Till innehåll på sidan

Svante Janson: Random Graphs

Time: Wed 2014-01-29 14.15 - 16.15

Lecturer: Svante Janson, Uppsala University

Location: Lecture hall Oskar Klein in Alba Nova


14:15-15:00: Precolloquium for PhD and master students by Fabio Lopes (Room Oskar Klein)

15:15-16:15: Colloquium lecture by Svante Janson (Room Oskar Klein)

16:15-17:00: Coffee and SMC social get-together

Abstract (Colloquium)

Random graphs are graphs generated by some random procedure. The main interest is in asymptotics for very large graphs.

The theory was started by a series of papers by Erdös and Renyi, beginning in 1959, where they studied many aspects of the random graph model G(n,m) with a fixed number of vertices n and a fixed number of edges m, all
possibilities having the same probability. This model and the closely related model G(n,p) where edges appear independently have since then been the standard models. I will discuss some typical problems and results,
including existence of small subgraphs, connectivity, and existence of a giant component.

A typical feature is that many properties show a threshold phenomenon:
random graphs with few edges (m or p above small in relation to n) will not have the property (except with a small probability), but as the number of edges grows, there is a rather sudden transition to a case where the property holds (except with a small probability).

In later years, this model has been complemented by many other random graph models. I will mention some of the more important, in particular the "configuration model" (Bollobas and others) and "preferential attachment"
(Barabasi-Albert and others).

Svante Janson grew up in Dalarna, Sweden. He left school at the age of 11 and began taking university courses in mathematics. He formally became a university student at the age of 12, and received  his bachelor in mathematics at Uppsala University at the age of 14. He defended his PhD thesis (supervised by Lennart Carleson) on his 22nd birthday (1977). He received a second PhD, this time in mathematical statistics, at the age of 28 (1984) and became professor in mathematics at Uppsala University 1987. He is member of the Swedish Academy of Sciences. Beside shorter post doc and similar research visits and one year at Stockholm University as docent, he has been at Uppsala University all the time.

Svante Janson's research covers several areas of mathematics: mathematical analysis, probability, combinatorics and random algorithms, and in  particular random graphs, the topic of the colloqium. Svante Janson has (by January 10, 2014 at 10.03) published 4 monographs and 288 papers with 152 collaborators.

