Tópicos em Combinatória Extremal
In this advanced-level course we will study some recent developments in extremal combinatorics, including:
• The absorption method: applications to decompositions of graphs and hypergraphs.
• Recent developments in graph Ramsey theory.
• The proof of the Erdös–Faber–Lovász conjecture by Kang, Kelly, Kühn, Methuku and Osthus.
• The proof of the Sensitivity Conjecture by Hao Huang.
• The resolution of the Happy Ending Problem by Andrew Suk.
• The breakthrough of Alweiss, Lovett, Wu and Zhang on the Sunflower Conjecture of Erdös and Rado.
• Recent developments on Turán numbers of bipartite graphs.
• The sparse blow-up lemma of Allen, Böttcher, Hán, Kohayakawa and Person.
• Applications of the asymmetric and efficient hypergraph container lemmas.
• Discrepancy: Littlewood polynomials, the Beck–Fiala theorem.
• Applications of the polynomial method in combinatorics, including the solution of the cap-set problem by Croot, Lev and Pach.
• Recent advances on sphere packing in high dimensions.
• Applications of combinatorial techniques in number theory.
 R. Alweiss, S. Lovett, K. Wu and J. Zhang, Improved bounds for the sunflower lemma, Ann. Math., 194 (2021), 795–815.
 B. Bollobás, Modern Graph Theory (Graduate Texts in Mathematics), Springer-Verlag, New York, 1998.
 H. Cohn and Y. Zhao, Sphere packing bounds via spherical codes, Duke Math. J., 163 (2014), 1965–2002.
 S. Glock, D. Kühn and D. Osthus, Extremal aspects of graph and hypergraph decomposition problems, Surveys in Combinatorics, Cambridge University Press, 2021.
 L. Guth, Polynomial Methods in Combinatorics, American Mathematical Society, 2016.
 H. Huang, Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture, Ann. Math., 190 (2019), 949–955.
 A. Suk, On the Erdos-Szekeres convex polygon problem, J. Amer. Math. Soc., 30 (2017), 1047–1053.
 D. Conlon, J. Fox and B. Sudakov, Recent developments in graph Ramsey theory, Surveys in Combinatorics, Cambridge University Press, 2015.
 C. Lee, Ramsey numbers of degenerate graphs, Ann. Math., 185 (2017), 791-829.
 A. Sah, Diagonal Ramsey via effective quasirandomness, Duke Math. J., to appear.