Related papers: An introduction to Geometric Manin's conjecture
Here we examine some connections between the notions of generalized arithmetic means, geodesics, Lagrange-Hamilton dynamics and Bregman divergences. In a previous paper we developed a predictive interpretation of generalized arithmetic…
In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
We study weak approximation and the Hilbert property for Campana points, both of importance in recent work on a Manin-type conjecture by Pieropan, Smeets, Tanimoto and Varilly-Alvarado. We show that weak weak approximation implies the…
We prove the Halo conjecture on the geometry of the eigencurve over the boundary of the weight space, predicted by Coleman-Mazur and Buzzard-Kilford.
Two conjectures recently proposed by one of the authors are disproved
A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.
In this paper we consider some possible approaches to the proof of the Riemann Hypothesis using the Li criterion.
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…
Geometric complexity theory (GCT) is an approach to the $P$ vs. $NP$ and related problems. A high level overview of this research plan and the results obtained so far was presented in a series of three lectures in the Institute of Advanced…
GKM theory is a powerful tool in equivariant topology and geometry that can be used to generalize classical ideas from (quasi)toric manifolds to more general torus actions. After an introduction to the topic this survey focuses on recent…
We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.
In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary $N\in \N$ and for {\it number fields}. The main new observation is a modification of a theorem due to Glenn Stevens for the…
The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan…
Geometrically convex functions constitute an interesting class of functions obtained by replacing the arithmetic mean with the geometric mean in the definition of convexity. As recently suggested, geometric convexity may be a sensible…
Geometric lower and upper estimates are obtained for invariant metrics on $\Bbb C$-convex domains containing no complex lines.
Gaussian correlation conjecture states that the Gaussian measure of the intersection of two symmetric convex sets is greater or equal to the product of the measures.
In this paper the circulant Hadamard conjecture is proved.
In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also…