6 papers
The Sharp Edges of Calabi-Yau Manifolds: Designing Symmetric Models for Ricci-flat Metrics
Viktor MirjaniÄ, Challenger Mishra
Computing Ricci-flat metrics on Calabi-Yau manifolds is challenging since no closed-form solutions are known. However, these computations are needed in order to make physical predi…
A Matter of Interest: Understanding Interestingness of Math Problems in Humans and Language Models
Shubhra Mishra, Yuka Machino, Gabriel Poesia +9
The evolution of mathematics is shaped importantly by interestingness: researchers choose which problems to pursue, and students choose which problems to engage with, based on expe…
Discovering mathematical concepts through a multi-agent system
Daattavya Aggarwal, Oisin Kim, Carl Henrik Ek +1
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model…
Calabi-Yau metrics through Grassmannian learning and Donaldson's algorithm
Carl Henrik Ek, Oisin Kim, Challenger Mishra
Motivated by recent progress in the problem of numerical Kähler metrics, we survey machine learning techniques in this area, discussing both advantages and drawbacks. We then revi…
A remark on weighted average multiplicities in prime factorisation
Viktor MirjaniÄ, Daattavya Aggarwal, Challenger Mishra
We study a generalisation of the quality of an ABC triple that we call the weighted average multiplicity (WAM), in which the logarithmic heights of prime factors are raised to a co…
Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces
Viktor MirjaniÄ, Challenger Mishra
Ever since Yau's non-constructive existence proof of Ricci-flat metrics on Calabi-Yau manifolds, finding their explicit construction remains a major obstacle to development of both…