Combinatorial Algebraic Topology & Applications IV

22 Jun 2026, 08:00 → 25 Jun 2026, 14:30 Europe/Rome

Aula Dini (Palazzo del Castelletto)

Luigi Caputi (University of Bologna), Carlo Collari (Università di Firenze), Giuliamaria Menara (Jussieu Institute of Mathematics)

The workshop “Combinatorial algebraic topology and applications” is at its fourth edition. The first, second, and third editions were held in Pisa at the Centro di Ricerca Matematica “E. De Giorgi” on the 27-28 November 2023 (link), 1-4 October 2024 (link), and 16-19 September 2025 (link), respectively. The main topics of the conference are combinatorics and algebraic topology (broadly intended), as well as their applications to different fields (e.g. data analysis, neural sciences and economics). The aim of the workshop is to gather researchers with common interest in the above topics and to create an atmosphere of discussion where to share ideas. For its fourth edition, the workshop will focus specifically on the following topics: applied (algebraic) topology, low-dimensional/geometric topology, and topological combinatorics. The workshop will consist of ten/twelve one-hour talks from invited speakers, along with contributed talks by selected participants. The talks will cover both theoretical and applied aspects of the subjects. The invited speakers are at different stages of the academic career, including professors, lecturers, PhD students and post-docs. Moreover, to stimulate discussion and exchange of ideas, the workshop will include free discussions, contributed talks, and possibly a problem session. We are committed to ensure gender balance as well as broad participation across academic backgrounds and career stages.

Registration is free, though mandatory, due to limitations in the number of participants.

Depending on funding limited support may be available for junior participants, with priority given to early registrations and contributed speakers.

The deadline for contributed talks and support is the 31st of March 2026.

The deadline for registration is the 30th of April 2026.

 

LIST OF CONFIRMED SPEAKERS

Valentina Bais (SISSA)

Bruno Benedetti (University of Miami)

Jelena Grbic (University of Southampton)

Dmitrii Korshunov (Institut de mathématiques de Jussieu –Paris Rive Gauche)

Jean- Baptiste Meilhan (Université Grenoble Alpes)

Pegah Pournajafi (Collège de France)

Francesca Pratali (Universiteit Utrecht)

Anne-Laure Thiel (Université Bourgogne Europe)

Francesco Vaccarino (Politecnico di Torino)

So Yamagata (Fukuoka University)

More information on the application procedure at the REGISTRATION PAGE.

 

Funded by:

- INdAM - GNSAGA
- Foundation Compositio Mathematica
- Università degli studi di Firenze

 

book-of-abstracts.pdf

Monday 22 June

08:40 Registration

09:25 Welcome Address (Prof. Malchiodi)

1 Topology and Combinatorics Uncovering Structures of Vietoris-Rips Complexes

I will explore the homotopy theory of Vietris-Rips complexes of hypercubes, focusing on the deep interplay between their topology and combinatorial structures. The goal is to understand key structural properties, such as higher connectivity, co-connectivity and the realisation of homotopy types, by introducing a new combinatorial-topological framework.
This is joint work with Martin Bendersky.

Speaker: Jelena Grbic (University of Southampton)

10:30 Coffee break

2 Khovanov-like categorifications of polynomials in matroid theory

Khovanov introduced a bigraded cohomology theory for links whose graded Euler characteristic recovers the Jones polynomial. Analogous Khovanov-like (co)homology theories have since been developed beyond knot theory, including chromatic cohomology for graphs and characteristic homology for hyperplane arrangements.
A matroid is a combinatorial structure that captures abstract notions of dependence, encompassing cycles in graphs and linear dependencies of vectors. In particular, matroids arise naturally from both graphs and hyperplane arrangements.
In this talk, we introduce (co)homology groups associated with certain polynomials of matroids. This is joint work with Takuya Saito.

Speaker: So Yamagata (Fukuoka University)

3 Localization of infinity-operads

Introduced by May and Boardman–Vogt to study iterated loop spaces, operads are combinatorial gadgets governing homotopy coherent algebraic structures on spaces —and in any other symmetric monoidal category. In homotopy theory, where spaces and objects are considered up to weak equivalence, algebraic structures must be encoded in a homotopy-invariant way. This is achieved using the more flexible formalism of “∞-operads”, which can be thought of as operads up to homotopy.

In the first part of this talk, I will introduce the theory of ∞-operads and their algebras, focusing on how the models of Lurie and Moerdijk–Weiss relate to partition posets and trees. I will then turn to operadic localization, the process of freely inverting a class of morphisms in an operad. This construction has proved to be a fundamental tool in the study of, for instance, factorization algebras and quantum field theory. Nevertheless, the general theory of operadic localization is still not fully understood, and many natural questions remain open. In the second part of the talk, I will present some new results in this direction, along with applications to the categories of algebras.

