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:
|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|
|Alheydis Geiger (MPI-MiS Leipzig)||Positive Del Pezzo Geometry|
|Frank Vallentin (Köln)||Extremal lattice problems (not in the bible)|
|Michael Walter (Bochum)||Combinatorics meets computation (and quantum information)|
Registration was opened until June 12.
Dates and Program
The workshop officially starts with a round of brief introductions at 12:30 on Wednesday, but you can arrive earlier at the IFF and use the morning for discussions even before the start. Please organise your own lunch.
|Wednesday June 28||Thursday June 29|
|10:00-12:00||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||Alheydis Geiger||11:30-12:30||Frank Vallentin|
|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.
The talks (and only the talks) will be streamed on Zoom. Please ask Thomas Kahle for the password (ideally before the meeting starts): https://ovgu.zoom.us/j/69967452907
The workshop takes place in the Fraunhofer IFF, Sandtorstr. 22 in Magdeburg. It is the glass building, not the colorful rounded one adjacent to it and not the MPI Magdeburg (which is on the opposite side of the road).
When you reach the building, please check in at the front desk. The seminar room is directly on the left after you enter.
Google Maps Links:
Lunch options include
- Cafeteria at Fraunhofer IFF
- OvGU Mensa
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.
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.
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.
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.
Positive Del Pezzo Geometry
Real, complex, and tropical algebraic geometry join forces in a new branch of mathematical physics called positive geometry. We develop the positive geometry of del Pezzo surfaces and their moduli spaces, viewed as very affine varieties. Their connected components are derived from polyhedral spaces with Weyl group symmetries. We study their canonical forms and scattering amplitudes, and we solve the likelihood equations. This is joint work with Nick Early, Marta Panizzut, Bernd Sturmfels and Claudia Yun.
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.