Laurent Bétermin

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All published works

Action	Title	Year	Authors
+ PDF Chat	On crystallization in the plane for pair potentials with an arbitrary norm	2024	Laurent Bétermin Camille Furlanetto
+	Structural transitions in interacting lattice systems	2024	Laurent Bétermin Ladislav Šamaj Igor Travěnec
+	Optimality of the triangular lattice for Lennard–Jones type lattice energies: a computer-assisted method	2023	Laurent Bétermin
+	Maximal theta functions universal optimality of the hexagonal lattice for Madelung-like lattice energies	2023	Laurent Bétermin Markus Faulhuber
+	On off-critical zeros of lattice energies in the neighborhood of the Riemann zeta function	2023	Laurent Bétermin Ladislav Šamaj Igor Travěnec
+	Three‐dimensional lattice ground states for Riesz and Lennard‐Jones–type energies	2022	Laurent Bétermin Ladislav Šamaj Igor Travěnec
+ PDF Chat	Stability of Z2 configurations in 3D	2021	Laurent Bétermin Manuel Friedrich Ulisse Stefanelli
+ PDF Chat	How well-conditioned can the eigenvector problem be?	2021	Carlos Beltrán Laurent Bétermin Peter J. Grabner Stefan Steinerberger
+	A variational principle for Gaussian lattice sums	2021	Laurent Bétermin Markus Faulhuber Stefan Steinerberger
+ PDF Chat	Lattice ground states for embedded-atom models in 2D and 3D	2021	Laurent Bétermin Manuel Friedrich Ulisse Stefanelli
+ PDF Chat	On energy ground states among crystal lattice structures with prescribed bonds	2021	Laurent Bétermin
+ PDF Chat	Effect of Periodic Arrays of Defects on Lattice Energy Minimizers	2021	Laurent Bétermin
+ PDF Chat	Crystallization to the Square Lattice for a Two-Body Potential	2021	Laurent Bétermin Lucia De Luca Mircea Petrache
+	How well-conditioned can the eigenvalue problem be?	2021	Carlos Beltrán Laurent Bétermin Peter J. Grabner Stefan Steinerberger
+ PDF Chat	Theta Functions and Optimal Lattices for a Grid Cells Model	2021	Laurent Bétermin
+	A variational principle for Gaussian lattice sums	2021	Laurent Bétermin Markus Faulhuber Stefan Steinerberger
+	Three-dimensional lattice ground states for Riesz and Lennard-Jones type energies	2021	Laurent Bétermin Ladislav Šamaj Igor Travěnec
+	Optimality of the triangular lattice for Lennard-Jones type lattice energies: a computer-assisted method	2021	Laurent Bétermin
+	Interplay between critical and off-critical zeros of two-dimensional Epstein zeta functions	2021	Laurent Bétermin Ladislav Šamaj Igor Travěnec
+ PDF Chat	On the optimality of the rock-salt structure among lattices with charge distributions	2020	Laurent Bétermin Markus Faulhuber Hans Knüpfer
+	Theta functions and optimal lattices for a grid cells model	2020	Laurent Bétermin
+	Angle-rigidity for $\mathbb{Z}^2$ configurations	2020	Laurent Bétermin Manuel Friedrich Ulisse Stefanelli
+	Stability of $\mathbb{Z}^2$ configurations in 3D	2020	Laurent Bétermin Manuel Friedrich Ulisse Stefanelli
+ PDF Chat	Note on Crystallization for Alternating Particle Chains	2020	Laurent Bétermin Hans Knüpfer Florian Nolte
+	On the optimality of the rock-salt structure among lattices with charge distributions	2020	Laurent Bétermin Markus Faulhuber Hans Knüpfer
+ PDF Chat	ON A LATTICE GENERALISATION OF THE LOGARITHM AND A DEFORMATION OF THE DEDEKIND ETA FUNCTION	2020	Laurent Bétermin
+ PDF Chat	Minimal Soft Lattice Theta Functions	2020	Laurent Bétermin
+	On the optimality of the rock-salt structure among lattices with charge distributions	2020	Laurent Bétermin Markus Faulhuber Hans Knüpfer
+	Theta functions and optimal lattices for a grid cells model	2020	Laurent Bétermin
+	Maximal Theta Functions -- Universal Optimality of the Hexagonal Lattice for Madelung-Like Lattice Energies	2020	Laurent Bétermin Markus Faulhuber
+ PDF Chat	Minimizing lattice structures for Morse potential energy in two and three dimensions	2019	Laurent Bétermin
+	A note on the maximum of a lattice generalization of the logarithm and a deformation of the Dedekind eta function	2019	Laurent Bétermin
+	On a lattice generalisation of the logarithm and a deformation of the Dedekind eta function	2019	Laurent Bétermin
