Related papers: Estimating Reeb chords using microlocal sheaf theo…

We give a uniform lower bound for the polynomial complexity of all Reeb flows on the spherization (S*M,\xi) over a closed manifold. Our measure for the dynamical complexity of Reeb flows is slow volume growth, a polynomial version of…

Let $f:\, S \to B$ be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus $g\geq 2$ with relative irregularity $q_f$. We show a sharp lower bound on the slope $\lambda_f$ of $f$. As a consequence, we prove a…

Given a projective morphism $f:X\to Y$ from a complex space to a complex manifold, we prove the Griffiths semi-positivity and minimal extension property of the direct image sheaf $f_\ast(\mathscr{F})$. Here, $\mathscr{F}$ is a coherent…

To fix the bundle moduli of a heterotic compactification one has to understand the Pfaffian one-loop prefactor of the classical instanton contribution. For compactifications on elliptically fibered Calabi-Yau spaces X this can be made…

We give an algorithm to determine whether a kernel sheaf over a smooth projective curve over an algebraically closed field is semistable. The algorithm uses symmetric powers to make destabilizing subbundles visible as global sections.

A slice distance for the class of weak abelian Lp-bundles in 3 dimensions was introduced in a previous article in collaboration with Tristan Rivi\`ere, where it was used to prove the closure of such class of bundles for the weak…

In this article it is shown that the equilateral triangle maximizes the Cheeger constant and minimizes the torsional rigidity among shapes having a fixed minimal width. The proof techniques use direct comparisons with simpler shapes,…

Let $\Lambda$ be a link of Legendrian spheres in the boundary of a subcritical $2n$-dimensional Weinstein manifold $X$. We show that, under some geometrical assumptions, the computation of the Legendrian contact homology of $\Lambda$ can be…

We give a procedure to ``average'' canonically $C^1$-close Legendrian submanifolds of contact manifolds. As a corollary we obtain that, whenever a compact group action leaves a Legendrian submanifold almost invariant, there is an invariant…

We derive new estimates for the first Betti number of compact Riemannian manifolds. Our approach relies on the Birman-Schwinger principle and Schatten norm estimates for semigroup differences. In contrast to previous works we do not require…

In these notes a recently developed technique for the computation of line bundle-valued sheaf cohomology group dimensions on toric varieties is reviewed. The key result is a vanishing theorem for the contributing components which depends on…

Using the microlocal theory of sheaves, we associate a category to each Weinstein manifold. By constructing a microlocal specialization functor, we show that exact Lagrangians give objects in our category, and that the category is invariant…

An important classification problem in Algebraic Geometry deals with pairs $(\E,\phi)$, consisting of a torsion free sheaf $\E$ and a non-trivial homomorphism $\phi\colon (\E^{\otimes a})^{\oplus b}\lra\det(\E)^{\otimes c}\otimes \L$ on a…

In this note, (rational) Betti numbers of homotopy colimits for toric diagrams and their classifying spaces are described in terms of sheaf cohomology over CW posets. We prove for any $T$-diagram $D$ over any CW poset that…

We prove a criterion for the existence of harmonic metrics on Higgs bundles that are defined on smooth loci of klt varieties. As one application, we resolve the quasi-etale uniformisation problem for minimal varieties of general type to…

Viterbo has conjectured that any Lagrangian in the unit co-disc bundle of a torus which is Hamiltonian isotopic to the zero-section satisfies a uniform bound on its spectral norm; a recent result by Shelukhin showed that this is indeed the…

We prove that the generic fibre of the Betti moduli space associated to any of the ten Painlev\'e equations coincides with the result of attaching Weinstein handles along the Stokes Legendrian, and provide Weinstein handlebody diagrams for…

In this paper we study the growth rate of a version of Legendrian contact homology, which we call strip Legendrian contact homology, in 3-dimensional contact manifolds and its relation to the topological entropy of Reeb flows. We show that:…

In this article, we first classify Legendrian self-shrinkers in $\mathbb{R}% ^{3}$ and $\mathbb{R}^{5}$. We then proved a Legendrian rigidity theorem, which can be regarded as an analogue of the result of Li-Wang \cite{lw}. More precisely,…

Lurie's theorem states that there exists a sheaf of ring spectra on the site of formally \'etale Deligne--Mumford stacks over the moduli stack of $p$-divisible groups of height $n$, which agrees with the classical Landweber exact functor…