Archive : Hallenbeck Grad Student Seminar

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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
Hamad El Kahza188Hamad El KahzaEwing 336<p><b>​Speaker: </b>Hamad El Kahza<br><b>Title: </b>On mathematical modeling of erosion and deposition in flow networks<br><b>Abstract: </b>Erosion and deposition are represented as the evolution of solid bodies as small particles get transported due to forces exerted by the fluid or air on the<br>solid contact interface, which lead to reconfiguration and change of structure of the medium. These processes arise in many environmental contexts, industrial applications and are notably complicated and challenging to study in experimental endeavors. In this work, we formulate novel and idealized mathematical models to examine the internal evolution of flow networks in cylindrical channels undergoing a unidirectional flow, using asymptotic and numerical techniques. Our model captures geometry evolution as particles get eroded from or deposited into the wall of the channels. Consequently, the structure channels’ radii expand and shrink, respectively, due to the interplay of erosion and deposition. A complete parametric sweep of the constructed model reveals that the final configuration of the structure can be predicted from the parameters of the system. Three different regimes are therefore observed within a single channel: (i) a dominant-deposition regime, (ii) a dynamic erosion-deposition regime, (iii)and a dominant-erosion regime.<br></p>10/20/2021 4:00:00 PM10/20/2021 5:00:00 PM

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