This is the list of topics for the seminar (sorry for the delay) -------------------------------------- (1) Lovász Local Lemma and Entropy Compression (presented by Sandro Roch and Stefan Felsner) This is a complex topic. For a talk a selection is necessary. Here are possible selections for a talk: [1a+1b] [1c+1d] [1b+1e] [1b+1f] SOURCE: A Constructive Proof of the General Lovász Local Lemma; Robin Moser and Gábor Tardos, Journal of the ACM, vol 57 (2010) 15 pages. LINK: 01a-Moser+Tardos.pdf SOURCE: Moser’s entropy compression argument terrytao.wordpress.com/2009/08/05/mosers-entropy-compression-argument/ LINK: 01b-Tao-blog.pdf SOURCE: Chapter 4: The Lovász Local Lemma (pages 39-42) Graph colouring and the probabilistic method; Michael Molloy and Bruce Reed. Algorithms and combinatorics Vol 23, Springer 2002 LINK: 01c-MR-Chapt_4.pdf SOURCE: Chapter 7: A First Glimpse of Total Colouring (pages 55-59) Graph colouring and the probabilistic method; Michael Molloy and Bruce Reed. Algorithms and combinatorics Vol 23, Springer 2002 LINK: 01d-MR-Chapt_7.pdf SOURCE: Acyclic edge-coloring using entropy compression; Louis Esperet and Aline Parreau European Journal of Combinatorics 34 (2013) 1019–1027 LINK: 01e-Esperet-Parreau.pdf SOURCE: New Approach To Nonrepetitive Sequences; Jarosław Grytczuk, Jakub Kozik and Piotr Micek1 Random Structures and Algorithms, vol 42 (2013) 214-225 LINK: 01f-Grytczuk-Kozik-Micek.pdf -------------------------------------- (2) Concentration Bounds (presented by Sandro Roch) This can also be broken into two topics, i.e., a talk may only cover one chapter. SOURCE: Chapter 10: Talagrand's Inequality and Colouring Sparse Graphs (pages 77-89) Graph colouring and the probabilistic method; Michael Molloy and Bruce Reed. Algorithms and combinatorics Vol 23, Springer 2002 LINK: 02a-MR-Chapt_10.pdf SOURCE: Chapter 11: Azuma's Inequality and a Strengthening of Brooks' Theorem (pages 91-103) Graph colouring and the probabilistic method; Michael Molloy and Bruce Reed. Algorithms and combinatorics Vol 23, Springer 2002 LINK: 02b-MR-Chapt_11.pdf -------------------------------------- (3) Sampling using Markov chains (presented by Sandro Roch) This can also be broken into two topics. In particular the three applicalions 'coloring', 'linear extensions' and 'matchings' need not be covered in a single talk. SOURCE: parts of chapters 3, 4, and 5 (pages 30-62) from the book: Counting, Sampling and Integrating: Algorithms and Complexity; Mark Jerrum Lectures in Mathematics, ETH Zürich. Birkhäuser 2003. LINK: 03-Jer3.3-5.4.pdf -------------------------------------- (4) Crossing numbers and random Graphs (presented by Rimma Hämäläinen) SOURCE: Crossing numbers of random graphs; Joel Spencer and Géza Tóth Random Structures and Algorithms, vol 21 (2002) 347-358 LINK: 04-Spencer+Toth.pdf -------------------------------------- (5) Drawing K_m,n on the sphere - Graphons (presented by Helena Bergold) SOURCE: Limiting crossing numbers for geodesic drawings on the sphere; Marthe Bonamy, Bojan Mohar and Alexandra Wesolek ArXiv: 2008.10459, 20 pages LINK: 05-Bonamy+Mohar+Wesolek.pdf -------------------------------------- (6) Szemeredi's regularity lemma (presented by Felix Schröder) another complex topic. It can be broken into two or cut down. SOURCE: Chapter 6 from Extremal and Probabilistic Combinatorics; Robert Morris and Roberto Imbuzeiro Oliveira LINK: 06a-Morris+Oliveira.pdf SOURCE: Regularity Lemma and its Applications; Tibor Szabó, FU Berlin, 8 pages LINK: 06b-Szabo.pdf SOURCE: A link from Spencer's homepage to a chapter of the 4th edition of the book (The Probabilistic Method; Noga Alon and Joel Spencer) 5 pages LINK: 06c-Spencer.pdf -------------------------------------- (7) Random Order Types (suggested by Manfred Scheucher / presented by Stefan Felsner) SOURCE: On Order Types of Random Point Sets; Olivier Devillers, Philippe Duchon, Marc Glisse, and Xavier Goaoc arXiv:1812.08525 LINK: 07-DDGG-OTypes.pdf -------------------------------------- (8) Randomized Optimization (presented by Stefan Felsner) SOURCE: Explicit and Implicit Enforcing – Randomized Optimization; Bernd Gärtner and Emo Welzl, in Computational Discrete Mathematics. Lect. Notes Comput. Sci. 2122, Springer (2001) 25-46. LINK: 08-Gaertner-Welzl.pdf -------------------------------------- (9) Randomized Approximation Algorithms (presented by Stefan Felsner) SOURCE: Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming; Michel Goemans and David Williamson, J. Assoc. Comput. Mach., vol 42 (1995) 1115-1145. LINK: 09a-Goemans-Williamson.pdf SOURCE: Chapter 1 from: Approximation algorithms and semidefinite programming; Bernd Gärtner and Jiří Matoušek, Springer 2012. LINK: 09b-Gaertner-Chapt1.pdf -------------------------------------- (10) Randomized Constructions for Delaunay Triangulations (presented by Stefan Felsner) SOURCE: Chapter 9 from: Computational geometry. Algorithms and applications. 3rd ed.; Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars Springer 2008. LINK: 10a-BCvKO-Chapt9.pdf SOURCE: Improved Incremental Randomized Delaunay Triangulation; Olivier Devillers Proc. Symposium on Computational Geometry 1998, ACM 106-115. LINK: 10b-Devillers.pdf SOURCE: Delaunay triangulation and randomized constructions; Olivier Devillers Encyclopedia of Algorithms 2016, 519-524. LINK: 10c-Dev-encycl.pdf --------------------------------------