Related papers: The Kropholler Conjecture
In this note we give a short proof of Arnold's conjecture for the zero section of a cotangent bundle of a closed manifold. The proof is based on some basic properties of Lagrangian spectral invariants from Floer theory.
We formulate the Hauptvermutung of Causal Set Theory in two mathematically well-defined but different ways one of which turns out to be wrong and the other one turns out to be true. A further result is that the Hauptvermutung is true if we…
This paper establishes a converse comparison theorem for real-valued decoupled forward backward stochastic differential equations with jumps.
This paper has been withdrawn by the author because Proposition 1 is not valid.
This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.
We are pleased to see that Jeckelmann has made many changes to the original version of his comment on our paper as a result of our response. Here is a copy of this powerful response that reveals problems in his previous results. However,…
An extension of the Helmholtz theorem is proved, which states that two retarded vector fields ${\bf F}_1$ and ${\bf F}_2$ satisfying appropriate initial and boundary conditions are uniquely determined by specifying their divergences…
In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.
In this paper, we present a constructive proof of Herschfeld's Convergence Theorem. Our formulation differs from Herschfeld's in a few ways: We consider radicals that nest transfinitely many times, as these are essential to the proof;…
A concise presentation of Schrodinger's ancilla theorem (1936 Proc. Camb. Phil. Soc. 32, 446) and its several recent rediscoveries.
We prove the $l^2$ Decoupling Conjecture for compact hypersurfaces with positive definite second fundamental form and also for the cone. This has a wide range of important consequences. One of them is the validity of the Discrete…
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
The union-closed sets conjecture (Frankl's conjecture) says that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in…
The paper has been withdrawn, since there is a mistake in Proposition 5.2. The result on the telescope conjecture for semihereditary rings is correct, but the characterization of the smashing subcategories of the derived category of…
The paper gives a unified and simple proof of both theorems and Cousin's theorem.
In this expository paper we introduce extended topological quantum field theories and the cobordism hypothesis.
First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…
We examine a logical foundation of depicting a Lorentz contraction of a Coulomb field (an electric field of a point charge in uniform motion) by means of the 'Lorentz contracted' field lines. Two existing arguments for a contraction of…
A convergence theorem for martingales with c\`adl\`ag trajectories (right continuous with left limits everywhere) is obtained in the sense of the weak dual topology on Hilbert space, under conditions that are much weaker than those required…
We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.