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We give a simple proof of a recently result concerning Hardy $q$-inequalities.

Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the…

We prove a modularity lifting theorem for minimally ramified deformations of two-dimensional odd Galois representations, over an arbitrary number field. The main ingredient is a generalization of the Taylor-Wiles method in which we patch…

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

In this note we compare the fracture squares from genuine equivariant stable homotopy theory and the fracture squares which appear in the Goodwillie tower for the norm functor.

Let G be a totally disconnected, locally compact group admitting a contractive automorphism f. We prove a Jordan-Holder theorem for series of f-stable closed subgroups of G, classify all possible composition factors and deduce consequences…

In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.

We prove a computable version of Hall's Harem Theorem and apply it to computable versions of Tarski's alternative theorem.

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.

In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…

We give an elementary proof of the group law for elliptic curves using explicit formulas.

We prove analogues of the Craig interpolation theorem for the continuous model theory of metric structures.

For odd primes we prove some structure theorems for finite $p$-groups $G$, such that $G''\neq 1$ and $|G'/G''|=p^3$. Building on results of Blackburn and Hall, it is shown that $\lcs G3$ is a maximal subgroup of $G'$, the group $G$ has a…

The paper is devoted to a somewhat idiosyncratic account of the theorem of de Bruijn-Erd\"{o}s and Hanani from the combinatorics of finite geometries and its various proofs. Among the proofs discussed are the original proofs by de…

We give a short proof of Waldhausen's homeomorphism theorem for orientable Haken 3-manifolds.

We prove Koll\'ar's injectivity theorem for globally $F$-regular varieties.

We will present a new proof of the Gromoll-Grove diameter rigidity theorem.