+	Crystallization to the square lattice for a two-body potential	2019	Laurent Bétermin Lucia De Luca Mircea Petrache
+	Optimal and non-optimal lattices for non-completely monotone interaction potentials	2019	Laurent Bétermin Mircea Petrache
+	On a lattice generalisation of the logarithm and a deformation of the Dedekind eta function	2019	Laurent Bétermin
+	Crystallization to the square lattice for a two-body potential	2019	Laurent Bétermin Lucia De Luca Mircea Petrache
+	Minimal Soft Lattice Theta Functions	2018	Laurent Bétermin
+	Local variational study of 2d lattice energies and application to Lennard–Jones type interactions	2018	Laurent Bétermin
+	On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal	2018	Laurent Bétermin Hans Knüpfer
+	Crystallization of one-dimensional alternating two-component systems	2018	Laurent Bétermin Hans Knüpfer Florian Nolte
+	Crystallization of one-dimensional alternating two-component systems	2018	Laurent Bétermin Hans Knüpfer Florian Nolte
+	Optimal lattice configurations for interacting spatially extended particles	2018	Laurent Bétermin Hans Knüpfer
+	Minimal Soft Lattice Theta Functions	2018	Laurent Bétermin
+	Optimal and non-optimal lattices for non-completely monotone interaction potentials	2018	Laurent Bétermin Mircea Petrache
+ PDF Chat	Local optimality of cubic lattices for interaction energies	2017	Laurent Bétermin
+ PDF Chat	Dimension reduction techniques for the minimization of theta functions on lattices	2017	Laurent Bétermin Mircea Petrache
+ PDF Chat	On Born's conjecture about optimal distribution of charges for an infinite ionic crystal	2017	Laurent Bétermin Hans Knüpfer
+	Local variational study of 2d lattice energies and application to Lennard-Jones type interactions	2016	Laurent Bétermin
+ PDF Chat	Renormalized Energy and Asymptotic Expansion of Optimal Logarithmic Energy on the Sphere	2016	Laurent Bétermin Étienne Sandier
+	Two-Dimensional Theta Functions and Crystallization among Bravais Lattices	2016	Laurent Bétermin
+	Local variational study of 2d lattice energies and application to Lennard-Jones type interactions	2016	Laurent Bétermin
+ PDF Chat	Lattices energies and variational calculus	2015	Laurent Bétermin
+	Energies de réseaux et calcul variationnel	2015	Laurent Bétermin
+	2D Theta Functions and Crystallization among Bravais Lattices	2015	Laurent Bétermin
+	Sufficient Condition for a Compact Local Minimality of a Lattice	2015	Laurent Bétermin
+	Minimization of energy per particle among Bravais lattices in ℝ<sup>2</sup>: Lennard–Jones and Thomas–Fermi cases	2014	Laurent Bétermin Peng Zhang
+	Minimization of energy per particle among Bravais lattices in R^2 : Lennard-Jones and Thomas-Fermi cases	2014	Laurent Bétermin Peng Zhang

Common Coauthors

Coauthor	Papers Together
Markus Faulhuber	7
Mircea Petrache	6
Hans Knüpfer	6
Igor Travěnec	5
Ladislav Šamaj	5
Stefan Steinerberger	4
Manuel Friedrich	4
Ulisse Stefanelli	4
Florian Nolte	3
Lucia De Luca	2
Carlos Beltrán	2
Peter J. Grabner	2
Peng Zhang	2
Hans Knüpfer	2
Camille Furlanetto	1
Lucia De Luca	1
Étienne Sandier	1
Hans Knüpfer	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Minimal theta functions	1988	Hugh L. Montgomery	29
+ PDF Chat	The crystallization conjecture: a review	2015	Xavier Blanc Mathieu Lewin	27
+	Universally optimal distribution of points on spheres	2006	Henry Cohn Abhinav Kumar	27
+	Two-Dimensional Theta Functions and Crystallization among Bravais Lattices	2016	Laurent Bétermin	27
+	Minima of Epstein’s Zeta function and heights of flat tori	2006	Peter Sarnak Andreas Strömbergsson	25
+ PDF Chat	From the Ginzburg-Landau Model to Vortex Lattice Problems	2012	Étienne Sandier Sylvia Serfaty	24
+ PDF Chat	A Minimum Problem for the Epstein Zeta-Function	1953	R. A. Rankin	22
+ PDF Chat	Energy Minimization, Periodic Sets and Spherical Designs	2011	Renaud Coulangeon Achill Schürmann	20
+ PDF Chat	Finite crystallization in the square lattice	2014	Edoardo Mainini Paolo Piovano Ulisse Stefanelli	19
+ PDF Chat	On a problem of Rankin about the Epstein zeta-function	1959	J. W. S. Cassels	18
+	Optimal and non-optimal lattices for non-completely monotone interaction potentials	2019	Laurent Bétermin Mircea Petrache	17
