38 citations · 102 across the 18 of their papers we have counts for
25 papers
The Amazon Nova Family of Models: Technical Report and Model Card
Amazon AGI, Aaron Langford, Aayush Shah +783
We present Amazon Nova, a new generation of state-of-the-art foundation models that deliver frontier intelligence and industry-leading price performance. Amazon Nova Pro is a highl…
Elliptic units for complex cubic fields
Nicolas Bergeron, Pierre Charollois, Luis E. García
We propose a conjecture extending the classical construction of elliptic units to complex cubic number fields . The conjecture concerns special values of the elliptic gamma func…
Eisenstein cohomology classes for over imaginary quadratic fields
Nicolas Bergeron, Pierre Charollois, Luis E. Garcia
We study the arithmetic of degree Eisenstein cohomology classes for locally symmetric spaces associated to over an imaginary quadratic field . Under natura…
On homology torsion growth
Miklos Abert, Nicolas Bergeron, Mikolaj Fraczyk +1
We prove new vanishing results on the growth of higher torsion homologies for suitable arithmetic lattices, Artin groups and mapping class groups. The growth is understood along Fa…
Tautological classes of hyper-Kähler manifolds. Erratum
Nicolas Bergeron, Zhiyuan Li
This note is an erratum to the paper "Tautological classes on moduli spaces of hyper-Kähler manifolds." Thorsten Beckman and Mirko Mauri have pointed to us a gap in the proof of \c…
Convergence of normalized Betti numbers in nonpositive curvature
Miklos Abert, Nicolas Bergeron, Ian Biringer +1
We study the convergence of volume-normalized Betti numbers in Benjamini-Schramm convergent sequences of non-positively curved manifolds with finite volume. In particular, we show…
Eigenfunctions and Random Waves in the Benjamini-Schramm limit
Miklos Abert, Nicolas Bergeron, Etienne Le Masson
We investigate the asymptotic behavior of eigenfunctions of the Laplacian on Riemannian manifolds. We show that Benjamini-Schramm convergence provides a unified language for the le…
Tautological classes on moduli space of hyperkähler manifolds
Nicolas Bergeron, Zhiyuan Li
In this paper, we discuss the cycle theory on moduli spaces $\cF_h$ of -polarized hyperkähler manifolds. Firstly, we construct the tautological ring on $\cF_h$ following the wor…
On special Lagrangian fibrations in generic twistor families of K3 surfaces
Nicolas Bergeron, Carlos Matheus
Filip showed that there are constants and such that the number of special Lagrangian fibrations of volume in a generic twistor family of K3 surfaces is $C\cdot…
A note on local rigidity
Nicolas Bergeron, Tsachik Gelander
The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and ho…
On the growth of L2-invariants of locally symmetric spaces, II: exotic invariant random subgroups in rank one
Miklos Abert, Nicolas Bergeron, Ian Biringer +4
In the first paper of this series (arxiv.org/abs/1210.2961) we studied the asymptotic behavior of Betti numbers, twisted torsion and other spectral invariants for sequences of latt…
The Relative Lie Algebra Cohomology of the Weil Representation
Jacob Ralston
We study the relative Lie algebra cohomology of with values in the Weil representation of the dual pair $\mathrm{Sp}(2k, \mathbb{R}) \times \mathrm{O}…
The Noether-Lefschetz conjecture and generalizations
Nicolas Bergeron, Zhiyuan Li, John Millson +1
We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree…
The Relative Lie Algebra Cohomology of the Weil Representation of SO(n,1)
Nicolas Bergeron, John J. Millson, Jacob Ralston
In Part 1 of this paper we construct a spectral sequence converging to the relative Lie algebra cohomology associated to the action of any subgroup of the symplectic group on t…
Twisted limit formula for torsion and cyclic base change
Nicolas Bergeron, Michael Lipnowski
Let be the group of complex points of a real semi-simple Lie group whose fundamental rank is equal to 1, e.g. $G= \SL_2 (\C) \times \SL_2 (\C)$ or $\SL_3 (\C)$. Then the fundam…
Torsion homology growth and cycle complexity of arithmetic manifolds
Nicolas Bergeron, Mehmet Haluk Sengun, Akshay Venkatesh
Let M be an arithmetic hyperbolic 3-manifold, such as a Bianchi manifold. We conjecture that there is a basis for the second homology of M, where each basis element is represented…
Local rigidity for PGL(3,C)-representations of 3-manifold groups
N. Bergeron, E. Falbel, A. Guilloux +2
Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by…
The Hodge conjecture and arithmetic quotients of complex balls
Nicolas Bergeron, John Millson, Colette Moeglin
Let be a closed Shimura variety uniformized by the complex -ball. The Hodge conjecture predicts that every Hodge class in $H^{2k} (S, \Q)$, , is algebraic. W…
On the growth of -invariants for sequences of lattices in Lie groups
Miklos Abert, Nicolas Bergeron, Ian Biringer +4
We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of…
On the growth of Betti numbers in -adic analytic towers
Nicolas Bergeron, Peter Linnell, Wolfgang Lück +1
We study the asymptotic growth of Betti numbers in tower of finite covers and provide simple proofs of approximation results, which were previously obtained by Calegari-Emerton, in…
Hodge type theorems for arithmetic manifolds associated to orthogonal groups
Nicolas Bergeron, John Millson, Colette Moeglin
We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geod…
On the growth of Betti numbers of locally symmetric spaces
Miklos Abert, Nicolas Bergeron, Ian Biringer +4
We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uni…
Tetrahedra of flags, volume and homology of SL(3)
Nicolas Bergeron, Elisha Falbel, Antonin Guilloux Antonin
In the paper we define a "volume" for simplicial complexes of flag tetrahedra. This generalizes and unifies the classical volume of hyperbolic manifolds and the volume of CR tetrah…
The asymptotic growth of torsion homology for arithmetic groups
Nicolas Bergeron, Akshay Venkatesh
When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is so, and conjecture precise conditio…