2 citations · 2 across the 5 of their papers we have counts for
6 papers
AIProver: Agentic Auto-Formalization of Mathematical Research via Certificate-Driven Evolving Harness
Prithwish Jana, Viet Bach Hoang, Logan Luna +9
Proof auto-formalization translates natural-language (NL) theorems and proofs into a formal language (FL) such as Lean, enabling mechanical verification. Despite rapid progress, re…
A Magnus group construction for a class of Borcherds algebras
Lisa Carbone, Elizabeth Jurisich
We construct a group associated to a class of Borcherds algebras that admit a direct sum decomposition into a Kac--Moody (or semi-simple) subalgebra and a pair of free Lie subalgeb…
Symmetries of Borcherds algebras
Lisa Carbone
We give an overview of the construction of Borcherds algebras, particularly the Monstrous Lie algebras constructed by Carnahan, where is an element of the Monst…
Kac--Moody Fibonacci sequences
Lisa Carbone, Pranav Shankar
We summarize known results on how to generate an infinite family of integer sequences from the root lattices of rank 2 Kac--Moody algebras. We compute and tabulate the first twenty…
Advancing mathematics research with generative AI
Lisa Carbone
The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their…
Interview with Hyman Bass
Hyman Bass, Lisa Carbone, Yvonne Lai
Interview with Hyman Bass, whose mathematical life has spanned seven decades.