Related papers: Nine-dimensional exceptional quotient singularitie…

We show that there is a strong minimal pair in the computably enumerable Turing degrees.

In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.

We prove a result on the existence of linear forms of a given Diophantine type.

We prove that solutions to elliptic equations in two variables in divergence form, possibly non-selfadjoint and with lower order terms, satisfy the strong unique continuation property.

We study special unipotent representations attached to complex exceptional Richardson orbits. As a consequence, we verify a conjecture of Achar and Sommers for these orbits.

We study nonnegative (psd) real sextic forms $q(x_0,x_1,x_2)$ that are not sums of squares (sos). Such a form has at most ten real zeros. We give a complete and explicit characterization of all sets $S\subset\mathbb{P}^2(\mathbb{R})$ with…

An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their…

In this note, we give a new nonexistence result of ternary extremal self-dual codes.

We study the singularities of the projective dual variety.

We announce the existence and uniqueness theorem for the scattering problem of three one-dimensional quantum particles interacting by repulsive finite pair potentials

We prove a curious identity for the Bernoulli numbers.

We prove that singularities of area minimizing hypersurfaces can be perturbed away in ambient dimensions 9 and 10.

We prove Manin's conjecture over imaginary quadratic number fields for a cubic surface with a singularity of type E_6.

We review exceptional field theories as the duality-covariant reformulation of maximal supergravity theories in ten and eleven dimensions, that make the underlying exceptional symmetries explicit. Beyond their structural role in unifying…

In this paper we study the local behavior of a solution to second order elliptic operators with sharp singular coefficients in lower order terms. One of the main results is the bound on the vanishing order of the solution, which is a…

A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…

We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.

We introduce and study the maximal unipotent finite quotient for algebraic group schemes in positive characteristics. Applied to Picard schemes, this quotient encodes unusual torsion. We construct integral Fano threefolds where such unusual…

We consider a surface that admits a $\mathbb{Q}$-Gorenstein degeneration to a cyclic quotient singularity $\frac{1}{dn^2}(1,dna-1)$. Under several technical assumptions, we construct $d$ exceptional vector bundles of rank $n$ which are…

This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.