33 citations · 88 across the 15 of their papers we have counts for
16 papers
Cone and constrained colorful Carathéodory Theorems
Pavle V. M. Blagojević, Roman N. Karasev, Bálint Zsigri
Holmsen proved in 2016 a generalization of the classical colorful Caratheodory theorem in which a matroid imposes additional constraints on the desired colorful transversal. His ap…
More bisections by hyperplane arrangements
Pavle V. M. Blagojević, Aleksandra Dimitrijević Blagojević, Roman Karasev +1
A union of an arrangement of affine hyperplanes in is the real algebraic variety associated to the principal ideal generated by the polynomial given as the produc…
Cutting a part from many measures
Pavle V. M. Blagojević, Nevena Palić, Pablo Soberón +1
Holmsen, Kynčl and Valculescu recently conjectured that if a finite set with points in that is colored by different colors can be partitioned into $…
Orthogonal shadows and index of Grassmann manifolds
Djordje Baralić, Pavle V. M. Blagojević, Roman Karasev +1
In this paper we study the action on real Grassmann manifolds and given by taking (appropriately oriented) orthogonal complemen…
Beyond the Borsuk-Ulam theorem: The topological Tverberg story
Pavle V. M. Blagojević, Günter M. Ziegler
Bárány's "topological Tverberg conjecture" from 1976 states that any continuous map of an -simplex to , for , maps points from disjoint f…
The topological transversal Tverberg theorem plus constraints
Pavle V. M. Blagojević, Aleksandra S. Dimitrijević Blagojević, Günter M. Ziegler
In this paper we use the strength of the constraint method in combination with a generalized Borsuk-Ulam type theorem and a cohomological intersection lemma to show how one can obt…
Local multiplicity of continuous maps between manifolds
Pavle V. M. Blagojević, Roman Karasev
Let and be smooth (real or complex) manifolds, and let be equipped with some Riemannian metric. A continuous map admits a local -multipl…
Barycenters of Polytope Skeleta and Counterexamples to the Topological Tverberg Conjecture, via Constraints
Pavle V. M. Blagojević, Florian Frick, Günter M. Ziegler
Using the authors' 2014 "constraints method," we give a short proof for a 2015 result of Dobbins on representations of a point in a polytope as the barycenter of points in a skelet…
Hyperplane mass partitions via relative equivariant obstruction theory
Pavle V. M. Blagojević, Florian Frick, Albert Haase +1
The Grünbaum-Hadwiger-Ramos hyperplane mass partition problem was introduced by Grünbaum (1960) in a special case and in general form by Ramos (1996). It asks for the "admissible"…
On complex highly regular embeddings and the extended Vassiliev conjecture
Pavle V. M. Blagojević, Frederick R. Cohen, Wolfgang Lück +1
A continuous map C^d -> C^N is a complex k-regular embedding if any k pairwise distinct points in C^d are mapped by f into k complex linearly independent vectors in C^N. Our centra…
Tverberg plus constraints
Pavle V. M. Blagojević, Florian Frick, Günter M. Ziegler
Many of the strengthenings and extensions of the topological Tverberg theorem can be derived with surprising ease directly from the original theorem: For this we introduce a proof…
The Schwarz genus of the Stiefel manifold and counting geometric configurations
Pavle Blagojević, Roman Karasev
In this paper we compute: the Schwarz genus of the Stiefel manifold with respect to the action of the Weyl group , and the Lust…
A tight colored Tverberg theorem for maps to manifolds
Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler
We prove that any continuous map of an N-dimensional simplex Delta_N with colored vertices to a d-dimensional manifold M must map r points from disjoint rainbow faces of Delta_N to…
Extensions of theorems of Rattray and Makeev
Pavle Blagojević, Roman Karasev
We consider extensions of the Rattray theorem and two Makeev's theorems, showing that they hold for several maps, measures, or functions simultaneously, when we consider orthonorma…
Optimal bounds for the colored Tverberg problem
Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler
We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of B…
The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes
Pavle V. M. Blagojević, Günter M. Ziegler
We compute the complete Fadell-Husseini index of the 8 element dihedral group D_8 acting on S^d \times S^d, both for F_2 and for integer coefficients. This establishes the complete…