+ PDF Chat	A lemma about the Epstein zeta-function	1964	Veikko Ennola	17
+ PDF Chat	Local optimality of cubic lattices for interaction energies	2017	Laurent Bétermin	17
+ PDF Chat	Notes on two lemmas concerning the Epstein zeta-function	1964	P. H. Diananda	17
+	On the Crystallization of 2D Hexagonal Lattices	2008	E Weinan Dong Li	17
+	Minimization of energy per particle among Bravais lattices in ℝ<sup>2</sup>: Lennard–Jones and Thomas–Fermi cases	2014	Laurent Bétermin Peng Zhang	16
+ PDF Chat	Dimension reduction techniques for the minimization of theta functions on lattices	2017	Laurent Bétermin Mircea Petrache	16
+	Local variational study of 2d lattice energies and application to Lennard–Jones type interactions	2018	Laurent Bétermin	16
+	Spherical designs and heights of Euclidean lattices	2014	Renaud Coulangeon Giovanni Lazzarini	15
+ PDF Chat	The sphere packing problem in dimension $24$	2017	Henry Cohn Abhinav Kumar Stephen D. Miller Danylo Radchenko Maryna Viazovska	15
+	Sur les fonctions absolument monotones	1929	Serge Bernstein	15
+ PDF Chat	Universal optimality of the $E_8$ and Leech lattices and interpolation formulas	2022	Henry Cohn Abhinav Kumar Stephen D. Miller Danylo Radchenko Maryna Viazovska	14
+ PDF Chat	Minimizing lattice structures for Morse potential energy in two and three dimensions	2019	Laurent Bétermin	14
+	On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal	2018	Laurent Bétermin Hans Knüpfer	13
+	Harmonic Analysis on Symmetric Spaces and Applications I	1985	Audrey Terras	13
+	Lowest Landau level functional and Bargmann spaces for Bose–Einstein condensates	2006	Amandine Aftalion Xavier Blanc Francis Nier	13
+	The ground state for soft disks	1981	Charles Radin	13
+ PDF Chat	Crystallization in Two Dimensions and a Discrete Gauss–Bonnet Theorem	2017	Lucia De Luca Gero Friesecke	13
+ PDF Chat	Spherical designs and zeta functions of lattices	2006	Renaud Coulangeon	13
+	On a problem about the Epstein zeta-function	1964	Veikko Ennola	13
+ PDF Chat	On the configuration of systems of interacting particle with minimum potential energy per particle	1979	W.J. Ventevogel B.R.A. Nijboer	12
+	Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions	2016	Markus Faulhuber Stefan Steinerberger	12
+ PDF Chat	Two-Component Bose-Einstein Condensates with a Large Number of Vortices	2002	Erich J. Mueller Tin-Lun Ho	12
+	Optimal lattice configurations for interacting spatially extended particles	2018	Laurent Bétermin Hans Knüpfer	11
+ PDF Chat	Face-Centered Cubic Crystallization of Atomistic Configurations	2015	Lisa Flatley Florian Theil	11
+ PDF Chat	Nonhexagonal Lattices From a Two Species Interacting System	2020	Senping Luo Xiaofeng Ren Juncheng Wei	10
+ PDF Chat	Periodic discrete energy for long-range potentials	2014	Douglas P. Hardin Edward B. Saff Brian Simanek	10
+	Extremals of determinants of Laplacians	1988	Brad Osgood Ralph S. Phillips Peter Sarnak	9
+ PDF Chat	The sphere packing problem in dimension $8$	2017	Maryna Viazovska	9
+ PDF Chat	Renormalized Energy and Asymptotic Expansion of Optimal Logarithmic Energy on the Sphere	2016	Laurent Bétermin Étienne Sandier	9
+ PDF Chat	Crystalline Ground States for Classical Particles	2005	András Sütö	8
+ PDF Chat	Local Energy Optimality of Periodic Sets	2018	Renaud Coulangeon Achill Schürmann	7
+ PDF Chat	Crystallization to the Square Lattice for a Two-Body Potential	2021	Laurent Bétermin Lucia De Luca Mircea Petrache	7
+ PDF Chat	Minimal Soft Lattice Theta Functions	2020	Laurent Bétermin	7
+ PDF Chat	The sphere packing problem in dimension 8The sphere packing problem in dimension 8	2017	Maryna Viazovska	7
+	A minimum problem for heat kernels of flat tori	1997	Albert Baernstein	7
+ PDF Chat	Ground State at High Density	2011	András Sütö	7
+ PDF Chat	New upper bounds on sphere packings I	2003	Henry Cohn Noam D. Elkies	7
+	Mutual interactions, potentials, and individual distance in a social aggregation	2003	Alex Mogilner L. Bent Äthan Spiros Leah Edelstein‐Keshet	7
+ PDF Chat	Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals	2015	Nicolas Rougerie Sylvia Serfaty	6