Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Friday, May 04, 2018, 12:15 pm

**Duration**: 45 minutes

**Location**: CAB G11

**Speaker**: Nati Linial (The Hebrew University of Jerusalem)

About 50 years ago Erdos and Renyi have started the systematic study of random graphs. Their results concern mostly the G(n,p) model of random graphs. Such a random graph G has n vertices and every pair of vertices is independently made adjacent with probability p. They have discovered many important phenomena in this realm and have, in particular determined the critical p at which G becomes connected, where it has for the first time a "ginat" connected component of linear size and more.

Over a decade ago Roy Meshulam and I initiated the study of high-dimensional counterparts X=X(d,n,p) of G(n,p) graph. Here X is a set system (technically it is a simplicial complex) on a set V of n vertices. It contains every set of cardinality d or less and it contains every subset of V of cardinality d+1 independently and with probability p. Note that X(1,n,p) is identical to G(n,p). There are natural analogs of connectivity, cycles cuts etc. that come from basic topology (not to worry - NO knowledge of topology is assumed....). We are now able to answer questions analogous to the Erdos-Renyi theory, although the theory is much richer and many unexpected complications arise.

The only required background to follow this talk includes basic combinatorics linear algebra and probability. This line of research is by now an active area of research.

My list of collaborators in this endeavor includes: R. Meshulam, Y. Peled, L. Aronshtam, T. Luczak, M. Rosenthal, I. Newman and Y. Rabinovich.

Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)

Previous talks by year: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M | admin login