In this seminar, we shall present and discuss a variety of recent developments in the (broadly understood) areas of extremal and probabilistic combinatorics that are not normally covered in the standard courses.

Students registering for the seminar are expected to possess working knowledge of basic graph theory notions and be familiar with basic concepts of discrete probability.

Due to the transition to online-only teaching, the schedule should be considered tentative for now. I will update is soon!

Below is a tentative list of topics to be discussed and presented during the seminar. Topics that have already been reserved are highlighted in light gray.

1. Maximum degrees of induced subgraphs of the hypercube
   Hao Huang, Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture, Ann. of Math. (2) 190 (2019), no. 3, 949–955 (arXiv)
2. The Erdős–Szekeres convex polygon problem
   Andrew Suk, On the Erdős–Szekeres convex polygon problem, J. Amer. Math. Soc. 30 (2017), no. 4, 1047–1053 (arXiv)
3. The fractional analogue of the Kahn–Kalai conjecture
   Keith Frankston, Jeff Kahn, Bhargav Narayanan, Jinyoung Park, Thresholds versus fractional expectation-thresholds, preprint (arXiv)
4. Constructing Ramsey graphs from optimally pseudo-random graphs
   Dhruv Mubayi, Jacques Verstraëte, A note on pseudorandom Ramsey graphs, preprint (arXiv)
5. Optimally pseudo-random clique-free graphs
   Anurag Bishnoi, Ferdinand Ihringer, Valentina Pepe, A construction for clique-free pseudorandom graphs, to appear in Combinatorica (arXiv)
6. Equiangluar lines
   Zilin Jiang, Jonathan Tidor, Yuan Yao, Shengtong Zhang, Yufei Zhao, Equiangular lines with a fixed angle, preprint (arXiv)
7. Random algebraic constructions of K_s,t-free graphs
   Boris Bukh, Random algebraic construction of extremal graphs, Bull. Lond. Math. Soc. 47 (2015), no. 6, 939–945 (arXiv)
8. Triangle decompositions via iterative absorption
   Ben Barber, Stefan Glock, Daniela Kühn, Allan Lo, Richard Montgomery, Deryk Osthus, Minimalist designs, to appear in Random Structures Algorithms (arXiv)
9. Random cliques in random graphs
   Oliver Riordan, Random cliques in random graphs, preprint (arXiv)
10. Ramsey goodness of paths
    Alexey Pokrovskiy, Benny Sudakov, Ramsey goodness of paths, J. Combin. Theory Ser. B 122 (2017), 384–390 (arXiv)
11. Monotone paths in edge-ordered graphs
    Matija Bucić, Matthew Kwan, Alexey Pokrovskiy, Benny Sudakov, Tuan Tran, Adam Zsolt Wagner, Nearly-linear monotone paths in edge-ordered graphs, preprint (arXiv)
12. Forbidden patterns in permutations and the Stanley–Wilf Conjecture
    Jacob Fox, Stanley–Wilf limits are typically exponential, to appear in Adv. Math. (arXiv)