time allows).
Title: The nth level fractional derivative and some of its properties.
Speaker: Dr. Yuri Luchko (Technical University of Applied Sciences Berlin, Germany)
Date: Wednesday, 10/27/2021
Time: 12:30pm – 1:30 pm
Room: Please contact L. Boyadzhiev for the Zoom link
Abstract
In this talk, we first discuss some general properties that should be satisfied by any one-parameter families of the fractional integrals and derivatives. Then we focus on a realization of this general schema in form of the Riemann-Liouville fractional integral and some corresponding fractional derivatives. In particular, we introduce the nth level fractional derivative that is a natural generalization of the fractional derivatives in the Riemann-Liouville, Caputo, and Hilfer senses ([1]). Then, following [2], we discuss the formulas for the Laplace transform of the nth level fractional derivative and its projector operator. Finally, the general solution to the fractional relaxation equation with the nth level fractional derivative is derived in explicit form in terms of the two-parameter Mittag-Leffler function.
References:
- Yu. Luchko: Fractional derivatives and the fundamental theorem of Fractional Calculus. Fract. Calc. Appl. Anal. 23 (2020), 939-966.
- 2. Yu. Luchko: On complete monotonicity of solution to the fractional relaxation equation with the nth level fractional derivative. Mathematics 2020, 8(9), 1561.
Title: Exact Controllability for the Wave Equation on Graphs
Speaker: Yuanyuan Zhao (University of Alaska Fairbanks)
Date: Wednesday, 09/29/2021
Time: 12:30pm – 1:30 pm
Room: Please contact L. Boyadzhiev for the Zoom link
Abstract
The talk is based on joint work with Sergei Avdonin (UAF) and Julian Edward (FIU). We consider initial boundary value problems and control problems for the wave equation on finite metric graphs with Dirichlet and Neumann controls. We propose new constructive algorithms for solving the initial boundary value problems and control problems on general graphs. We show through examples on a lasso graph that the wave equation on a graph with cycles is exactly controllable if the Neumann controllers are placed at the active vertices and Dirichlet controllers are placed at the active edges. The proofs for the shape and velocity controllability are purely dynamical, while the proof for the full controllability utilizes both dynamical and moment method approaches.
