Related papers: Effective constructions in plethysms and Weintraub…

We propose a conjectural extension to positive characteristic case of a well known Deligne's theorem on the existence of super fiber functors. We prove our conjecture in the special case of semisimple categories with finitely many…

We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at…

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

In this article, stimulated by the effectiveness in Berndtsson's solution of the openness conjecture and continuing our solution of Demailly's strong openness conjecture, we discuss conditions to guarantee the effectiveness of the…

Mekler's construction is a powerful technique for building purely algebraic structures from combinatorial ones. Its power lies in the fact that it allows various model-theoretic tameness properties of the combinatorial structure to transfer…

In this paper we describe a general strategy for approaching the Weinstein conjecture in dimension three. We apply this approach to prove the Weinstein conjecture for a new class of contact manifolds (planar contact manifolds). We also…

We study semigroup algebras arising from lattice polytopes, compute their volume polynomials (particularizing work of Hochster), and establish strong Lefschetz properties (generalizing work of the first three authors). This resolves several…

Beginning from the resolution of the Dirichlet L function, using the inner product formula between two infinite-dimensional vectors in the complex space, the author proved the baffling problem--Hecke conjecture.

We prove a conjectured relationship among resultants and the determinants arising in the formulation of the method of moving surfaces for computing the implicit equation of rational surfaces formulated by Sederberg. In addition, we extend…

Instead of dealing with cumbersome binomial identities, we prove Callan's result using generating functions.

We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic…

Let F and G be homogeneous polynomials in disjoint sets of variables. We prove that the Waring rank is additive, thus proving the symmetric Strassen conjecture, when either F or G is a power, or F and G have two variables, or either F or G…

We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.

Using results of Hironaka-Matsumura and Faltings, we prove a strong version of the well known Fulton-Hansen connectivity theorem for weighted projective spaces. As a consequence we get the following result. If $Y$ is an irreducible…

Plethysm coefficients $\mathsf{a}_{\mu[\nu]}^\lambda$ are the structure coefficients of the plethysm of Schur functions $s_\mu[s_\nu] = \sum_{\lambda} \mathsf{a}_{\mu[\nu]}^\lambda s_\lambda$. We study a bivariate generating function of…

We describe a new method for constructing a weight structure $w$ on a triangulated category $C$. For a given $C$ and $w$ it allow us to give a fairly comprehensive (and new) description of those triangulated categories consisting of…

We construct explicit resolutions of Weyl modules by divided powers and of co-Specht modules by permutational modules. We also prove a conjecture of Boltje-Hartmann on resolutions of co-Specht modules.

We show that under mild hypotheses on a proper algebraic space $X$, the functors of taking its symmetric powers and its \'{e}tale realisation commute up to weak equivalence. We conclude an effective version of the Dold-Thom theorem for the…

We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…

A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…