Alpoge and Granville (separately) gave novel proofs that the primes are infinite use Ramsey Theory. In particular, they Van der Waerden's Theorem some number theory. We prove using an easier theorem from Theory, namely Schur's Theorem, theory (Elsholtz independently obtained same proof were infinite). we n=3 case of Fermat's last theorem. also apply our method to show other domains have irreduc...

Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. It is desirable to classify the computational complexity of VCSPs depending on a fixed set of allowed cost functions in the input. Recently, the computational complexity of all VCSPs for finite sets of cost functions over finite domains has been classified in this sense. Many natural optimi...

In this article, we exhibit a large class of Banach spaces whose open unit balls are bounded symmetric homogeneous domains. These Banach spaces, which we call J*-algebras, are linear spaces of operators mapping one Hilbert space into another and have a kind of Jordan tripte product structure. In particular, all Hilbert spaces and all B*--algebras are J*-algebras. Moreover, all four types of the...

The classic Leftover Hash Lemma (LHL) is often used to argue that certain distributions arising from modular subset-sums are close to uniform over their finite domain. Though very powerful, the applicability of the leftover hash lemma to lattice based cryptography is limited for two reasons. First, typically the distributions we care about in lattice-based cryptography are discrete Gaussians, n...

Decorrelation theory has recently been proposed in order to address the security of block ciphers and other cryptographic primitives over a nite domain. We show here how to extend it to in nite domains, which can be used in the Message Authentication Code (MAC) case. In 1994, Bellare, Kilian and Rogaway proved that CBC-MAC is secure when the input length is xed. This has been extended by Petran...

We study generalized fixed-point equations over idempotent semirings and provide an efficient algorithm for the detection whether a sequence of Kleene’s iterations stabilizes after a finite number of steps. Previously known approaches considered only bounded semirings where there are no infinite descending chains. The main novelty of our work is that we deal with semirings without the boundedne...

We study diagonal estimates for the Bergman kernels of certain model domains in C near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as we...