8 citations · 20 across the 9 of their papers we have counts for
12 papers
Kazhdan constants for Chevalley groups over the integers
Marek Kaluba, Dawid Kielak
We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than , these ar…
Spectral gap for the cohomological Laplacian of
Marek Kaluba, Piotr Mizerka, Piotr W. Nowak
We show that the cohomological Laplacian in degree 1 in the group cohomology of is a sum of hermitian squares in the algebra $\mathbb{M}_n(\mathbb…
Hyperbolic generalized triangle groups, property (T) and finite simple quotients
Pierre-Emmanuel Caprace, Marston Conder, Marek Kaluba +1
We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan's property (T). Some of them are significantly shorter than the previously know…
Random Polytope Descriptors
Michael Joswig, Marek Kaluba, Lukas Ruff
We introduce a class of random polytopes which simultaneously generalizes several known constructions. While being fairly general, these polytopes are also computationally exceptio…
Polymake.jl: A new interface to polymake
Marek Kaluba, Benjamin Lorenz, Sascha Timme
We present the Julia interface Polymake.jl to polymake, a software for research in polyhedral geometry. We describe the technical design and how the integration into Julia makes it…
On property (T) for and
Marek Kaluba, Dawid Kielak, Piotr W. Nowak
We prove that has Kazhdan's property (T) for every . Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same state…
Certifying numerical estimates of spectral gaps
Marek Kaluba, Piotr Nowak
We establish a lower bound on the spectral gap of the Laplace operator on special linear groups using conic optimisation. In particular, this provides a constructive (but computer…
Constructions of exotic actions on product manifolds with an asymmetric factor
Zbigniew Błaszczyk, Marek Kaluba
We explore transformation groups of manifolds of the form , where is an asymmetric manifold, i.e. a manifold which does not admit any non-trivial action of a finit…
Effective topological complexity of spaces with symmetries
Zbigniew Błaszczyk, Marek Kaluba
We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly diff…
On equivariant and invariant topological complexity of smooth -spheres
Zbigniew Błaszczyk, Marek Kaluba
We investigate equivariant and invariant topological complexity of spheres endowed with smooth non-free actions of cyclic groups of prime order. We prove that semilinear $\mathbb{Z…
On Representation of the Reeb Graph as a Sub-Complex of Manifold
Marek Kaluba, Wacław Marzantowicz, Nelson Silva
The Reeb graph is one of the fundamental invariants of a smooth function with isolated critical points. It is defined as the quotient s…
Non-symplectic actions on complex projective spaces
Marek Kaluba, Wojciech Politarczyk
We construct smooth actions of arbitrary compact Lie groups on complex projective spaces, such that the corresponding transformations arising from the group action do not preserve…