87 citations · 259 across the 22 of their papers we have counts for
23 papers
A finite arithmetic form of Robin's inequality and its equivalence to the Riemann hypothesis
Challenger Mishra, Rahul Sarkar
Robin's inequality reformulates the Riemann hypothesis as a bound on the sum-of-divisors function . We introduce a finite-truncation version of Robin's inequality determined int…
Balanced Metrics Know About SYZ
Per Berglund, Tristan Hübsch, Vishnu Jejjala +2
Numerical Ricci-flat metrics on Calabi-Yau manifolds are becoming increasingly accurate. However, they often lack the interpretability required to extract theoretical insights. In…
Hermitian Yang--Mills connections on general vector bundles: geometry and physical Yukawa couplings
Challenger Mishra, Justin Tan
We compute solutions to the Hermitian Yang-Mills equations on holomorphic vector bundles via an alternating optimisation procedure founded on geometric machine learning. The pr…
cymyc -- Calabi-Yau Metrics, Yukawas, and Curvature
Per Berglund, Giorgi Butbaia, Tristan Hübsch +4
We introduce \texttt{cymyc}, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associate…
Precision String Phenomenology
Per Berglund, Giorgi Butbaia, Tristan Hübsch +4
Calabi--Yau compactifications of the heterotic string provide a promising route to recovering the four-dimensional particle physics described by the Standard Model.…
Physical Yukawa Couplings in Heterotic String Compactifications
Giorgi Butbaia, Damián Mayorga Peña, Justin Tan +4
One of the challenges of heterotic compactification on a Calabi-Yau threefold is to determine the physical Yukawa couplings of the resulting four-dimensional $\ma…
Learning to be Simple
Yang-Hui He, Vishnu Jejjala, Challenger Mishra +1
In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite s…
Mathematical conjecture generation using machine intelligence
Challenger Mishra, Subhayan Roy Moulik, Rahul Sarkar
Conjectures have historically played an important role in the development of pure mathematics. We propose a systematic approach to finding abstract patterns in mathematical data, i…
A physics-informed search for metric solutions to Ricci flow, their embeddings, and visualisation
Aarjav Jain, Challenger Mishra, Pietro Liò
Neural networks with PDEs embedded in their loss functions (physics-informed neural networks) are employed as a function approximators to find solutions to the Ricci flow (a curvat…
Machine Learned Calabi-Yau Metrics and Curvature
Per Berglund, Giorgi Butbaia, Tristan Hübsch +4
Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural…
Machine Learning for Optical Motion Capture-driven Musculoskeletal Modelling from Inertial Motion Capture Data
Abhishek Dasgupta, Rahul Sharma, Challenger Mishra +1
Marker-based Optical Motion Capture (OMC) systems and associated musculoskeletal (MSK) modelling predictions offer non-invasively obtainable insights into in vivo joint and muscle…
Neural Network Approximations for Calabi-Yau Metrics
Vishnu Jejjala, Damian Kaloni Mayorga Pena, Challenger Mishra
Ricci flat metrics for Calabi-Yau threefolds are not known analytically. In this work, we employ techniques from machine learning to deduce numerical flat metrics for the Fermat qu…
Baryons from Mesons: A Machine Learning Perspective
Yarin Gal, Vishnu Jejjala, Damian Kaloni Mayorga Pena +1
Quantum chromodynamics (QCD) is the theory of the strong interaction. The fundamental particles of QCD, quarks and gluons, carry colour charge and form colourless bound states at l…
Getting CICY High
Kieran Bull, Yang-Hui He, Vishnu Jejjala +1
Supervised machine learning can be used to predict properties of string geometries with previously unknown features. Using the complete intersection Calabi-Yau (CICY) threefold dat…
Machine Learning CICY Threefolds
Kieran Bull, Yang-Hui He, Vishnu Jejjala +1
The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a c…
Chemical Oscillation in Ultracold Chemistry
Subhrajit Modak, Priyam Das, Challenger Mishra +1
We demonstrate the occurrence of oscillatory reactions in the ultra-cold chemistry of atom-molecular Bose-Einstein condensate. Nonlinear oscillations in the mean-field dynamics occ…
Discrete Symmetries of Complete Intersection Calabi-Yau Manifolds
Andre Lukas, Challenger Mishra
In this paper, we classify non-freely acting discrete symmetries of complete intersection Calabi- Yau manifolds and their quotients by freely-acting symmetries. These non-freely ac…
Highly Symmetric Quintic Quotients
Philip Candelas, Challenger Mishra
The quintic family must be the most studied family of Calabi-Yau threefolds. Particularly symmetric members of this family are known to admit quotients by freely acting symmetries…
Calabi-Yau Threefolds With Small Hodge Numbers
Philip Candelas, Andrei Constantin, Challenger Mishra
We present a list of Calabi-Yau threefolds known to us, and with holonomy groups that are precisely SU(3), rather than a subgroup, with small Hodge numbers, which we understand to…
Hodge Numbers for CICYs with Symmetries of Order Divisible by 4
Philip Candelas, Andrei Constantin, Challenger Mishra
We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method…
The Family Problem: Hints from Heterotic Line Bundle Models
Andrei Constantin, Andre Lukas, Challenger Mishra
Within the class of heterotic line bundle models, we argue that N=1 vacua which lead to a small number of low-energy chiral families are preferred. By imposing an upper limit on th…
New cross-phase modulated localized solitons in coupled atomic-molecular BEC
Challenger Mishra, Priyam Das, Krishna Rai Dastidar +1
The interacting atom-molecule BEC (AMBEC) dynamics is investigated in the mean field ap- proach. The presence of atom-atom, atom-molecule and molecule-molecule interactions, couple…
Grey solitons in doped nonlinear fibers
Challenger Mishra, T. N. Dey, P. K. Panigrahi
Grey solitons, with complex envelope, are obtained as exact solutions of the coupled system describing doped optical nonlinear fibers. The phase degree of freedom plays a crucial r…