Using a certain well-posed ODE problem introduced by Shilnikov in the sixties, Minervini proved the currential “fundamental Morse equation” of Harvey–Lawson but without the restrictive tameness condition for Morse gradient flows. Here, we construct l…
To each automorphism of a spherical building, there is a naturally associated opposition diagram, which encodes the types of the simplices of the building that are mapped onto opposite simplices. If no chamber (that is, no maximal simplex) of the bui…
Let G be a connected reductive group over a p-adic number field F. We propose and study the notions of G–modules and G–modules over the Robba ring, which are exact faithful F-linear tensor functors from the category of G-representations on finite-dim…
What is the maximum number of copies of a fixed forest T in an n-vertex graph in a graph class as ? We answer this question for a variety of sparse graph classes . In particular, we show that the answer is where is the size of the largest stable set…
Let be a finite Galois extension of p-adic number fields, and let be an r-dimensional unramified representation of the absolute Galois group , which is the restriction of an unramified representation . In this paper, we consider the -equivariant loca…
For a smooth strongly convex Minkowski norm , we study isometries of the Hessian metric corresponding to the function . Under the additional assumption that F is invariant with respect to the standard action of , we prove a conjecture of Laugwitz state…
Involution Schubert polynomials represent cohomology classes of K-orbit closures in the complete flag variety, where K is the orthogonal or symplectic group. We show they also represent -equivariant cohomology classes of subvarieties defined by upper-l…
Immanants are functions on square matrices generalizing the determinant and permanent. Kazhdan–Lusztig immanants, which are indexed by permutations, involve
specializations of Type A Kazhdan–Lusztig polynomials, and were defined by Rhoades and …
We prove -boundedness of oscillating multipliers on symmetric spaces of noncompact type of arbitrary rank, as well as on a wide class of locally symmetric spaces.
For fixed , consider the set of dilated squares modulo . Rudnick and Sarnak conjectured that, for Lebesgue, almost all such the gap-distribution of is consistent with the Poisson model (in the limit as N tends to infinity). In this paper, we prove …