8 citations · 18 across the 9 of their papers we have counts for
9 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…
A complete formalization of Fermat's Last Theorem for regular primes in Lean
Alex Best, Christopher Birkbeck, Riccardo Brasca +3
We formalize a complete proof of the regular case of Fermat's Last Theorem in the Lean4 theorem prover. Our formalization includes a proof of Kummer's lemma, that is the main obstr…
Fermat's Last Theorem for regular primes
Alex J. Best, Christopher Birkbeck, Riccardo Brasca +1
We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \emph{Lean} theorem prover and its mathematical library \emph{mathlib}. This is an im…
Overconvergent Hilbert modular forms via perfectoid modular varieties
Christopher Birkbeck, Ben Heuer, Chris Williams
We give a new construction of -adic overconvergent Hilbert modular forms by using Scholze's perfectoid Shimura varieties at infinite level and the Hodge--Tate period map. The de…
On the -adic Langlands correspondence for algebraic tori
Christopher Birkbeck
We extend the results by R.P. Langlands on representations of (connected) abelian algebraic groups. This is done by considering characters into any divisible abelian topological gr…
-adic slopes of Hilbert modular forms over
Christopher Birkbeck
We show that for arithmetic weights with a fixed finite order character, the slopes of (for ) acting on overconvergent Hilbert modular forms of level are indepe…
Slopes of overconvergent Hilbert modular forms
Christopher Birkbeck
We give an explicit description of the matrix associated to the operator acting on spaces of overconvergent Hilbert modular forms over totally real fields. Using this, we com…
Extensions of Vector Bundles on the Fargues-Fontaine Curve
Christopher Birkbeck, Tony Feng, David Hansen +4
We completely classify the possible extensions between semistable vector bundles on the Fargues-Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple…
The Jacquet-Langlands correspondence for overconvergent Hilbert modular forms
Christopher Birkbeck
We use results by Chenevier to interpolate the classical Jacquet-Langlands correspondence for Hilbert modular forms, which gives us an extension of Chenevier's results to totally r…