Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
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EC Seminar: Recent progress on the Bollobás-Nikiforov conjecture
The Bollobás–Nikiforov Conjecture is a proposed strengthening of Nikiforov’s spectral Turán theorem, itself a refinement of the classical Turán’s theorem. Although the conjecture has a simple statement, nearly two decades of effort have not yielded a complete solution. In this talk, I will discuss the recent resolution of the Bollobás-Nikiforov conjecture for triangle-free graphs and regular graphs, as well as a variant of the conjecture that employs weaker dependencies. Our approaches draw a connection between spectral graph theory, optimization, and weighted Turán problems. This is joint work with Gabriel Coutinho and Thomás J. Spier.
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