An EPSRC funded workshop

In recent years, the analysis of thin branched structures has become very popular in Mathematical Physics. The main reason is the increasing technological feasibility of manufacturing nano-structures at an atomic level, requiring a detailed quantum mechanical analysis of the problem. Thin branched structures occur for example in micro-electronics and in opto-electronics. It is essential to understand the theoretical analysis of such media in order to be able to engineer materials with certain prescribed properties. One important question is whether a material conducts or transmits light e.g. for semi-conductors or photonic crystals. Much work is need on a mathematical analysis of branched structures providing a large class of (at least approximately) solvable models.

This workshop will focus on the question to what extent branched structures can be understood by their decomposition into simple building blocks according to the underlying network structure. In addition, we shall investigate the extent to which thin branched structures and their properties can approximately be described by the one-dimensional limit and the underlying network structure.

The workshop will take place from Monday, May 26, 2014 to Friday, May 30, 2014 (noon) with an arrival date of Sunday, May 25, 2014 pm. and will be held at Gregynog Hall a conference centre owned and managed by the University of Wales.

Invited speakers include:

  • Pavel Exner (Doppler Institute Prague), Daniel Grieser (Oldenburg Germany), Matthias Langer (Strathclyde UK), Graeme Milton (Utah, US), Olaf Post (Durham) and Ian Wood (Kent UK)

Timetable

Monday
8.00 Breakfast
9.30 Ian Wood (Kent): The boundary triples framework and PDEs (I)
10.30 Coffee
11.30 Matthias Langer (Strathclyde): The boundary triples framework and PDEs (II)
13.00 Lunch
15.00 Informal discussions
16.00 Tea
17.00 Olaf Post (Durham): Shrinking domains: known results using operator theory methods
19.00 Dinner
20.00 Wine reception

Tuesday
8.00 Breakfast
9.30 Daniel Grieser (Oldenburg Germany): Fat graphs and conical singularities
10.30 Coffee
11.30 Informal discussion
13.00 Lunch
15.00 Informal discussions
16.00 Tea
17.00 Open problems
19.00 Dinner

Wednesday
8.00 Breakfast
9.30 Pavel Exner (Doppler Institute Prague): Spectral asymptotics of singular Schrödinger operators with strong attractive coupling
10.30 Coffee
11.30 Stepan Man'ko (Doppler Institute Prague): Schrödinger operators with singular potentials
13.00 Lunch
15.00 Informal discussions
16.00 Tea
17.00 Open problems
19.00 Workshop dinner

Thursday
8.00 Breakfast
9.30 Graeme Milton (Utah, US): A characterization of the response of electromagnetic circuits
10.30 Coffee
11.30 Informal discussions
13.00 Lunch
Free afternoon
19.00 Dinner

Friday
8.00 Breakfast
9.30 Round up session
10.30 Coffee
11.30 Informal discussions
12.00 Lunch

Registration & Accommodation

Registration, which includes full board at Gregynog Hall (breakfast, lunch, dinner and morning and afternoon coffee) is £450.

Accommodation is on-site and is included in the registration fee. For further information and registration please contact one of the organizers: