Conveners
Contributed Talks
- Marek Filakovsky (Masaryk University)
- Pritam Chandra Pramanik (Institute for Advancing Intelligence (IAI), TCG CREST)
- David Mosquera Lois (Universidade de Vigo)
Contributed Talks
- Grigory Solomadin (PU Marburg)
- Nikola Sadovek (MPI CBG Dresden)
- Clemens Bannwart (Università di Modena e Reggio Emilia)
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Pritam Chandra Pramanik (Institute for Advancing Intelligence (IAI), TCG CREST)
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,...
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Nikola Sadovek (MPI CBG Dresden)
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...
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Clemens Bannwart (Università di Modena e Reggio Emilia)
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,...
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Grigory Solomadin (PU Marburg)
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...
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David Mosquera Lois (Universidade de Vigo)
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...
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Marek Filakovsky (Masaryk University)
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...
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