报告时间：2026年11月5日 10:00开始

报 告 人：Ferdinand Ihringer（南方科技大学 助理教授）

报告地点：9-113

报告题目：Two New Ramsey-type Results

报告摘要：For Ramsey numbers $R(s, t)$, it is very easy to find good probabilistic constructions, but seemingly very hard to find explicit constructions. In the first part of the talk, we give a construction showing that, uniformly for integers $3 \leq s \leq t$, as $t \to \infty$, \[R( s,t ) \geq t^{(1-o(1)) \log s / \log(\log s + 1) }. \] This is joint work with Sam Mattheus. For fixed $s$, this improves the dependence on $s$ in the general off-diagonal construction of Alon and Pudl\'ak. In particular, $R(33, t) \geq t^{2.1-o(1)}$, to our knowledge, the first explicit construction showing $R(s, t) \geq t^c$ for some fixed $s$ and some $c>2$. In the diagonal case, it improves the leading constant in the exponent of the classical Frankl--Wilson bound.

In the second part of the talk will be concerned with finding clique free optimally pseudorandom graph, a problem due to Alon and Krivelevich. For $K_3$-freeness this has been solved by Alon. Here we present the first progress on this work, completely solving the case of $K_4$-freeness. This gives a third proof for $R(4, t) = t^{3-o(1)}$, an improvement for constructive Ramsey numbers $R(4, t)$, and a variety of applications to problems such as MaxCut, graph factors, and the Lov\'asz $\vartheta$-function. Joint work with Jie Han and Hendrik Van Maldeghem.

报告人简介：Ferdinand Ihringer, Assistant Professor at the Southern University of Science and Technology (SUSTech). He received his PhD in 2015 from Justus-Liebig-Universität Gießen under the supervision of Klaus Metsch. He held post-doctoral positions at Universität Gießen, University of Regina, Hebrew University of Jerusalem and Ghent University. His research interests include extremal combi-natorics, finite geometry and spectral graph theory. His works have appeared in journals such as Combinatorica, JCTA, JCTB and IEEE Transactions on Information Theory. He has served on the editorial board of Journal of Combinatorial Theory, Series A since 2025.