Related papers: On the DDVV Conjecture and the Comass in Calibrate…

A special class of solutions to the generalised WDVV equations related to a finite set of covectors is investigated. Some geometric conditions on such a set which guarantee that the corresponding function satisfies WDVV equations are found…

We prove the famous Faber intersection number conjecture and other more general results by using a recursion formula of $n$-point functions for intersection numbers on moduli spaces of curves. We also present some vanishing properties of…

The coarse geometric Novikov conjecture provides an algorithm to determine when the higher index of an elliptic operator on a noncompact space is nonzero. The purpose of this paper is to prove the coarse geometric Novikov conjecture for…

We provide a representation of the (signed) BMV-measure by stochastic means and prove positivity of the respective measures in dimension $d=3$ in several non-trivial cases by combinatorial methods.

The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.

We prove a conjecture of Roe by constructing unified warped cones that violate the coarse Baum-Connes conjecture. Interestingly, the reason for this is probably not what Roe expected, as the obstruction arises in odd rather than even…

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

We introduce the concepts of an amazing hypercube decomposition and a double shortcut for it, and use these new ideas to formulate a conjecture implying the Combinatorial Invariance Conjecture of the Kazhdan--Lusztig polynomials for the…

We prove that Alexandrov's conjecture relating the area and diameter of a convex surface holds for the surface of a general ellipsoid. This is a direct consequence of a more general result which estimates the deviation from the optimal…

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, contrary to small deviationresults. In this note we present a novel application of a smalldeviations inequality to a problem related to the diameters of…

We introduce two valuation-based deviations on convex bodies. Using a construction that allows us to associate to these deviations "intrinsic" pseudometrics, we establish various results which capture information about the underlying…

This is the last in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…

In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.

The conjectures of Manin and Peyre are confirmed for a certain threefold.

In this paper, we show that the derivative of the genus-1 Virasoro conjecture for Gromov-Witten invariants along the direction of quantum volume element holds for all smooth projective varieties. This result provides new evidence for the…

We prove an existence theorem for convex hypersurfaces of prescribed Gauss curvature in the complement of a compact set in Euclidean space which are close to a cone.

This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.