Related papers: A short proof of Cramer's theorem in R
In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.
We give a general setting for Cram\'er's large deviations theorem for the empirical means of a sequence of i.i.d. random vectors, which contains Cram\'er's theorem in a Banach space and Sanov's theorem. ----- Nous \'etablissons un cadre…
We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding…
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
In this paper we present a monotonicity which extends a classical theorem of A. Schur comparing the chord length of a convex plane curve with a space curve of smaller curvature. We also prove a Schur's Theorem for spherical curves, which…
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
In this paper, we prove Gromov's flat corner domination conjecture in all dimensions. As a consequence, we answer positively the Stoker conjecture for convex Euclidean polyhedra in all dimensions. By applying the same techniques, we also…
We present an exposition of the proof of the induced bipartite Ramsey Theorem.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.
Edwards' Theorem establishes duality between a convex cone in the space of continuous functions on a compact space and the set of representing or Jensen measures for this cone. In this paper we prove non-compact versions of this theorem.
The theorem of orthogonal-orthogonal duality of Rowe, Repka, and Carvalho is proven by a method based on characters that is very different from theirs and akin to Helmers's half a century earlier proof of the analogous sympletic-symplectic…
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
We present a geometric proof for the duality theorem of linear programming. Besides being self-contained and simple, the present approach also provides a transparent way for understanding this fundamental result.
We present a short proof of Reisner's Theorem, characterizing which simplicial complexes have a Cohen-Macaulay face ring. In some cases, we can also express some homological invariants of the face ring in terms of the reduced homology of…
By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac's theorem on chordal graphs.
We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…
We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.