기초과학연구원 이산수학그룹
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We consider the spanning tree embedding problem in dense graphs without bipartite holes and sparse graphs. In 2005, Alon, Krivelevich and Sudakov asked for determining the best possible spectral gap forcing an $(n,d,\lambda)$-graph to be $T(n, \Delta)$-universal. In this talk, we introduce our recent work on this conjecture. |
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In 2006, Tao established the Gaussian counterpart of the celebrated Green-Tao theorem on arithmetic progressions of primes. In this talk, I will explain the extension of Tao's theorem and the Green-Tao theorem to the case of general number fields. Our combinatorial tool is the relative hypergraph removal lemma by Conlon-Fox-Zhao. I will discuss the difficulties … |
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