### Project 14: "Random graphs on a surface"

*This project is running since 2015.*

Principal investigator: Mihyun Kang

Graz University of Technology, Austria.

*Mentor for*: Kloas, Moosmüller; Carl.

### DK Student

**Second phase of the doctoral program:**

**Nicola del Guidice**(Italy; since September 2016)

*Mentors*: Michael Kerber, Christopher Dowden, Philipp Sprüssel.

### Associated Students

**Second phase of the doctoral program:****Christoph Koch**(Germany; April 2012 - November 2016)

*Email*: ckoch@math.tugraz.at

*Mentors*: Wolfgang Woess, Oliver Cooley.

*PhD Defense*: November 25, 2016.

*Referees*: Mihyun Kang (TU Graz), Michael Krivelevich (Tel Aviv University), and Angelika Steger (ETH Zürich).

*Examiners*: Angelika Steger, Wolfgang Woess.**Michael Moßhammer**(Austria; since October 2015)

*Email*: mosshammer@math.tugraz.at

*Mentors*: Johannes Wallner, Philipp Sprüssel.

### Project description (pdf-file)

The main research field of Mihyun Kang is random discrete structures, in particular random graphs, random graph processes and random planar graphs. The main objectives are to study their asymptotic properties and limit behaviour (e.g. evolution, phase transition, critical behaviour, component size distribution) and to investigate their structural, enumerative and algorithmic aspects (e.g. symmetry, connectivity, random generation). In comparison with the classical Erdos-Renyi random graphs, additional constraints imposed on random graphs (e.g. planarity, degree) lead to serious difficulties in the analysis. To circumvent these difficulties and to achieve the objectives, problems are approached by means of the combination of complementary methods, such as probabilistic methods, graph theoretic methods, differential equations method, methods from analytic combinatorics (e.g. singularity analysis, saddle point method), and algorithmic methods (e.g. Boltzmann sampler). Through her own projects and intensive cooperation with leading researchers in this area, Kang has developed novel approaches and has brought new perspectives to problems in her research field, e.g. analytic approaches to determine the component size distribution in random graph processes and random planar graphs.