Gnedin, Alexander Gorin, Vadim Kerov, Sergei
Published in
Journal of Algebraic Combinatorics

A block character of a finite symmetric group is a positive definite function which depends only on the number of cycles in a permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the characters to descent representations and the coinvariant algebra of \documentclass[12pt]{minimal} \usepackage{...

Maulik, Davesh Toda, Yukinobu
Published in
Inventiones mathematicae

In this paper, we propose an ansatz for defining Gopakumar–Vafa invariants of Calabi–Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem–Li, which is itself based on earlier ideas of Hosono–Saito–Takahashi. We conjecture that these invariants are equivalent to other curve-counting ...

Graham, C.Robin Lee, John M
Published in
Advances in Mathematics

Patakfalvi, Zsolt
Published in
Advances in Mathematics

We prove Viehwegʼs hyperbolicity conjecture over compact bases and over bases with non-uniruled compactification. The most general case of the conjecture states that the base space of a maximal variation family of smooth projective manifolds with semi-ample canonical sheaf is of log-general type.

Colding, Tobias Holck Naber, Aaron
Published in
Geometric and Functional Analysis

Consider a limit space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(M_\alpha,g_\alpha,p_\alpha)\stackrel{GH}{\rightarrow} (Y,d_Y,p)}$$\end{document}, where the \do...

Gilkey, Peter B
Published in
Advances in Mathematics

Kokarev, Gerasim
Published in
Advances in Mathematics

We study the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces. We describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations. The principal results include the general regularity properties of ...

Khovanova, Tanya
Published in
The Mathematical Intelligencer

I present and discuss a puzzle about wizards invented by John H. Conway.

Delaunay, Christophe Jouhet, Frédéric
Published in
Advances in Mathematics

The main aim of this article is to compute all the moments of the number of pℓ-torsion elements in some type of finite abelian groups. The averages involved in these moments are those defined for the Cohen–Lenstra heuristics for class groups and their adaptation for Tate–Shafarevich groups. In particular, we prove that the heuristic model for Tate–...

Felikson, Anna Shapiro, Michael Tumarkin, Pavel
Published in
Advances in Mathematics

We construct geometric realizations for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston [10] to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute the growth rate of these cluster algebras, provide the positivit...