Program

The schedule can be downloaded here. The whole program including all abstracts can be downloaded here.

On Thursday evening (starting 19:30) there is a get together with all participants in the Gasthausbrauerei Stiefel-Bräu close to the St. Johanner Markt. All talks, lunches, and the conference dinner will be on campus.

Departure: There is a city bus leaving the university at 16:15, arriving at the train station at 16:39, nicely connecting to the 16:52 train to Frankfurt (city and airport), the 17:01 train to Kaiserlautern (with connecting S-Bahn to Mannheim), the 17:04 train to Koblenz (change there for Cologne and arrive at 21:05) or the 17:14 train to Strasbourg.

Invited Speakers

The following speakers will give an invited plenary lecture.

• Dominique Foata (Strasbourg): Descents and decreases, rises and increases
  Abstract: There have been several successful attempts to construct a noncommutative version or a q-analog of the celebrated MacMahon Master Theorem. However those q-analogs sitting in noncommutative algebras remain so far noninstrumental in word enumeration. Another approach consists of embedding the MacMahon Master identity into a multivariable environment, taking classical word statistics, such as descents and rises, into account. This provides a new tool for calculating several q-factorial series of generating polynomials for symmetric groups by multivariable statistics.
  
• Daniela Kühn (Birmingham): Hamilton cycles in graphs and digraphs
  Abstract: In my talk I will discuss several conjectures on Hamilton cycles in graphs and directed graphs. Here are 2 examples of such conjectures.
  A classical result on Hamilton cycles is Dirac's theorem which states that every graph on n vertices with minimum degree at least n/2 contains a Hamilton cycle. Nash-Williams showed that such a graph even contains many edge-disjoint Hamilton cycle and in 1971 he proposed a conjecture about the maximal number of edge-disjoint Hamilton cycles one can guarantee.
  A conjecture of Kelly from 1968 states that every regular tournament can be decomposed into edge-disjoint Hamilton cycles. (A tournament is an orientation of a complete graph.)
  I will describe recent results towards these and related conjectures and mention some open problems. The results in this talk will be joint work with Demetres Christofides, Peter Keevash, Fiachra Knox, Richard Mycroft, Deryk Osthus and Andrew Treglown.
  
• Gabriele Nebe (RWTH Aachen): An extremal even unimodular lattice of dimension 72
  Abstract: From the theory of modular forms it is known that the minimum of an even unimodular lattice of dimension n is always ≤2 ⌊n/24⌋ + 2. Lattices achieving this bound are called extremal. Of particular interest are extremal unimodular lattices in the so called “jump dimensions”, these are the multiples of 24. There are four even unimodular lattices known in the jump dimensions, the Leech lattice Λ, the unique even unimodular lattice in dimension 24 without roots, and three lattices called P_48p, P_48q, P_48n, of dimension 48 which have minimum 6. It was a long standing open problem whether there exists an extremal 72-dimensional unimodular lattice. Many people tried to construct such a lattice, or to prove its non-existence. Most of these attempts are not documented, all constructed lattices contained vectors of norm 6. On August 11 this year I discovered such an extremal lattice. (see arXiv)
  
• Marc Noy (UPC Barcelona): Asymptotic enumeration of maps and graphs
  Abstract: In the 1960s, in his series of fundamental “census” papers, Tutte founded the enumerative theory of planar maps. Since then, the theory has grown enormously, extending to maps on surfaces, to unembedded graphs on surfaces, and to minor-closed classes of graphs. We will pay particular attention to properties of random planar graphs, and discuss basic parameters and also extremal parameters like maximum degree, diameter, and largest k-connected components. For instance, with high probability a random (labelled) planar graph with n vertices has 2.21*n edges, a connected component containing n-O(1) vertices, a block (2-connected component) containing 0.96*n vertices, maximum degree 2.53*log(n), and diameter of order roughly n^1/4. The talk will be kept at a non-technical level, giving at some point brief indications on the tools needed from complex analysis.
  

Kolkom 2010

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