23 citations · 34 across the 15 of their papers we have counts for
5 papers · 1 filter
Existentially defining valuations in function fields over large fields
Nicolas Daans
Let be a large field such that is not algebraically closed and a function field in one variable. Extending techniques and results from earlier work with Be…
Decidability of polynomial equations over function fields in positive characteristic
Nicolas Daans
Let be a field of positive characteristic with no algebraically closed subfield. Let be a function field over and transcendental over . Refining a result o…
The u-invariant of function fields in one variable
Karim Johannes Becher, Nicolas Daans, Vlerë Mehmeti
The u-invariant of a field is the largest dimension of an anisotropic quadratic torsion form over the field. In this article we obtain a bound on the u-invariant of function fields…
Pythagoras numbers for infinite algebraic fields
Nicolas Daans, Stevan Gajović, Siu Hang Man +1
We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1168
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…