2024-2025 Colloquia
Title: Multiplication Is to Addition as Addition Is to What?
Speaker: Dr. Howard Sporn (Queensborough COmmunity College)
Date: Wednesday, April 9, 2025
Time: 12:30 pm - 1:30 pm
Room: S-213 (Dr. Joseph Bertorelli Classroom)
Abstract
When children are first taught about multiplication of the natural numbers, it is usually presented as repeated addition. Later, raising to an exponent is presented as repeated multiplication. Then the following analogy is obvious: addition is to multiplication as multiplication is to be raising to an exponent. An interesting question is to ask what happens if we go in the other direction. That is, multiplication is to addition as addition is to what? In this talk, we will answer this question and show that there are several possible operations that could be used to answer the question. Some of them will be presented in connection with algebraic semi rings. We will also get into a bit of "tropical" geometry.
Title: SKT metrics on the exceptional Lie group G2
Speaker: Dr. David Pham (Queensborough COmmunity College)
Date: Wednesday, March 19, 2025
Time: 12:30 pm - 1:30 pm
Room: S-213
Abstract
A strong Kahler with torsion (SKT) metric arose in the work of string theorists (Strominger, Gates, and Hull) in the 1980s as it relates to the geometry of the extra dimensions in string theory. From a mathematical point of view, an SKT metric is a Hermitian manifold (M,g,J) where the fundamental 2-form is pluriclosed. In particular, every Kahler manifold is SKT, but not the converse is not true. In this talk, we construct a family of left-invariant SKT metrics on the exceptional Lie group G2 where the complex structure J is given by the Samelson construction. The SKT metrics have the feature of being right invariant with respect to a certain maximal torus T of G2. The family of SKT metrics we construct is a 3-parameter family and represents all left-invariant SKT metrics on (G2,J) which satisfy this right invariance with respect to T. This work is motivated by a 2023 paper of Fino and Grantcharov where (among other things) they carried out a similar calculation for the Lie group SO(9).
Title: Revealing Randomness: Accessible Strategies for Deepening Statistical Understanding
Speaker: Dr. Venessa N. Singhroy (Queensborough COmmunity College)
Date: Monday, February 24, 2025
Time: 2:00 pm - 2:50 pm
Room: S-214
Abstract
Grasping the concept of random selection is essential for understanding statistical methodologies, yet students frequently struggle with its nuances. This presentation highlights an engaging instructional activity designed to clarify randomness while exposing inherent biases in human decision-making. Used in undergraduate Statistics and Psychology courses, the exercise asks students to select names, revealing misconceptions about randomness and the influence of cognitive biases. The findings underscore the importance of deeper comprehension and suggest refinements to enhance student engagement. By incorporating Data Visualization and Data Analysis, this multi-method approach integrates qualitative insights with quantitative assessment, offering a practical strategy for educators to strengthen students’ understanding of randomness in statistics.
Reference: Singhroy, V., Robertson, R., C Stroumbakis, K. Does a Name Make a Difference? Teaching Random Selection in the Classroom. Numeracy, 18(1), 2.
Title: Some Recent Results in Fractional Bessel-like Ordinary and Partial Differential Equations
Speaker: Dr. Pavel B. Dubovski, Stevens Institute of Technology, NJ
Date: Wednesday, October 16, 2024
Time: 12:30 pm - 1:30 pm
Room: S-213 (Dr. Joseph Bertorelli Classroom)
Abstract
We study ordinary and partial differential equations involving fractional Bessel-like operators.
Our work presents new results on the existence and uniqueness of solutions and explores methods for constructing these solutions, particularly within the framework of fractional series. As a key outcome, the methods we propose, that combine integral transforms with fractional series, enable the analysis of quasi-Euler and constant-coefficient equations. Additionally, these techniques can be applied to elliptic-like PDEs with fractional Cauchy-Euler operators, which are a specific case of the Bessel operator. We also observe a hyper-dimensionality phenomenon in certain fractional differential equations, where an unexpectedly large number of linearly independent solutions exist. These theoretical findings are supported by computational evidence. The results presented are from joint work with L. Boyadzhiev and J. Slepoi.
In the second part of the talk, P. Dubovski will introduce a collaborative project on writing a textbook on fractional analysis. Currently, there is no comprehensive textbook suited for undergraduate or graduate students, and this project, in collaboration with De Gruyter publishers, aims to address that gap.
References:
Fract. Calc. Appl. Anal. 2021, 2022; IOIP Series 2021; J. Math. Sci. 2022; J. Appl. Analysis 2023; Mathematics 2024.
Fract. Calc. Appl. Anal. 2021, 2022; IOIP Series 2021; J. Math. Sci. 2022; J. Appl. Analysis 2023; Mathematics 2024.
Short Bio:
P. Dubovski received his Ph.D. in Mathematical Physics from Moscow State University and his Dr.Sc. from the Institute of Numerical Mathematics, Russian Academy of Sciences. Since 2003, he has been with Stevens Institute of Technology. His research focuses on mathematical kinetics and modeling, integral equations, hydrodynamics, integrable probability, and fractional analysis.
