Combinatorial Algebraic Topology & Applications IV

Contribution List

5. Contributed Talks

Contributed Talks

32. Khovanov-like categorifications of polynomials in matroid theory

So Yamagata (Fukuoka University)

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)

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...

23. Representing 4-manifolds via branched coverings

Valentina Bais (SISSA)

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...

24. TBA

Bruno Benedetti (University of Miami)

26. TBA

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

28. TBA

Pegah Pournajafi (Collège de France)

30. TBA

Anne-Laure Thiel (Université Bourgogne Europe)

31. TBA

Francesco Vaccarino (Politecnico di Torino)

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

Jelena Grbic (University of Southampton)

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.

27. When welded knot theory becomes useful for topology

Jean- Baptiste Meilhan (Université Grenoble Alpes)

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...