Related papers: A Lower Bound for the Large Sieve with Square Modu…

In this note we provide several lower bounds for the volume of a geodesic ball within the injectivity radius in a $3$-dimensional Riemannian manifold assuming only upper bounds for the Ricci curvature.

We study the average size of shifted convolution summation terms related to the problem of Quantum Unique Ergodicity on ${\rm SL}_2 (\mathbbm{Z})\backslash \mathbbm{H}$. Establishing an upper-bound sieve method for handling such sums, we…

We give a lower bound for the degree of a finite cover of a hyperbolic 3-manifold which fibers over the circle, in terms of volume, the diameter of the manifold and other new invariants.

For $G$ a complex reductive group and $B \subseteq G$ a Borel subgroup, we provide a reduction rule for certain weight multiplicities in Demazure modules $V_\lambda^w$: given a weight $\mu$ on a face of the associated weight polytope…

We prove, under suitable conditions, that there exist wall-crossing and reduction morphisms for moduli spaces of stable log pairs in all dimensions as one varies the coefficients of the divisor.

We extend the littlest modular seesaw to a Grand Unified scenario based on $SU(5)$ endowed with three modular $S_4$ symmetries. We leverage symmetry protected zeroes in the leptonic and down quark sectors to suppress deviations to the…

We present a new proof of the "arithmetic" large sieve inequality, starting from the corresponding "harmonic" inequality, which is based on an amplification idea. We show that this also adapts to give some new sieve inequality for modular…

In this article we give a proof of Serre's conjecture for the case of odd level and arbitrary weight. Our proof does not depend on any generalization of Kisin's modularity lifting results to characteristic 2 (moreover, we will not consider…

The result in the title is proven, using the Selberg estimate on the leading eigenvalue of the non-Euclidean Laplacian, and the method of conformal volumes of Li and Yau.

We present an explicit method to produce upper bounds for the dimension of the moduli spaces of complete integral Gorenstein curves with prescribed symmetric Weierstrass semigroups.

It is proved that uniformly bounded simple modules over higher rank super-Virasoro algebras are modules of the intermediate series, and that simple modules with finite dimensional weight spaces are either modules of the intermediate series…

For three dimensional complete Riemannian manifolds with scalar curvature no less than one, we obtain the sharp upper bound of complete stable minimal surfaces' diameter.

We give a lower bound on the Ulrich complexity of hypersurfaces of dimension $n \ge 6$. The bound improves the result in [BES] for $n \le 78$.

This is an addendum to the paper of Braun and Fl{\o}ystad ([BF]) on the bound for the degree of a smooth surface in $\pfour$ not of general type. Using their construction and the regularity of curves in $\pthree$, one may lower the bound a…

We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.

We show that the Hodge filtration of a tempered Hodge module is generated by the lowest piece of its Hodge filtration. As a consequence, we prove the main conjecture of [SV] in the special case of tempered representations of real reductive…

We provide a bound on the dimension of Schur multiplier of a finite dimensional nilpotent Lie superalgebra which is more precise than the previous bounds on the dimension of Schur multiplier of Lie superalgebra.

We find the exact lower bound of the discrepancy of shifted Niedereiter's sequences.

We prove a new lower bound for the Frobenius norm of the inverse of an non-negative matrix. This bound is only a modest improvement over previous results, but is sufficient for fully resolving a conjecture of Harwitz and Sloane, commonly…

In this paper we study the sections of the canonical line bundle on the moduli space of parabolic semistable vector bundles with trivial determinant and fixed parabolic structure of type $\underline{\lambda}=(\lambda_1,..., \lambda_s)$…