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Archive : Discrete Mathematics

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Michael Tait, VillanovaMichael Tait, VillanovaZoom<br>Title: Graphs with large spectral radius <br> <br>Abstract: In this talk we will discuss what subgraphs can be guaranteed if a graph has a large eigenvalue. This is the spectral analog of the Tur\'an problem and was first raised by Brualdi and Solheid. We will give an overview of how to prove theorems in this area and will discuss some intuition for how to guess what the extremal graph(s) should be. As an example, we will characterize graphs of maximum spectral radius that do not contain a friendship graph. This latest theorem is joint work with Sebi Cioaba, Lihua Feng, and Xiao-Dong Zhang <br> 9/25/2020 8:00:00 PM9/25/2020 9:00:00 PMFalse
Annie Raymond, University of Massachusetts AmherstAnnie Raymond, University of Massachusetts AmherstTitle: Simple Graph Density Inequalities with no Sum of Squares Proofs <br> Abstract: Establishing inequalities among graph densities is a central pursuit in extremal graph theory. One way to certify the nonnegativity of a graph density expression is to write it as a sum of squares or as a rational sum of squares. In this talk, we will explore how one does so and we will then identify simple conditions under which a graph density expression cannot be a sum of squares or a rational sum of squares. These results extend to the powerful frameworks of flag algebras by Razborov and graph algebras by Lovász and Szegedy. This is joint work with Greg Blekherman, Mohit Singh, and Rekha Thomas. 9/11/2020 8:00:00 PM9/11/2020 9:00:00 PMFalse
Abdullah Zafar (University of Toronto & Sports Performance Analytics Inc.)Abdullah Zafar (University of Toronto & Sports Performance Analytics Inc.)EWG 336Title:Team Passing and Movement Analysis in Professional Football: Applied Discrete Methods <br><br> Abstract: Joint work with Farzad Yousefian Ball movement is critical in football performance and match outcome as it is the primary method by which players ‘interact’ with each other. Interactions between players, over time, create specific patterns which form the collective passing behaviour of a team. Complementary to ball movement is player movement and positioning, which allows for passing opportunities to be created. To explore the modelling of both passing and movement behaviour, a total of 17 matches of a professional Portuguese football club in the Primeira Liga, 64 matches of the 2018 FIFA World Cup and 5 matches from the Canadian Women’s Team at FISU 2017 were analyzed using match video and iSCOUT software. Passing behaviour was modelled to illustrate higher-order relations between players to identify differences in play style between teams using graphs, simplicial complexes, and homology groups. Optimization of team selection and passing behaviour, based on player availability and team style, was explored using hyper-graphs and hyper simplices. Finally, algebraic braids were utilized to discretize player movement patterns within a team context as a means of integrating passing and movement analysis. 5/14/2020 6:00:00 PM5/14/2020 7:00:00 PMFalse
Xiaoye Liang, WPI and Anhui University, ChinaXiaoye Liang, WPI and Anhui University, ChinaZoom<br> Title: Irreducible T-modules of the Johnson scheme<br> Abstract: The classification of (P and Q)-polynomial scheme is the central problem in algebraic combinatorics: (P and Q)-polynomial schemes are not only interesting for their own sake but also important as underlying space for coding/design theory. This talk focuses on a typical (P and Q)-polynomial scheme — Johnson scheme. Terwilliger algebra will be introduced as it is an important tool to classify association scheme. In our work, all irreducible T-modules of the Johnson scheme are determined.5/7/2020 6:00:00 PM5/7/2020 7:00:00 PMFalse

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