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Archive : Hallenbeck Grad Student Seminar

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Joseph Nakao192Joseph NakaoEwing 336<p>​<span class="wrap-text"><strong>Title:</strong> A new Eulerian-Lagrangian finite volume (ELFV)<br> method for solving convection-diffusion equations<br> and hyperbolic conservation laws</span><br></p>12/8/2021 5:00:00 PM12/8/2021 6:00:00 PM
Dheer Noal, University of Delaware191Dheer Noal, University of DelawareEwing 336<p>​Title: Spectral Tur\'an Problems<br>Abstract: In this talk, we will investigate the largest value of the spectral radius of the adjacency matrix among all $n$-vertex graphs that do not contain some subgraph. We will compare the structures of the Tur\' an-extremal and spectral extremal graphs for some examples. The odd wheel $W_{2k+1}$ is the graph formed by joining a vertex to a cycle of length $2k$. The $(k,r)$-fan is the graph consisting of $k$ copies of the complete graph $K_r$ which intersect in a single vertex, and is denoted by $F_{k,r}$. We show that for small odd wheels and all fans, the spectral extremal graphs are among the Tur\’an-extremal graphs on $n$ vertices, but for larger wheels the family of spectral extremal graphs and the family of Turán-extremal graphs are disjoint. We will give an overview of similar results and describe a method that may help us find new ones. This is joint work with Sebastian Cioab\u a (University of Delaware), Liying Kang (Shanghai University), Yongtao Li (Hunan University), Zhenyu Ni (Shanghai University), Michael Tait (Villanova University) and Jing Wang (Shanghai University). ​<br></p>12/1/2021 5:00:00 PM12/1/2021 6:00:00 PM
Kamal Joshi190Kamal JoshiEwing 336<p><strong>​</strong><strong>Title:</strong> On projective planes and their polynomial representations<br></p><p><strong>Abstract:</strong> Projective planes can be considered as ordinary planes with some additional points called “points at infinity” and a line at infinity. This addition enriches the geometric structure of the planes hugely. Side by side, the algebraic structure underlying these planes develop into many new systems with fascinating features. One of the approaches to studying the planes is then to study these algebraic structures, and through suitable polynomials representing the geometric actions on the points of the plane, we can find the correlation between geometric features and algebraic features. In this talk, a general introduction along these lines will be presented.​<br></p>11/10/2021 5:00:00 PM11/10/2021 6:00:00 PM
Vladislav Taranchuk, University of Delaware189Vladislav Taranchuk, University of DelawareEWG336<p><strong>T​</strong><span class="wrap-text"><strong>itle:</strong> Algebraically Defined Graphs and their Applications<br><strong>Abstract:</strong> Over the past few decades, algebraically defined graphs have gained a lot of attention due to their applications to some difficult problems in graph theory and finite geometry. In this talk, we will discuss the notions of algebraically defined graphs and give examples of how they are applied to various problems in graph theory. We will also discuss some recent results by Dr. Felix Lazebnik and myself in the area. </span><br></p>10/27/2021 4:00:00 PM10/27/2021 5:00:00 PM

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