172 citations · 846 across the 36 of their papers we have counts for
42 papers
Learning Topological Features of -invariants
Brandon Robinson, Shimal Harichurn, Fabian Ruehle +3
Machine learning and data analysis techniques have recently emerged as powerful tools for identifying patterns and formulating conjectures in mathematical research, most notably in…
Class Numbers, Congruent Numbers and Umbral Moonshine
Miranda C. N. Cheng, John F. R. Duncan, Michael H. Mertens
In earlier work we initiated a program to study relationships between finite groups and arithmetic geometric invariants of modular curves in a systematic way. In the present work w…
Quantum Modular -Invariants
Miranda C. N. Cheng, Ioana Coman, Davide Passaro +1
We study the quantum modular properties of -invariants of closed three-manifolds. Higher depth quantum modular forms are expected to play a central role for general…
Learning Lattice Quantum Field Theories with Equivariant Continuous Flows
Mathis Gerdes, Pim de Haan, Corrado Rainone +2
We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer a…
Class Numbers, Cyclic Simple Groups and Arithmetic
Miranda C. N. Cheng, John F. R. Duncan, Michael H. Mertens
Here we initiate a program to study relationships between finite groups and arithmetic-geometric invariants in a systematic way. To do this we first introduce a notion of optimal m…
Cone Vertex Algebras, Mock Theta Functions, and Umbral Moonshine Modules
Miranda C. N. Cheng, Gabriele Sgroi
We describe a family of indefinite theta functions of signature that can be expressed in terms of trace functions of vertex algebras built from cones in lattices. The famil…
3-Manifolds and VOA Characters
Miranda C. N. Cheng, Sungbong Chun, Boris Feigin +4
By studying the properties of -series -invariants, we develop a dictionary between 3-manifolds and vertex algebras. In particular, we generalize previously known ent…
Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows
Pim de Haan, Corrado Rainone, Miranda C. N. Cheng +1
We propose a continuous normalizing flow for sampling from the high-dimensional probability distributions of Quantum Field Theories in Physics. In contrast to the deep architecture…
Entangled q-Convolutional Neural Nets
Vassilis Anagiannis, Miranda C. N. Cheng
We introduce a machine learning model, the q-CNN model, sharing key features with convolutional neural networks and admitting a tensor network description. As examples, we apply q-…
Vertex operator superalgebra/sigma model correspondences: The four-torus case
Vassilis Anagiannis, Miranda C. N. Cheng, John Duncan +1
We propose a correspondence between vertex operator superalgebras and families of sigma models in which the two structures are related by symmetry properties and a certain reflecti…
Modular Exercises for Four-Point Blocks -- I
Miranda C. N. Cheng, Terry Gannon, Guglielmo Lockhart
The well-known modular property of the torus characters and torus partition functions of (rational) vertex operator algebras (VOAs) and 2d conformal field theories (CFTs) has been…
Three-Manifold Quantum Invariants and Mock Theta Functions
Miranda C. N. Cheng, Francesca Ferrari, Gabriele Sgroi
Mock modular forms have found applications in numerous branches of mathematical sciences since they were first introduced by Ramanujan nearly a century ago. In this proceeding we h…
Covariance in Physics and Convolutional Neural Networks
Miranda C. N. Cheng, Vassilis Anagiannis, Maurice Weiler +3
In this proceeding we give an overview of the idea of covariance (or equivariance) featured in the recent development of convolutional neural networks (CNNs). We study the similari…
3d Modularity
Miranda C. N. Cheng, Sungbong Chun, Francesca Ferrari +2
We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d theories where such str…
TASI Lectures on Moonshine
Vassilis Anagiannis, Miranda C. N. Cheng
The word moonshine refers to unexpected relations between the two distinct mathematical structures: finite group representations and modular objects. It is believed that the key to…
K3 Elliptic Genus and an Umbral Moonshine Module
Vassilis Anagiannis, Miranda C. N. Cheng, Sarah M. Harrison
Umbral moonshine connects the symmetry groups of the 23 Niemeier lattices with 23 sets of distinguished mock modular forms. The 23 cases of umbral moonshine have a uniform relation…
Attractive Strings and Five-Branes, Skew-Holomorphic Jacobi Forms and Moonshine
Miranda C. N. Cheng, John F. R. Duncan, Sarah M. Harrison +3
We show that certain BPS counting functions for both fundamental strings and strings arising from fivebranes wrapping divisors in Calabi--Yau threefolds naturally give rise to skew…
Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules
Miranda C. N. Cheng, John F. R. Duncan
In this work we consider an association of meromorphic Jacobi forms of half-integral index to the pure D-type cases of umbral moonshine, and solve the module problem for four of th…
Weight One Jacobi Forms and Umbral Moonshine
Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey
We analyze holomorphic Jacobi forms of weight one with level. One such form plays an important role in umbral moonshine, leading to simplifications of the statements of the umbral…
K3 String Theory, Lattices and Moonshine
Miranda C. N. Cheng, Sarah M. Harrison, Roberto Volpato +1
In this paper we address the following two closely related questions. First, we complete the classification of finite symmetry groups of type IIA string theory on $K3\times \mathbb…
Generalised Umbral Moonshine
Miranda C. N. Cheng, Paul de Lange, Daniel P. Z. Whalen
Umbral moonshine describes an unexpected relation between 23 finite groups arising from lattice symmetries and special mock modular forms. It includes the Mathieu moonshine as a sp…
Optimal Mock Jacobi Theta Functions
Miranda C. N. Cheng, John F. R. Duncan
We classify the optimal mock Jacobi forms of weight one with rational coefficients. The space they span is thirty-four-dimensional, and admits a distinguished basis parameterized b…
Landau-Ginzburg Orbifolds and Symmetries of K3 CFTs
Miranda C. N. Cheng, Francesca Ferrari, Sarah M. Harrison +1
Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite sym…
Equivariant K3 Invariants
Miranda C. N. Cheng, John F. R. Duncan, Sarah M. Harrison +1
In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the in…