# Michael Farber

**discipline**Mathematics

### Research project

This research will address problems of applied algebraic topology and will develop mathematical methods relevant to various applications in engineering, biology, statistics and network science.

We shall also employ methods of applied algebraic topology to tackle some classical pure topological open questions (the Whitehead Conjecture).

The first part of this research studies various manifolds of linkages; our efforts will be focused on analysing new classes of linkages (linkages with telescopic legs, fixed-angle linkages, linkages in high-dimensional spaces, as well as topological invariants of manifolds of linkages with random length parameters) which require development of novel mathematical tools.

The second part of this research is an attempt to exploit our recent results about probabilistic

confirmation of the Whitehead conjecture to obtain a deterministic solution of this classical open problem.

The mathematical theory of random simplicial complexes which we plan to develop in this reasearch, may find applications in the theory of large networks. Traditionally one models networks by graphs with nodes representing objects and edges representing connections between the objects.

However if we are interested not only in pairwise relations between the objects but also in relations between multiple objects we may use the high dimensional simplicial complexes

instead of graphs as mathematical models of networks.

### Biography

Michael Farber is Professor of Pure Mathematics at the School of Mathematical Sciences at the Queen Mary University of London (UK). He holds a Ph.D. in Physical and Mathematical Sciences from Baku State University in Azerbaijan. His main research interests are focused on applied algebraic topology, a new mathematical discipline studying mathematical problems arising in engineering, statistics and computer science. Applied algebraic topology also uses topological techniques to solve problems in various scientific and industrial applications (such as data analysis, computer vision etc).

### Selected publications

'Geometry and topology of random 2-complexes', with A.E. Costa, *Israel Journal of Mathematics,* vol. 209 no. 2, 2015, pp. 883-927.

'Fundamental groups of clique complexes of random graphs,Transactions of the LMS', with A.E. Costa, & D. Horak, *Transactions of the London Mathematical Society*, vol. 2, no. 1, 2015, pp. 1-32.

'Large random simplicial complexes, III; the critical dimension', with A.E. Costa, *Journal of Knot Theory and Its Ramifications*, 2017, vol. 26, no. 2, 2017.

'The asphericity of random 2-dimensional complexes', with A.E. Costa, *Random Structures & Algorithms,* vol. 46, no. 2, 2015, pp. 261-273.

'Large random simplicial complexes, II, the fundamental group', with A.E. Costa, *Journal of Topology and Analysis. *[forthcoming].

### discipline

## John Klein

**fellow**

**EURIAS cohort**2017/2018

**discipline**Mathematics

### institut

**fellow**

**EURIAS promotion**2013/2014

**discipline**History

**fellow**

**EURIAS promotion**2014/2015

**discipline**Art History

**fellow**

**EURIAS promotion**2012/2013

**discipline**Religious Studies

**fellow**

**EURIAS promotion**2015/2016

**discipline**History