Session Index
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Faculty/Graduate Session A
9:35am--11:10am, Zoom Fac/Grad A
Speakers: Samantha Pezzimenti, Elie Abdo, Yusuf Z Gurtas, Lindsay Dever, Eva Goedhart
Faculty/Graduate Session B
9:35am--11:10am, Zoom Fac/Grad B
Speakers: Myung Song, Eric Landquist, Wing Hong Tony Wong, Jeongsu Kyeong
Faculty/Graduate Session A, Zoom Fac/Grad A
9:35am, Samantha Pezzimenti (Penn State Brandywine)
Legendrian Knot Mosaics
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All smooth knots can be built out of a set of 11 mosaic tiles. The mosaic number is a knot invariant which measures smallest size mosaic that can be used to build the knot. In this talk, we discuss a variation of these tiles that can be used to build Legendrian knots, which are knots that satisfy an extra geometric condition. We explore analogous invariants for Legendrian knots and properties of these Legendrian knot mosaics. In particular, we present an infinite sequence of Legendrian knots whose mosaic numbers are only realized when their crossing numbers are not. This work is joint with Abhinav Pandey.
Close Abstract9:55am, Elie Abdo (Temple University)
Hartogs Extension Phenomenon
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Several theorems that hold in the theory of one complex variable cannot be generalized to the theory of several complex variables. For example, the zeros of a non-constant holomorphic function in $\mathbb{C}$ are isolated. This fact is no longer true in higher complex dimensions as a consequence of Hartogs Extension Phenomenon. In this talk, we prove this latter theorem, which states that if $0<a<b$, then every holomorphic function in $D(0,b) \times D(0,b) \setminus \overline{D(0,a) \times D(0,a)} \subset \mathbb{C} \times \mathbb{C}$ extends analytically to $D(0,b) \times D(0,b) \subset \mathbb{C} \times \mathbb{C}$. Here, $D(0,r) \subset \mathbb{C}$ denotes the disc in the complex plane of center $0$ and radius $r > 0$.
Close Abstract10:15am, Yusuf Z Gurtas (Queensborough Community College, CUNY)
Synthetic Division by Binomials of Degree Greater Than 1
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Synthetic division is a powerful method of dividing polynomials by binomials of the form $x-c$. In this talk division of polynomials by binomials of degree greater than 1 will be presented.
Close Abstract10:35am, Lindsay Dever (Bryn Mawr College)
Prime geodesics on compact hyperbolic 3-manifolds
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The study of hyperbolic 3-manifolds draws deep connections between number theory, geometry, topology, and quantum mechanics. An important geometric invariant of a hyperbolic 3-manifold is the set of its closed geodesics, which are parametrized by their length and holonomy. Sarnak and Wakayama showed in 1999 that holonomies of geodesics of increasing lengths become equidistributed throughout the circle. In this talk, I will present new results including a refined count of length and holonomy which implies equidistribution in shrinking intervals.
Close Abstract10:55am, Eva Goedhart (Williams College)
Of Card Tricks and Happy Numbers
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You might wonder what card tricks have to do with happy numbers and how numbers can be happy in the first place. Come find out! I’ll explain what the connection is and show you some neat results about sequences of happy numbers.
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Faculty/Graduate Session B, Zoom Fac/Grad B
9:35am, Myung Song (Kuztown University of Pennsylvania)
Using Metaheuristic Methods for Variable Selection
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Variable (or feature) selection has been one of old topics in regression models. Beside many classical approaches, some metaheuristic approaches from the optimization research such as GA (Genetic Algorithm) or SA (Simulated Annealing) have been developed so far. These methods have a considerable advantage to deal with high dimensional problems over the conventional methods, but they must control associated fine-tuning parameters, which is very hard in practice. In this paper, Jaya, one of the parameter-free approaches will be suggested and explored. Many methods such as GA, TBO, and Jaya will be compared to one another with the results from real-world datasets.
Close Abstract9:55am, Eric Landquist (Kutztown University)
An Open Applied Calculus Textbook and a New OER Funding Model
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Open Educational Resources (OER) are resources for academic use, such as software, textbooks, ancillary material, etc., that are free to use, modify, and distribute. Adoption of OER has been linked to better performance in coursework due to greater access to course materials, especially among students eligible for Pell Grants. In this talk, I will discuss one of my open textbook projects, Open Applied Calculus, and show how anyone can get involved in its development. A certain number of PASSHE faculty can also receive a $200 honorarium for a brief review and a small contribution to the textbook's development. This leads to the second point of the talk. What incentive is there to develop and maintain a free textbook or other open course material? There are traditional models, such as professional development, grant funding, and sabbatical work. However, I will suggest some additional ways to fund OER development that may be new to the academic world. Many of these methods are currently used by many nonacademic content creators to fund their creative works such as blogs, vlogs, and podcasts, for example. I welcome your thoughts and ideas.
Close Abstract10:15am, Wing Hong Tony Wong (Kutztown University of Pennsylvania)
Two new notions on graph labeling
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In this talk, we introduce two new notions on graph labeling: sum index and difference index. We will present the definitions, as well as some interesting results and open questions.
Close Abstract10:35am, Jeongsu Kyeong (Temple University)
$\pi$ is irrational
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In 1766, Johann Heinrich Lambert proved the fundamental fact that $\pi$ is irrational, i.e., that it can not be written as the quotient of two integers. In 1947, Ivan Niven gave an elegant one-page proof of this fact which only uses elementary calculus and which appeared that year in the Bulletin of the American Mathematical Society. In this talk, I will present the history of the problem and Niven's argument.
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