Geometry, Algebra and Combinatorics of Moduli Spaces and Configurations VIII

This is the 8th edition of the graduate school held in Toblach in winter 2017, winter 2018, winter 2019, winter 2020, winter 2023, winter 2024 and winter 2025. There will be three 5 hours minicourses, some talks and ample time for discussion.

Mini-courses

• Ivan Marin, Université de Picardie-Jules Verne, Complex braid groups and their Hecke algebras.
• Christian Stump, Ruhr-Universität Bochum, Algebraic and enumerative invariants of finite graded bounded posets. [show abstract]

  Abstract:
  In this lecture series, I present classical and modern combinatorial invariants of such posets and their unifying nature across algebraic combinatorics. These invariants include classical structures such as the Möbius function, characteristic polynomial, incidence algebra, chain polynomial, ab-index, and (flag) f- and h-vectors. I also present recently defined families of polynomials associated to such a poset that gained a lot of attention in algebraic combinatorics: the Poincaré-extended ab-index, flag coarse Hilbert-Poincaré series, and Chow polynomial. I discuss their properties such as their unimodality, log-concavity, gamma-positivity, and real-rootedness. Throughout the lecture series, I will in particular discuss known results and conjectures for interesting families of examples: boolean lattices, (ordered) set partition lattices, intersection posets of hyperplane arrangements, lattices of flats of matroids, simplicial posets, shellable posets, and posets that admit R-labelings.
  [Hide abstract]

• Mattia Talpo, Università di Pisa, Logarithmic geometry and tropicalization. [show abstract]

  Abstract: Logarithmic geometry is an enhanced version of algebraic geometry, where varieties are equipped with an extra sheaf of monoids, whose sections should be somehow thought of as ``monomial regular functions’’, and which is essentially of a combinatorial nature. Prototypical examples (and building blocks in some sense) are affine toric varieties. This extra structure is often useful when dealing with degenerations of smooth objects, and, correspondingly, compactifications of certain moduli spaces. There are also fruitful connections to tropical geometry, a piecewise-linear, combinatorial version of algebraic geometry, via a tropicalization procedure, leveraging on the close relationship between a toric variety and its fan. I will give an introduction to these topics and their relationship, also mentioning relevant past and current applications.
  [Hide abstract]

Venue

The school will be held in Dobbiaco (Toblach) at the Kulturzentrum Grand Hotel Centro Culturale, in "La Sala degli Specchi". Kulturzentrum Grand Hotel Centro Culturale is located in front of Toblach train station (see the map).
Participants are expected to arrive on Sunday 31/5 and to leave on Friday 5/6 after lunch.

Registration and support

Participants are required to register by filling in this registration form.
It would be very helpful for the organization if you fill in the form as soon as possible, thanks!

Limited funding will be available to cover local expenses (lodging, breakfast and dinner) of few Master or PhD students.
To apply for financial support you are required to fill in the same form.
The deadline to apply for funding is February 28, 2026.
Again, we encourage to apply as soon as possible in order to help the organization, thanks!

For any question, you can contact the organizers at the following email address: toblachconfigurations@gmail.com.

This workshop is supported by:

MUR, Dipartimento di eccellenza di Matematica, University of Pisa.

Dipartimento di matematica, Università di Bologna.

Instituto Nazionale Di Alta Matematica INDAM.

GNSAGA, INDAM.

University "La Sapienza" of Rome, Progetti di Ateneo Representation Theory and Applications, 2023-2024.

Organizers: Filippo Callegaro, Michele D'Adderio , Luis Ferroni , Marco Franciosi , Roberto Pagaria and Paolo Papi.