Related papers: The lonely runner conjecture holds for nine runner…
We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for…
Six conjectures on pairs of consecutive primes are listed in this paper, together with examples for each case.
We prove an almost sure invariance principle for a random walker among i.i.d. conductances in $\Z^d$, $d\geq 2$. We assume conductances are bounded from above but we dot require they are bounded from below.
We prove Shokurov's index conjecture for quotient singularities.
Zagier provided eleven conjectural rank two examples for Nahm's problem. All of them have been proved in the literature except for the fifth example, and there is no $q$-series proof for the tenth example. We prove that the fifth and the…
We present here a system with collection of random walks relaying a signal in one dimension in the presence of delays. We are interested in the time for a signal to travel from one end (start) to the other end (finish) of the lined group of…
Consider $n$ runners running on a circular track of unit length with constant speeds such that $k$ of the speeds are distinct. We show that, at some time, there will exist a sector $S$ which contains at least $|S|n+ \Omega(\sqrt{k})$…
We give a one-sentence proof of McLaughlin and Rundell's inverse uniqueness theorem.
In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.
Assuming the abc conjecture with $\epsilon=1/6$, we use elementary methods to show that only finitely many $s$-Cullen numbers are repunits, aside from two known infinite families. More precisely, only finitely many positive integers $s$,…
Gives a short proof of Dehornoy's latest result. The same simple argument (and more) was discovered by Laver's student Larue.
We show that Generic Green's conjecture holds for generic binary curves, through a detailed analysis of the family of scrolls containing fixed rational normal curves.
The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the 1D lattice random walk in discrete time. We determine the survival probability of the random walker in…
We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z^d that is an extension of a result of Bolthausen, Sznitman and Zeitouni (2003). We use this result, along with the lace expansion for…
Monogamy of entanglement means that an entangled state cannot be shared with many parties. The more parties, the less entanglement between them. In this paper, we give a simple proof of this property and provide an upper bound of the number…
We provide a short proof of the 1-dimensional flat chain conjecture.
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
There is no trivial mathematics, there are only trivial mathematicians! A mathematician is trivial if he or she believes that there exists trivial mathematics. Being a non-trivial mathematician myself, I will describe ten different proofs…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.