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We study the Fibered Isomorphism Conjecture of Farrell and Jones in L-theory for groups acting on trees. In several cases we prove the conjecture. This includes wreath products of abelian groups and free metabelian groups. We also deduce…
This paper combines the post-Minkowskian expansion of general relativity with the language of intersection theory. Because of the nature of the soft limit inherent to the post-Minkowskian expansion, the intersection-based approach is of…
We prove that a conjecture of Fomin, Fulton, Li, and Poon, associated to ordered pairs of partitions, holds for many infinite families of such pairs. We also show that the bounded height case can be reduced to checking that the conjecture…
We use quilted Floer theory to construct functor-valued invariants of tangles arising from moduli spaces of flat bundles on punctured surfaces. As an application, we show the non-triviality of certain elements in the symplectic mapping…
The present article is the first in a series whose ultimate goal is to prove the Kotschick-Morgan conjecture concerning the wall-crossing formula for the Donaldson invariants of a four-manifold with b^+ = 1. The conjecture asserts that the…
In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.
In this article, we prove the following interpolation problem: if the composition of a function and a regular map between affine varieties is a regular function, then there exists a global regular function of the target variety that…
We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent…
In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…
Chv\'{a}tal's conjecture in extremal combinatorics asserts that for any decreasing family $\mathcal{F}$ of subsets of a finite set $S$, there is a largest intersecting subfamily of $\mathcal{F}$ consisting of all members of $\mathcal{F}$…
We prove a conjecture of F. Chapoton relating certain enumerative invariants of (a) the cluster complex associated by S. Fomin and A. Zelevinsky to a finite root system and (b) the lattice of noncrossing partitions associated to the…
Let G be a cocompact lattice in a virtually connected Lie group or the fundamental group of a 3-manifold. We prove the K-theoretic Farrell-Jones Conjecture (up to dimension one) and the L-theoretic Farrell-Jones Conjecture for G, where we…
We present a simple proof of the Poincar\'e gauge invariance of general relativity and Einstein-Cartan theory, in the context of the corresponding bundle of affine frames.
The theorem is proved that generalizes the Gelfand generalization of the Paley-Wiener tauberian theorem to general abelian topological semigroups with invariant measure. Several corollaries of this theorem are given.
We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in any dimension over an arbitrary field.
We show that the class of groups satisfying the K- and L-theoretic Farrell-Jones conjecture is closed under taking graph products of groups.
We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.
We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.
We formulate, and provide strong evidence for, a natural generalization of a conjecture of Robert Coleman concerning Euler systems for the multiplicative group over arbitrary number fields.