Speaker: Francesca Pratali (Universiteit Utrecht)

15:30 Coffee break

Contributed Talks

Conveners: Marek Filakovsky (Masaryk University), David Mosquera Lois (Universidade de Vigo), Pritam Chandra Pramanik (Institute for Advancing Intelligence (IAI), TCG CREST)

Tuesday 23 June

4 TBA

Speaker: Bruno Benedetti (University of Miami)

10:30 Coffee break

5 Diagrammatic Hochschild Cohomology, Incidence Algebras, and Filtrations

The Hochschild cohomology of a diagram of algebras, as introduced by Gerstenhaber and Schack, provides a natural framework for studying the cohomological properties of presheaves of algebras indexed by a small category. In this talk, we revisit and develop the connection between the Gerstenhaber--Schack complex and the Baues--Wirsching cohomology of categories, showing that a spectral sequence converging to diagrammatic Hochschild cohomology has its second page described by higher limits over the twisted arrow category.
A key simplification arises when restricting to diagrams of homological epimorphisms: the Baues--Wirsching cohomology reduces to classical functor cohomology over the indexing category, and the presence of a terminal object forces the spectral sequence to collapse. As a main application, we consider filtrations of finite simplicial complexes and the associated diagrams of incidence algebras. Exploiting the fact that injective simplicial maps induce surjective homological epimorphisms of incidence algebras, and the classical result that simplicial cohomology is Hochschild cohomology, we show that the diagrammatic Hochschild cohomology of such a filtration recovers the simplicial cohomology of the final complex.
The spectral sequence itself, however, carries richer information: its first page contains the classical persistent module of the filtration. At the same time, higher columns encode additional data whose geometric meaning remains an open question.

Speakers: Francesco Vaccarino (Politecnico di Torino), Luigi Caputi (University of Bologna)

Free Discussion: Problem session

Wednesday 24 June

6 When welded knot theory becomes useful for topology

Welded knot theory is a combinatorial and diagrammatic extension of classical knot theory. It arises naturally as a quotient of virtual knot theory, introduced in the early 2000s by Kauffman and by Goussarov–Polyak–Viro.
The aim of this talk is to present several results showing that welded knot theory turns out to be a relevant and effective tool for topology — not only in knot theory, but also in the study of knotted surfaces in 4-space.
This talk assumes no specialized background in topology.

Speaker: Jean- Baptiste Meilhan (Université Grenoble Alpes)

10:30 Coffee break

7 Quantum groups meet graphs

Quantum groups and graph theory may seem like distant areas, yet intriguing connections emerge when they intersect. After an introduction to the notion of quantum automorphism groups of finite graphs, we will focus on 0-hyperbolic graphs and a computation of their quantum automorphism group. If time permits, we will also show how their quantum symmetries can be fully understood through their classical properties, due to their structural constraints. This talk is based on joint work with Amaury Freslon and Paul Meunier.

Speaker: Pegah Pournajafi (Collège de France)

8 Representing 4-manifolds via branched coverings

Branched coverings can be seen a way to represent a ''complicated manifolds'' M in terms of
- a ''simpler'' manifold N (the target of the branched coverig),
-a codimension two subcomplex K in N (the branch set),
-a representation of the fundamental group of the complement of K into a permutation group (the monodromy).

By a classical result of Alexander, every piecewise linear manifold admits a branched covering onto the sphere. On the other hand, given an arbitraty manifold N, its topology might restrict the set of manifolds arising as its branched coverings.

I will talk about a recent joint work with Riccardo Piergallini and Daniele Zuddas, where we prove that, given a closed connected 4-manifold N with no 1- and 3-handles, there is a simple d-fold branched covering from M to N if and only if d times the intersection lattice of N isometrically embeds into the intersection lattice of M. We also give conditions on the degree and on the regularity of the branch set.

Speaker: Valentina Bais (SISSA)

15:30 Coffee break

Contributed Talks

Conveners: Clemens Bannwart (Università di Modena e Reggio Emilia), Grigory Solomadin (PU Marburg), Nikola Sadovek (MPI CBG Dresden)

20:00 Social dinner

Thursday 25 June

9 TBA

Speaker: Dmitrii Korshunov (Institut de mathématiques de Jussieu – Paris Rive Gauche)

10:30 Coffee break

10 TBA

Speaker: Anne-Laure Thiel (Université Bourgogne Europe)

12:00 End of conference