1 citations · 1 across the 7 of their papers we have counts for
7 papers
Progress in Formalizing Sphere Packing in Dimension 8
Sidharth Hariharan, Christopher Birkbeck, Seewoo Lee +4
In 2016, Viazovska famously solved the sphere packing problem in dimension , using modular forms to construct a 'magic' function satisfying optimality conditions determined by C…
Module lattices and their shortest vectors
Nihar Gargava, Vlad Serban, Maryna Viazovska +1
We study the shortest vector lengths in module lattices over arbitrary number fields, with an emphasis on cyclotomic fields. In particular, we sharpen the techniques of arXiv:2308.…
Integral Matrices of Fixed Rank over Number Fields
Nihar Gargava, Vlad Serban, Maryna Viazovska +1
We prove an asymptotic formula for the number of fixed rank matrices with integer coefficients over a number field K/Q and bounded norm. As an application, we derive an approximate…
Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning
Anja Surina, Amin Mansouri, Lars Quaedvlieg +4
Discovering efficient algorithms for solving complex problems has been an outstanding challenge in mathematics and computer science, requiring substantial human expertise over the…
Mean Value for Random Ideal Lattices
Nihar Gargava, Maryna Viazovska
We investigate the average number of lattice points within a ball for the th cyclotomic number field, where the lattice is chosen at random from the set of unit determinant idea…
Polynomial Freiman-Ruzsa, Reed-Muller codes and Shannon capacity
Emmanuel Abbe, Colin Sandon, Vladyslav Shashkov +1
In 1948, Shannon used a probabilistic argument to show the existence of codes achieving a maximal rate defined by the channel capacity. In 1954, Muller and Reed introduced a simple…