Algomanet – spring 2025
Basic information
The two Algomanet courses given by Jan Volec and Xuding Zhu, which are scheduled for the spring 2025, will take place in the week June 30 – July 4 at the Charles University in Prague. The courses will be delivered on site only, starting at 9am on Monday June 30 and concluding in late afternoon on Friday July 4.
The registration for the Algomanet courses is now open.
You can register by filling in the form.
Any questions can be directed to Zdeněk Dvořák (rakdverz0k4z=99h@iuukcuE83BjLh.mffULa6k8ZBB.cunitcEtvve=T.cz).
It is possible to register for both or just one of the two courses offered.
The courses are primarily intended for those affiliated with the participating universities,
however, we are able to offer a limited number of places to students from other universities, too.
Registration deadline: Monday May 26, 2025
Unfortunately, there is no financial support available in addition to that offered by individual sites to their own students. However, if the absence of financial support can prevent you from participating, please get in touch to discuss possible options.
Jan Volec: Flag algebra method
Flag algebras provides a systematic tool for applying double counting and
Cauchy-Schwarz formulas in the setting of counting substructures in (large)
discrete objects (graphs, hypergraphs, permutations, set of points in the
plane). The method was pioneered by Razborov in 2007, building up on a previous
work of Bondy. Since then, it has successfully solved a number of open
questions in extremal combinatorics.
In this course, we will first introduce the general framework of flag algebras
together with closely related notions from graph limits, and then focus on
applications of the framework in graph theory, permutations and Ramsey theory.
Xuding Zhu: Applications of Combinatorial Nullstellensatz to graph colourings
The Combinatorial Nullstellensatz gives a sufficient condition for a polynomial P(x1, x2, . . . , xn) ∈ F[x1, x2, . . . , xn] to have a non-zero point in a given grid S1×S2×. . .×Sn, where Si ⊆ F. Many combinatorial problems can be stated as the existence of a non-zero point of a polynomial in a certain grid, and hence have the potential of applying Combinatorial Nullstellensatz. This series of lectures explains some applications of Combinatorial Nullstellensatz to graph coloring and related problems. We focus on methods that show certain monomials in the expansion of a polynomial are non-vanishing, i.e., having non-zero coefficients. These include Alon-Tarsi orientations, interpolation formula and permanent method. These methods are illustrated with applications to problems in list colouring of graphs, vertex-edge weighting of graphs, list of forbidden out-degree orientations of graphs, etc.