Goins, Edray Iga, Kevin Kostiuk, Jordan Stiffler, Kory

An ordering of colours in an Adinkra leads to an embedding of this Adinkra into a Riemann surface $X$, and a branched covering map $\beta_X:X\to\mathbb{CP}^1$. This paper shows how the dashing of edges in an Adinkra determines a signed permutation version of the monodromy group, and shows that it is isomorphic to a Salingaros Vee group.

Johnson-Freyd, Theo

We classify $N{=}1$ SVOAs with no free fermions and with bosonic subalgebra a simply connected WZW algebra which is not of type $\mathrm{E}$. The latter restriction makes the classification tractable; the former restriction implies that the $N{=}1$ automorphism groups of the resulting SVOAs are finite. We discover two infinite families and nine exc...

Taormina, Anne Wendland, Katrin

The conformal field theoretic elliptic genus, an invariant for N=(2,2) superconformal field theories, counts the BPS states in any such theory with signs, according to their bosonic or fermionic nature. For K3 theories, this invariant is the source of the Mathieu Moonshine phenomenon. There, the net number of quarter BPS states is positive for any ...

Borsten, L. Duff, M. J. Fernández-Melgarejo, J. J. Marrani, A. Torrente-Lujan, E.
Published in
Journal of High Energy Physics

We study General Freudenthal Transformations (GFT) on black hole solutions in Einstein-Maxwell-Scalar (super)gravity theories with global symmetry of type E7. GFT can be considered as a 2-parameter, a, b ∈ ℝ, generalisation of Freudenthal duality: x→xF=ax+bx˜\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfont...

Borinsky, Michael Vogtmann, Karen

We prove that the rational Euler characteristic of $\operatorname{Out}(F_n)$ is always negative and its asymptotic growth rate is $\Gamma(n- \frac32)/\sqrt{2\pi} \log^2 n$. This settles a 1987 conjecture of J. Smillie and the second author. We establish connections with the Lambert $W$-function and the zeta function.

Bambozzi, Federico Murro, Simone

Given an abelian group G endowed with a T-pre-symplectic form, we assign to it a symplectic twisted group *-algebra W_G and then we provide criteria for the uniqueness of states invariant under the ergodic action of the symplectic group of automorphism. As an application, we discuss the notion of natural states in quantum abelian Chern-Simons theor...

Kapovich, Michael Liu, Beibei

In this paper, we generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2,C) to geometrically infinite discrete subgroups Γ of isometries of negatively pinched Hadamard manifolds X. We then generalize a theorem of Bishop to prove that every discrete geometrically infinite isometry subgroup Γ has a se...

Bridson, MR Evans, DM Liebeck, MW Segal, D

He, Yang-Hui Kim, Minhyong

We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Using finite groups and finite rings as a concrete playground, we find that questions such as identification of simple groups by "looking" at the Cayley table or correctly mat...

Dey, Subhadip Kapovich, Michael

We extend several notions and results from the classical Patterson-Sullivan theory to the setting of Anosov subgroups of higher rank semisimple Lie groups, working primarily with invariant Finsler metrics on associated symmetric spaces. In particular, we prove the equality between the Hausdorff dimensions of flag limit sets, computed with respect t...