May 23 and May 27, 2019
Mini-course of Dr. Hamid Reza Daneshpajouh (Iran).
Title: An introduction to topological combinatorics
Day 1: Thursday, May 23, 10:45 — 12:15 and 13:45 — 15:15, Aud.430 Main Building
Day 2: Monday, May 27, 10:45 — 12:15 and 13:45 — 15:15, Aud.532 Main Building
Dec 06 — Dec 10, 2018.
Mini-course of three lectures by Prof. Nelli Litvak (University of Twente, Netherlands).
Title: Scale-free networks.
Lecture 1: Thursday, Dec 06, Aud. 115 Applied Math Building, 13:45 — 15:20
Lectures 2 and 3: Monday, Dec 10, Aud. 418 Arctic (Физтех.Арктика), 10:45 — 13:45
Abstract: How many connections a node in a network has? One of the most stunning properties of real-life networks, such as world wide web, internet, food webs, and social networks, is that the number of connections has huge variability. Some nodes have only few connections, and some have millions. Mathematically, we model this phenomenon using the so-called `power law’ distributions. Most of the real-life networks have power laws. This has motivated the development of many new models and tools in network science and the theory of random graphs. This series of three lectures is about properties of power law distributions, and three basic random graph models for power law networks: generalized random graph model, configuration model, and preferential attachment model. Students will also receive several problems to get familiar with the models and methods discussed during the lecture.
Book: R. van der Hofstad. Random Graphs and Complex Networks. Volume 1. Cambridge Series in Statistical and Probabilistic Mathematics (2017) ISBN 978-1-107-17287-6. Available here.
Lectures 2-3: partially material of: Sections 6.1, 6.2, 6.3, 6.6, 7.1, 7.2, 7.4, 8.1, 8.2, 8.4, partially 8.6. Problems: Problem set 3.
Dec 07, 2018
Talk at Seminar, Prof. Nelli Litvak (University of Twente, Netherlands).
Title: Mean Field Analysis of Personalized PageRank with Implications for Local Graph Clustering
Friday, Dec 07, Aud. 115 Applied Math Building, 18:30 — 20:00.
Abstract: We analyse a mean-field model of Personalized PageRank on the Erdös-Rényi random graph containing a denser planted Erdös-Rényi subgraph. We investigate the regimes where the values of Personalized PageRank concentrate around the mean-field model. We also study the optimization of the damping factor, the only parameter in Personalized PageRank. Our theoretical results help to understand the applicability of Personalized PageRank and its limitations for local graph clustering. This is a joint work with Konstantin Avrachenkov and Arun Kadavankandy.