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We study several fairness notions in allocating indivisible chores (i.e., items with non-positive utilities) to agents, who have additive and submodular cost functions. The fairness criteria we are co...
An important well-known result of Rota describes the relationship between the M¨obius functions of two posets related by a Galois connection. We present an analogous result relating the antipodes of...
This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. The limit theorems are universal depending solely on the limiting behavior ...
The focus of this paper is on proportional reasoning, emphasising its pervasiveness throughout the mathematics curriculum, but also highlighting its elusiveness.
Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metr...
Motivated to study the geometry of the exotic spheres constructed in [5], we derive a necessary condition for non-negative sectional curvature in certain total spaces of Riemannian submersions with to...
In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-form...
Abstract: We construct Yang-Mills connections on SO(n)-bundles over spheres equipped with the Euclidean metric. We use a cohomogeneity one group action on the bundle to reduce the Yang-Mills-equation ...
Abstract: We study the irreducible decomposition under Sp(2n, R) of the space of torsion tensors of almost symplectic connections. Then a description of all symplectic quadratic invariants of torsion-...
We look at natural foliations on the Painlev´e VI moduli space of regular connections of rank 2 on P1−{t1, t2, t3, t4}. These foliations are fibrations,and are interpreted in terms of the ...
We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generaliza-tion of...
In [4] we defined a notion of parallel transport along superpaths in a supermanifold coming from a vector bundle with connection over the supermanifold. In this note, we show that the converse is also...
We compute explicitly the monodromy representations of "cyclotomic" analogs of the Knizhnik--Zamolodchikov differential system. These are representations of the type B braid group $B_n^1$. We show ho...
We investigate the Lawson genus 2 surface by methods from integrable system theory. We prove that the associated family of flat connections comes from a family of flat connections on a 4−punctur...
We construct the Kuranishi spaces, or in other words, the versal deformations, for the following classes of connections with fixed divisor of poles D:all such connections, as well as for its subclasse...

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