Related papers: A finiteness theorem for low-codimensional nonsing…
We study subvarieties of very general complete intersections $X\subset \mathbb{P}^n$ of multidegree $(d_1,\dots,d_c)$, when $d:= d_1+\dots +d_c$ is sufficiently large. In a seminal paper Ein proved that if $d\geq 2n-c-k+2$, any…
A $\lambda$-quiddity of size $n$ is an $n$-tuple of elements from a fixed set, which is a solution to a matrix equation that arises in the study of Coxeter's friezes. The study of these solutions involves in particular the use of a notion…
Family puzzle asks why the Standard Model (SM) features exactly 3 families of quarks and leptons. Motivated by topological constraints, we study 4-dimensional fermionic anomalies with discrete $Z_n$ symmetry, classified by the 5d spin…
A conjecture of Coleman implies that only finitely many quaternion algebras over the rational numbers can be the endomorphism $\mathbf{Q}$-algebras of abelian surfaces over the complex numbers which can be defined over $\mathbf{Q}$. One may…
We describe several families of non-unitary coset conformal field theories that possess truly marginal couplings. These generalize the known examples of Wess-Zumino-Witten models on supergroups such as PSU(n|n) or OSP(2n+2|2n). Our…
In this paper we consider genus one equations of degree n, namely a (generalised) binary quartic when n = 2, a ternary cubic when n = 3, and a pair of quaternary quadrics when n = 4. A new definition for the minimality of genus one…
We prove that there are only finitely many isoparametrically foliated closed connected Riemannian manifolds with bounded geometry, fixed dimension $n\neq5$, and finite fundamental group, up to foliated diffeomorphism. In addition, we…
Let $X$ be a connected component of the maximal orthogonal grassmannian of a generic $n$-dimensional quadratic form $q$ with trivial Clifford invariant. Consider the canonical epimorphism $\phi$ from the Chow ring of $X$ to the associated…
In this paper we provide a criteria for geometric finiteness of Kleinian groups in general dimension. We formulate the concept of conformal finiteness for Kleinian groups in space of dimension higher than two, which generalizes the notion…
In recent years, several efforts have focused on identifying new families of scattered polynomials. Currently, only three families in $\mathbb{F}_{q^n}[X]$ are known to exist for infinitely many values of $n$ and $q$: (i) pseudoregulus-type…
We study $\mathbb{Z}_2$-graded identities of Lie superalgebras of the type $b(t), t\ge 2$, over a field of characteristic zero. Our main result is that the $n$-th codimension is strictly less than $(\dim b(t))^n$ asymptotically. As a…
Assuming the weak Bombieri-Lang conjecture, we prove that a generalization of Hilbert's irreducibility theorem holds for families of geometrically mordellic varieties (for instance, families of hyperbolic curves). As an application we prove…
We explore a continuum of observably and usefully inequivalent, finite-dimensional off-shell representations of worldline N=4-extended supersymmetry, differing from one another only in the value of a "tuning parameter." Their dynamics turns…
In this article we show that non-singular quadrics and non-singular Hermitian varieties are completely characterized by their intersection numbers with respect to hyperplanes and spaces of codimension 2. This strongly generalizes a result…
The class of Riemannian orbifolds of dimension n defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many members up to orbifold homeomorphism. Furthermore, any class of…
We prove lower bounds on the density of regular minimal cones of dimension less than seven provided the complements of the cones are topologically nontrivial.
Motivated by recent work of Lawrence-Venkatesh and Lawrence-Sawin, we show that non-isotrivial families of subvarieties in abelian varieties have big monodromy when twisted by generic rank one local systems. While Lawrence-Sawin discuss the…
In 1983 Silverman and Tate showed that the set of points in a 1-dimensional family of abelian varieties where a section of infinite order has `small height' is finite. We conjecture a generalisation to higher-dimensional families, where we…
We prove the existence of a family of non-trivial solutions of the Liouville equation in dimensions two and four with infinite volume. These solutions are perturbations of a finite-volume solution of the same equation in one dimension less.…
We show that the third cohomology of the finite general linear group $GL_6(\mathbb{F}_2)$ with trivial mod 2 coefficients is non-zero. The necessarily unique non-trivial element restricts to the third Milgram-Priddy class.