24 Hours of Combinatorial Synergies

On June 28/29 2023 in Magdeburg, this workshop will serve as a forum for scientific exchange and coordination of project proposals for the SPP.

There will be six scientific talks, the abstracts are collected at the bottom of this page:

Speaker Title
Paolo Benincasa (MPI Physics) Combinatorial structures from cosmology
Sarah Brauner (Minnesota/MPI-MiS) Configuration spaces and combinatorial algebras
Mareike Fischer (Greifswald) The combinatorics of evolutionary tree reconstruction
Irem Portakal (TU München) Combinatorics of correlated equilibria
Frank Vallentin (Köln) Extremal lattice problems (not in the bible)
Michael Walter (Bochum) Combinatorics meets computation (and quantum information)


Registration is free but mandatory. Please fill this form before June 12.

If you are not eligable for DFG funding but want to participate in the BBQ on June 28 we might need to charge 60 EUR for food and beverages. We will contact you again in this case.

Dates and Program

Wednesday June 28 Thursday June 29
09:00-12:00 Informal Discussion 09:00-10:00 Sarah Brauner
12:30-13:15 Welcome & Introductions 10:00-10:30 Coffee
13:15-14:15 Michael Walter 10:30-11:30 Mareike Fischer
14:15-15:15 Irem Portakal 11:30-12:30 Frank Vallentin
15:15-16:00 Coffee 13:30-17:00 Informal Discussion
16:00-17:00 Paolo Benincasa
18:00-22:00 BBQ on Campus

Some members of the programm committee will be available to discuss the SPP inner workings, project proposals, etc. for the entire duration of the workshop, including the informal discussion slots.


Funding + Accomodation

There is funding available for all participants who are eligable to apply within the SPP.

The funding covers travel (Deutsche Bahn, 2nd class) and accomodation for one night 28.6.

You need to book yourself and file reimbursement with the DFG after the workshop. After registration you will also receive a formal invitation by the DFG containing the reimbursement form and further information.

We had a number of rooms reserved in the IBIS Styles. The reservation deadline for those is over. If you ticked the box during registration, your room is reserved under your name.

If you book yourself, the DFG limits hotel costs to 82,60 EUR / night (including breakfast). As this is often not achievable, also slightly higher costs can be reimbursed. Please book within reasonable limits and document your choices. Also make sure that the invoice is for the Deutsche Forschungsgemeinschaft and that the name of the guest (i.e. you) is printed on it.


Paolo Benincasa

Combinatorial structures from cosmology

Recent years have seen the emergence of combinatorial structures for describing the probability distributions of physical phenomena in both particle physics and cosmology. I will provide a gentle overview on the subject, focusing on the so-called cosmological polytopes. I will describe their definition in terms of a differential form, named canonical form, which reflect their facet structure and constitutes the link to physics, as well as to weighted graphs. I will conclude illustrating some open questions.

Sarah Brauner

Configuration spaces and combinatorial algebras

In this talk, I will discuss connections between configuration spaces, an important class of topological space, and combinatorial algebras arising from the theory of reflection groups. In particular, I will present work relating the cohomology rings of some classical configuration spaces—such as the space of n ordered points in Euclidean space—with Solomon’s descent algebra and the peak algebra. The talk will be centered around two questions. First, how are these objects related? Second, how can studying one inform the other? This is joint, on-going work with Marcelo Aguiar and Vic Reiner.

Mareike Fischer

The combinatorics of evolutionary tree reconstruction

(partially joint work with Mirko Wilde)

One of the oldest and perhaps the simplest optimization criterion to reconstruct a phylogenetic tree from data such as DNA is Maximum Parsimony (MP). This criterion is purely combinatorial and does not require any model assumptions concerning the underlying evolutionary process. And yet, even today, more than 50 years after its introduction into mathematical phylogenetics, MP gives rise to intriguing mathematical questions, for instance: Does the biological intuition that MP works well when mutation rates in the evolutionary process are small hold true? Can every tree be uniquely encoded by the set of all so-called characters that have a certain parsimony score on this tree? Does every MP tree contain an MP subtree?

Although the MP principle is purely combinatorial and can easily be understood, answering these questions turns out to be surprisingly difficult. In my presentation, I will  introduce you to the combinatorics of mathematical phylogenetics using the example of Maximum Parsimony, and at the same time I will point out the beauty of complex simplicity.

Frank Vallentin

Extremal lattice problems (not in the bible)

Lattices (discrete subgroups of n-dimensional Euclidean spaces) are ubiquitous objects in mathematics.

Typical classes of extremal lattice problems are finding good lattices with respect to some parameter, for instance minimizing packing density, maximizing covering density, or minimizing the quantization constant. The "bible" on these extremal lattice problems is the book "Sphere packings, lattices, and groups" [SPLAG] by Conway and Sloane. The first edition appeared in 1988, the third edition in 1998 and "like the bible, [SPLAG] contains no proofs. This is of course only half true."

Science and technology advances and there is need for lattices which are good for other parameters or properties not yet treated in the bible, like minimizing potential energy, max-min polarization, minimizing Euclidean distortion, coloring the Voronoi cells, or polynomial time decodability.

In this talk I will introduce these extremal lattice problems, explain some (combinatorial) techniques to attack them, and review open problems.