Titel Datum
Philip Maini: Modelling collective cell motion 2018‑09‑26
Leslie Greengard: Inverse problems in acoustic scattering and cryo-electron microscopy 2018‑04‑11
James Norris: Scaling limits for planar aggregation with subcritical fluctuations 2018‑03‑21
Sofia Olhede: Network Data Analysis 2018‑02‑07
Viviane Baladi: Analytical tools for dynamics with singularities, including Sinai billiards 2017‑11‑29
Gerard van der Geer 2017‑09‑27
János Pach 2017‑06‑07
Alicia Dickenstein 2017‑04‑05
Arno Kuijlaars: Universality in random matrix theory 2017‑02‑25
Karen Smith 2016‑12‑07
Jeff Steif: Noise Sensitivity of Boolean Functions and Critical Percolation 2016‑10‑28
Martin Hairer: Taming infinities. 2016‑09‑29
Mattias Jonsson: Complex, tropical and non-Archimedean geometry 2016‑06‑01
Yulij Ilyashenko: Towards the global bifurcation theory on the plane 2016‑04‑27
Volodymyr Mazorchuk: (Higher) representation theory 2016‑03‑09
Tobias Ekholm: Knot contact homology, Chern-Simons, and topological strings 2016‑02‑10
Dmitry Khavinson: "Between two truths of the real domain, the easiest and shortest path quite often passes through the complex domain." P. Painleve, 1900. A variation on the theme of analytic continua 2015‑12‑12
Kathryn Hess: A calculus for knot theory 2015‑11‑06
Gregory F. Lawler: Self-avoiding motion 2015‑10‑09
Claudio Procesi: Analytic and combinatorial aspects of the Non Linear Schroedinger equation (NLS) on a torus 2015‑05‑27
Alexander Razborov: Continuous Combinatorics 2015‑03‑18
Christiane Tretter: Operator theory and applications: a successful interplay 2015‑02‑04
Michael Rathjen: Is Cantor’s continuum problem still open? 2014‑10‑15
Irene Fonseca: Variational Methods in Materials and Image Processing 2014‑09‑03
Ib Madsen: Moduli Spaces and Topology 2014‑06‑11
Mikko Salo: Can one hear the shape of a space? 2014‑03‑27
Svante Janson: Random Graphs 2014‑01‑29
Mireille Bousquet-Mélou: Self-avoiding walks 2014‑05‑07
Kristian Seip: Analysis on polydiscs 2013‑11‑27
Bernd Sturmfels: The Euclidean Distance Degree 2013‑10‑09
Christoph Thiele: L^p theory for outer measures and applications 2013‑09‑25
Antti Kupiainen: Critical Multiplicative Chaos 2013‑05‑15
Günther Uhlmann: Cloaking: Science Meets Science Fiction 2013‑04‑24
Anatoliy Fomenko: Topological classification of Hamiltonian equations with symmetries. Application to physics and mechanics 2013‑02‑27
Jan-Erik Roos: Classical Lie algebras contra infinite-dimensional positively graded Lie algebras 2013‑02‑06
Hendrik Lenstra: Escher and the Droste effect 2012‑12‑12
Bo Berndtsson: Complex Brunn-Minkowski theory 2012‑11‑21
Martin Aigner: From Irrational Numbers to Perfect Matchings: 100 Years of Markov’s Uniqueness Problem 2012‑10‑10
Vladimir Rokhlin: Accurate Randomized Algorithms of Numerical Analysis 2012‑05‑19
Martin R. Bridson: Discrete groups: A story of geometry, complexity, and imposters 2012‑04‑11
Mats Gyllenberg: Rock, scissors, paper — what a children's game can tell us about evolution 2012‑03‑14
Persi Diaconis: Who Needs Positivity? 2012‑02‑10
Wendelin Werner: Random surfaces, random geometries 2011‑12‑14
Ragni Piene: The problematic art of counting 2011‑11‑16
Günter M. Ziegler: On some partition problems and their configuration spaces 2011‑10‑12
Carles Broto: Local aspects of groups and loop spaces 2011‑05‑11
Bernd Sturmfels: Quartic Curves and their Bitangents 2011‑02‑02
Torsten Ekedahl: The Sato-Tate conjecture 2010‑11‑03
Jesper Grodal: Finite loop spaces 2010‑11‑10
Amol Sasane: An analogue of Serre’s Conjecture and Control Theory 2010‑10‑13
Reiner Werner: Quantum correlations - how to prove a negative from finitely many observations 2010‑09‑29
Warwick Tucker: Validated Numerics - a short introduction to rigorous computations 2010‑09‑22
Idun Reiten: Cluster categories and cluster algebras 2010‑09‑01
Stefano Demichelis: Use and misuse of mathematics in economic theory 2010‑05‑26
Gregory G. Smith: Old and new perspectives on Hilbert functions 2010‑04‑14
Tony Geramita: Sums of Squares: Evolution of an Idea. 2010‑03‑31
Jens Hoppe: Non-commutative curvature and classical geometry 2010‑03‑24
Margaret Beck: Understanding metastability using invariant manifolds 2010‑03‑03
Jan-Erik Björk: Glimpses from work by Carleman 2010‑02‑10
Sandra Di Rocco: Interaction between Convex and Algebraic Geometry 2009‑12‑16
Alexander Gorodnik: Arithmetic Geometry and Dynamical Systems 2009‑11‑18
Laurent Bartholdi: Insanely twisted rabbits 2009‑11‑18
Nils Dencker: The spectral instability of differential operators 2009‑11‑04
Peter Jagers: Extinction: how often, how soon, and in what way? 2009‑10‑21
Norbert Peyerimhoff: Expander graphs — some background and new examples 2009‑10‑07
Saharon Shelah: Hilbert's First Problem and the number four 2009‑09‑23
Jürg Kramer: Irrationality of √2 and Arakelov Geometry 2009‑09‑09