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 onlineonly teaching, the schedule should be considered tentative for now. I will update is soon!
March 9
Introduction; presentation of topics
March 23
Monotone paths in edgeordered graphs
March 30
Maximum degrees of induced subgraphs of the hypercube
April 20
The Erdős–Szekeres convex polygon problem
April 27
Random algebraic constructions of K
_{s,t}free graphs
May 4
Ramsey goodness of paths
May 25
The fractional analogue of the Kahn–Kalai conjecture
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.

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)

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)

The fractional analogue of the Kahn–Kalai conjecture
Keith Frankston, Jeff Kahn, Bhargav Narayanan, Jinyoung Park, Thresholds versus fractional expectationthresholds, preprint (arXiv)

Constructing Ramsey graphs from optimally pseudorandom graphs
Dhruv Mubayi, Jacques Verstraëte, A note on pseudorandom Ramsey graphs, preprint (arXiv)

Optimally pseudorandom cliquefree graphs
Anurag Bishnoi, Ferdinand Ihringer, Valentina Pepe, A construction for cliquefree pseudorandom graphs, to appear in Combinatorica (arXiv)

Equiangluar lines
Zilin Jiang, Jonathan Tidor, Yuan Yao, Shengtong Zhang, Yufei Zhao, Equiangular lines with a fixed angle, preprint (arXiv)

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)

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)

Random cliques in random graphs
Oliver Riordan, Random cliques in random graphs, preprint (arXiv)

Ramsey goodness of paths
Alexey Pokrovskiy, Benny Sudakov, Ramsey goodness of paths, J. Combin. Theory Ser. B 122 (2017), 384–390 (arXiv)

Monotone paths in edgeordered graphs
Matija Bucić, Matthew Kwan, Alexey Pokrovskiy, Benny Sudakov, Tuan Tran, Adam Zsolt Wagner, Nearlylinear monotone paths in edgeordered graphs, preprint (arXiv)

Forbidden patterns in permutations and the Stanley–Wilf Conjecture
Jacob Fox, Stanley–Wilf limits are typically exponential, to appear in Adv. Math. (arXiv)