The workshop “Recent Developments on Lattice Polytopes in Leipzig” was held from January 20 to January 23, 2026, at the Max Planck Institute for Mathematics in the Sciences. It brought together more than 70 participants from institutions across many countries, including Austria, Belgium, Canada, Colombia, France, Germany, Greece, Hungary, Japan, Spain, Sweden, and the USA. The workshop was highly active and featured many fruitful discussions, with numerous insightful questions following the talks from both early-career and senior researchers. The presentations focused on polytopes arising from graphs, matroids, posets, and other combinatorial objects, as well as new developments and insights in the Ehrhart theory of lattice polytopes.

The 94th meeting of the Séminaire Lotharingien de Combinatoire took place from September 14 to September 17, 2025, already for the fourth time at the beautiful Evangelische Akademie in Bad Boll (Germany) at the foot of the Schwäbischen Alb.

Once again, we enjoyed two great lecture series, this time mostly about a structure we all appreciate very much: polynomials.

Matt BECK (San Francisco State University) introduced us to the world of "q-Ehrhart polynomials" as recently introduced by Chapoton. We were presented various versions of Brion's Theorem of point counts in lattice polytopes and fascinating new research directions.

Jang-Soo KIM (Sungkyunkwan University, Suwon) developed in the second lecture series the "Combinatorics of Orthogonal Polynomials", with many examples and combinatorial counting arguments, and a nice picture with Sylvie Corteel after a great breakthrough on lecture hall tableaux.

We in addition had 16 contributed talks, and we once again very much enjoyed the atmosphere, the friendly staff, and the surrounding hills and villages.

The conference Modern Perspectives on Geometry of Numbers took place at BTU Cottbus from September 9–12, 2025. It brought together participants who use methods from the geometry of numbers in areas such as metric convex geometry, combinatorics, integer and combinatorial optimization, energy-minimizing point configurations, asymptotic convexity theory, toric geometry, and algebraic geometry.

Prof. Christian Haase (FU Berlin) gave a series of lectures on toric geometry, while Prof. Alexander Litvak (University of Alberta) delivered lectures on the MM∗-estimates. Researchers at different stages of their careers were well represented. The conference provided an excellent opportunity to establish new connections and strengthen existing ones, and the overall atmosphere was very friendly and welcoming.

The social program included a conference dinner and a kayak tour, further supporting informal exchange among participants.

The second annual meeting of the Priority Program took place from 3–5 September 2025 at Leibniz University Hannover. It was attended by approximately 80 participants, around a third of whom were PhD and master's students. The scientific program comprised invited presentations reflecting the core themes of the program. In addition, short contributed talks showcased first success stories of ongoing projects within the program. The next annual meeting will take place in Frankfurt in September 2026 and will be organized by Raman Sanyal and Thorsten Theobald.

The 3-day workshop Combinatorial Synergies EAST took place at MPI-MiS in Leipzig, March 19-21 2025. It was dedicated to Geometric Combinatorics, Algebraic Combinatorics, and related fields. It proved to be a unique opportunity for regional networking within the DFG priority program SPP 2458 "Combinatorial Synergies". Lectures have been presented by speakers from Berlin, Chemnitz, Cottbus, Greifswald, Jena, Leipzig and Magdeburg. A particular outcome have been many fruitful discussions across the borders of ongoing projects and the thematic areas in the priority program.

From August 28 to September 2, 2025, the summer school "Nonlinear Optimization and Combinatorics" was organized by Christian Kirches, Timo de Wolff, Thorsten Theobald, Birte Ostermann, Nikolas Rieke and Jonas Ellwanger at TU Braunschweig. It covered a set of independent, but thematically connected lecture series covering general nonlinear optimization, polynomial optimization and the intersection of optimization and combinatorics. Michael Joswig (TU Berlin and MPI Leipzig) provided a lecture series on "The Tropical Geometry of Shortest Paths", Pietro Belotti (Polictecnico di Milano) and Sven Leyffer (Argonne National Laboratory, USA) a lecture series on "Advances in Mixed Integer Nonlinear Optimization" and Didier Henrion (LAAS-CNRS Toulouse and Czech Technical University Prague) a lecture series on "The Moment-SOS Hierarchy for Polynomial Optimization". The summer school was attended by 43 students, mostly on the Ph.D. student level. It also included exercise sessions, where people worked together in groups, as well as a poster session, where the participants presented their own research. The website of the summer school can be found here: https://www.iaa.tu-bs.de/AppliedAlgebra/SummerSchool2025/Summer_school_2025.html.

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.