A small SPP2458 funded workshop took place at Ruhr-University Bochum, from May 12 to May 16, 2025.

The programme consisted of a mere 10 selected talks on recent developments in the field of hyperplane arrangements leaving ample time for discussions and collaborations. Participants came from as far afield as Japan and as near as Bochum.

The Algebraic Statistics Conference 2025 (AlgStat2025) was held from March 24 to 28, 2025 at the Technical University of Munich in Garching. The event brought together researchers in algebraic statistics, applied algebraic geometry, and related fields, with strong participation from early-career scientists.

The scientific program featured keynote lectures by Karel Devriendt, Eliana Duarte, Elizabeth Gross, Kaie Kubjas, Sonja Petrović, Elina Robeva, Jose Rodriguez, Frank Röttger, Liam Solus, and Bernd Sturmfels. In addition to the invited talks, the conference included contributed talks, a poster session, and many informal discussions about future directions for the field.

The conference was organized by Carlos Améndola (TU Berlin), Mathias Drton (TU Munich), Benjamin Hollering (TU Munich), and Thomas Kahle (OvGU Magdeburg), with local organization by Andrea Grant (TU Munich), Bettina Haas (TU Munich), and Benjamin Hollering (TU Munich). It received support from the European Research Council (ERC), the DFG Priority Program SPP 2458 “Combinatorial Synergies,” and the Alexander von Humboldt Foundation.

The idea for this spring school stems from the SPP's first annual meeting where we realized that many (junior) researchers do not know about the Dynkin classification. The spring school took place at Ruhr University Bochum, March 31-April 4, 2025. Each of the five days of the school were covered by one of the professors in the Algebra Group at Ruhr University:

• Christian Stump: Coxeter groups and root systems

• Gerhard Röhrle: Lie groups and Lie algebras

• Karin Baur: Cluster algebras

• Markus Reineke: Quiver representation theory

• Alexander Ivanov: Simple singularities

The Winter School and Workshop on Polytopes 2025 took place from February 24 to 28, 2025 in Osnabrück. It was attended by around 80 participants, around half of whom were PhD and Master's students. The 2-day school consisted of three mini-courses: Florian Besau gave an introduction to Random Polytopes, Katharina Jochemko took us on a journey in Lattice point enumeration and Vincent Pilaud talked about Combinatorics of polytopes. The scientific program of the workshop consisted of six invited one-hour talks as well as nine 25-minutes talks. Moreover, on Thursday, a poster session with wine-and-cheese took place. The poster award went to Jilian Eddy.

The Workshop "Wachspress Geometry" was organized by Rainer Sinn and Martin Winter and took place September 24 - 25, 2024 at the University of Leipzig.

Its goal was to bring together researchers with a shared interest in Wachspress Geometry and to present this field to a broad mathematical audience. In a total of ten talks the various perspectives on this newly emerging field were presented, ranging from adjoint polynomials and Wachspress models, to Amplituhedra and geometric rigidity. The workshop was well-attended, with approximately 15 early-career and 10 senior participants. At least 4 research projects started at this event.

The kick-off meeting of the priority program took place from September 11 to 13, 2024 in Osnabrück. It was attended by 76 participants, around half of whom were PhD and Master's students.

The scientific program consisted of a scientific presentation on each of the nine core topics of the SPP. In addition, there was a mentoring session for prospective and current PhD students, as well as an event in the form of a World Cafe, which served to network the projects.

The next annual conference will take place in Hannover in September 2025, organized by Michael Cuntz.

The 36th International Conference on Formal Power Series and Algebraic Combinatorics took place at Ruhr University Bochum, Germany in July 22-26, 2024. Arguably the most important conference series in Algebraic Combinatorics featured invited talks by

• Carolina Benedetti (Universidad de los Andes, Colombia)

• Michael Joswig (Technische Universität Berlin & MPI MiS Leipzig, Germany)

• Satoshi Murai (Waseda University, Japan)

• Rosa Orellana (Dartmouth College, United States)

• Nicholas Proudfoot (University of Oregon, United States)

• Markus Reineke (Ruhr-Universität Bochum, Germany)

• Lisa Sauermann (Massachusetts Institute of Technology, United States)

• Kris Shaw (University of Oslo, Norway)

• Josephine Yu (Georgia Institute of Technology, United States)

and as well 27 contributed talks and 87 posters chosen by the program committee among 205 submissions. The more than 300 participants enjoyed a full week of great events, excursions, cake, sunshine, and an icecream featured closing event.

The summer school "Algebraic Combinatorics" took place at the MPI Leipzig on July 15. - 17. 2024 as a satelite event of the FPSAC 2024. It features three main lecture series by

• Chris Eur: Log-concave rainbows and where to find them

• Greta Panova: Computational Complexity in Algebraic Combinatorics

• Vic Reiner: The Koszul Property in Algebraic Combinatorics

Each lecture series was accompanied with exercise sessions for the more than 100 participants from Germany, Europe, and abroad.

The lecture series held by Professor Uli Walther (Purdue University, USA) took place at Ruhr-University Bochum within the DFG Priority Programme 2458 "Synergies in Combinatorics" in June 2024. The lecture series was attended by a dozen PhD students and Postdocs.
The topics covered consisted of the following:

• Matroids, matroidal polynomials, examples of these, including Kirchhoff polynomials, configuration polynomials, multivariable Tutte polynomials, matroid support polynomials.

• Feynman diagrams and Feynman integrands (which are also matroidal). A discussion on torus actions on these hypersurfaces. The singular locus of certain matroidal polynomials - for configuration polynomials when the matroid is sufficiently connected, discuss irreducibility, size of singular locus, comparison between Jacobian ideal and a certain corank 2 determinantal ideal, Cohen-Macaulayness of these. The special case of the free resolution of the singular locus of the Kirchhoff polynomial of a complete graph.

• For matroidal polynomials in general, it was explained that they have rational singularities, and in the homogeneous case that they are F-regular.

The DFG sent out the decision letters for (almost) all proposals on April 18-19. We expect the job openings to be published under Job openings soon, and also that (again almost) all positions to be filled before the first Priority Program Annual Conference in September in Osnabrück.