Combinatorial Algebraic Topology & Applications IV

Contribution List

25. Topology and Combinatorics Uncovering Structures of Vietoris-Rips Complexes

Jelena Grbic (University of Southampton)

22/06/2026, 09:30

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.

32. Khovanov-like categorifications of polynomials in matroid theory

So Yamagata (Fukuoka University)

22/06/2026, 11:00

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...

29. Localization of infinity-operads

Francesca Pratali (Universiteit Utrecht)

22/06/2026, 14:30

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...

24. TBA

Bruno Benedetti (University of Miami)

23/06/2026, 09:30

31. Diagrammatic Hochschild Cohomology, Incidence Algebras, and Filtrations

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

23/06/2026, 11:00

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...

27. When welded knot theory becomes useful for topology

Jean- Baptiste Meilhan (Université Grenoble Alpes)

24/06/2026, 09:30

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...

28. Quantum groups meet graphs

Pegah Pournajafi (Collège de France)

24/06/2026, 11:00

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...

23. Representing 4-manifolds via branched coverings

Valentina Bais (SISSA)

24/06/2026, 14:30

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...

26. TBA

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

25/06/2026, 09:30

30. TBA

Anne-Laure Thiel (Université Bourgogne Europe)

25/06/2026, 11:00

38. A Combinatorial Hopf-trace formula and its applications to combinatorial Borsuk-Ulam type theorems

Pritam Chandra Pramanik (Institute for Advancing Intelligence (IAI), TCG CREST)

Contributed Talks

Classical results in equivariant topology (e.g., Borsuk--Ulam theorem, $\mathbb{Z}_p$-Borsuk--Ulam theorem etc.) have numerous important applications in combinatorics. In this paper, we prove a Hopf--trace type formula, which is a purely combinatorial identity, involving no homology. This theorem provides a unified combinatorial framework for several results in equivariant topology. In fact,...

40. A necessary and sufficient condition for k-transversals

Nikola Sadovek (MPI CBG Dresden)

Contributed Talks

In 1988 Goodman and Pollack asked for a necessary and sufficient condition for a family of convex sets in R^d to admit a k-transversal (a k-dimensional affine subspace that intersects each set in the family) for any 0≤k≤d-1. Helly’s classical theorem corresponds to the case k=0, while Goodman, Pollack, and Wenger obtained a condition for k=d-1. In this talk, we will present a solution to the...

39. Canonical chain complexes for Morse-Smale vector fields

Clemens Bannwart (Università di Modena e Reggio Emilia)

Contributed Talks

In 1960, Smale defined a filtration of a closed smooth manifold by the unstable manifolds of fixed points and closed orbits of a Morse-Smale vector field defined on it, and derived generalized Morse inequalities. This suggests that, similarly to the Morse complex of Morse-Smale functions, even in the presence of closed orbits, Morse-Smale vector fields admit canonical chain complexes,...

41. Cohomology for GKM manifolds and orbit spaces

Grigory Solomadin (PU Marburg)

Contributed Talks

In this talk, for any GKM4 manifold M^2n (with (S1)^k torus action) that is either Hamiltonian or satisfies n-k=1 we prove generators-and-relations description of the respective equivariant cohomology ring. The proof follows in two steps. We prove extension of the respective GKM graph to a torus graph (i.e. as in k=n case) using sheaves on graphs and Kuroki's obstruction. An extension of GKM...

37. Homotopic Distance: Combinatorial Models and Computable Lower Bounds

David Mosquera Lois (Universidade de Vigo)

Contributed Talks

The homotopic distance D(f,g) between two continuous maps measures how far they are from being homotopic. It provides a common framework for classical invariants such as the Lusternik–Schnirelmann category and topological complexity, and it admits a natural interpretation in terms of sectional category. In this talk, I will discuss recent developments on homotopic distance, with special...

36. Topology of robust clique complexes of grid-like graphs

Marek Filakovsky (Masaryk University)

Contributed Talks

We study k-robust clique complexes - a family of simplicial complexes that generalizes the traditional clique complex. Here, a subset of vertices forms a simplex provided it does not contain an independent set of size k. We investigate these complexes for square sequence graphs, a class of bipartite graphs that are constructed by iteratively attaching "squares" = 4-cycles. This class includes...