The purpose of the meeting is to share ideas and connect up combinatorics in the Netherlands, as well as to showcase the depth and breadth of Dutch combinatorial research.
We've planned a handful of invited speakers, a limited number of short contributed talks, a flurry of lightning talks, and opportunities for informal discussion.
The activities are planned to take place in the historic centre of Utrecht at the Museum Speelklok. This is within walking distance of Utrecht Centraal train station. Due to logistic difficulties, remote participation is not possible.
Registration is free, but required, through the following link: registration form (deadline 27 February). Included are coffee/tea and a closing borrel on the Tuesday.
An incomplete list of lunch possibilities nearby: Soep-er Utrecht (soup), FLFL Utrecht (falafel), KEEK bakkerij (bakery), Broodje Ben (sandwiches), Broodje Mario (sandwiches), Tijm, Copper branch (vegan), De rechtbank, Poké perfect. There are many more.
Arising from Hoffman and Singleton's study of Moore graphs, strongly regular graphs play an important role in algebraic graph theory. Strongly regular graphs can be construct from various geometric objects, such as finite geometries and generalized quadrangles. Certain geometric properties, such as having a regular point, can be studied in the context of graphs, using combinatorial and algebraic tools. We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs containing such a vertex, thereby, answering a question posed by Gardiner, Godsil, Hensel, and Royle. As a by-product of our characterisation, we are able to give new constructions of infinite families of strongly regular graphs and compute many small sporadic examples; for example, we find 135478 new strongly regular graphs with parameters (85,20,3,5). This is joint work with Edwin van Dam.
Counting walks on lattices subject to a variety of conditions (on the
step sets and boundary conditions) has been a very active topic in
enumerative combinatorics, due to many links with probability theory,
statistical physics, random geometry and algorithms but also due to the
rich algebraic and analytic properties of the corresponding generating
functions. In this talk I will discuss the enumeration of walks on the
square lattice with prescribed winding angle around the origin.
Applications include the enumeration of excursions in cones of various
opening angles, statistics of winding angles of random walks and loops,
and even some electronic properties of 2d materials in physics.
Interior point methods are not worse than Simplex ±
Whereas interior point methods provide polynomial-time linear programming algorithms, the running time bounds depend on bit-complexity or condition measures that can be unbounded in the problem dimension. This is in contrast with the classical simplex method that always admits an exponential bound. We introduce a new polynomial-time path-following interior point method where the number of iterations also admits a combinatorial upper bound $O(2^n n^{1.5} \log n)$ for an $n$-variable linear program in standard form. This complements previous work by Allamigeon, Benchimol, Gaubert, and Joswig (SIAGA 2018) that exhibited a family of instances where any path-following method must take exponentially many iterations.
The number of iterations of our algorithm is at most $O(n^{1.5} \log n)$ times the number of segments of any piecewise linear curve in the wide neighborhood of the central path. In particular, it matches the number of iterations of any path following interior point method up to this polynomial factor.
The overall exponential upper bound derives from studying the ‘max central path’, a piecewise-linear curve with the number of pieces bounded by the total length of n shadow vertex simplex paths.
This is joint work with Xavier Allamigeon (INRIA / Ecole Polytechnique), Georg Loho (U. Twente), Bento Natura (LSE), Laszlo Vegh (LSE).
I will survey the recent bounds on linear trifferent codes and minimal codes that we have obtained by using equivalences with finite geometric objects called blocking sets. I will also discuss a new explicit construction of all of these objects, based on expander graphs and asymptotically good codes.
Based on joint work(s) with Noga Alon, Shagnik Das, Jozefien D'haeseleer, Dion Gijswijt, Alessandro Neri, and Aditya Potukuchi.
16:00
Closing borrel
For abstracts of all talks, consult the following booklet
This is the second edition in an intended series; the first edition took place in Eindhoven in May 2022. This meeting also borrows some spirit from two earlier workshops in Utrecht: UGW 2013 and UCW 2014.
