Publications related to Modular group

Six-dimensional sphere packing and linear programming

Maryna Viazovska, Matthew De Courcy-Ireland, Maria Margarethe Dostert

We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn- Triantafillou [Math. Comp. 91 (2021), pp. 491 ...

Amer Mathematical Soc2024

The unipotent mixing conjecture

Philippe Michel

We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves. ...

Hebrew Univ Magnes Press2023

Twist Accumulation in Conformal Field Theory: A Rigorous Approach to the Lightcone Bootstrap

Jiaxin Qiao

We prove that in any unitary CFT, a twist gap in the spectrum of operator product expansion (OPE) of identical scalar quasiprimary operators (i.e. phi x phi) implies the existence of a family of quasiprimary operators O t,l with spins l ->.infinity and twi ...

SPRINGER2023

Experimental investigation on the bending response of reuse-ready timber slabs – The Pixel Slab System

Corentin Jean Dominique Fivet, Edisson Xavier Estrella Arcos, Johnny Syriani

Current construction practices follow linear economic models of "take-make-dispose" that result in substantial material landfilling after the end-of-life of buildings. This issue takes relevance given the construction industry's significant stake in the hi ...

International Association for Shell and Spatial Structures (IASS)2023

A finiteness result for p-adic families of Bianchi modular forms

Vlad Serban

We study p-adic families of cohomological automorphic forms for GL(2) over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. We show ho ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Fourier uniqueness and interpolation in Euclidean space

Martin Peter Stoller

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

EPFL2022

Load bearing device

Corentin Jean Dominique Fivet, Jan Friedrich Georg Brütting, Dario Redaelli, Alex-Manuel Muresan

The present relates to a device being used in modular building construction comprising at least one flat load support comprising a first main face and a second main face, at least one elongated load support designed for being coupled with said flat load su ...

2021

3D Printed Motor-Sensory Module Prototype for Facial Rehabilitation

Jamie Paik, Amir Firouzeh, Matthew Aaron Robertson

This work demonstrates the first 3D printed wearable motor-sensory module prototype designed for facial rehabilitation, focusing on facial paralysis. The novelty of the work lies in the fast fabrication of the first fully soft working prototype, including ...

MARY ANN LIEBERT, INC2022

Urban cells: Extending the energy hub concept to facilitate sector and spatial coupling

Kavan Javanroodi, Amarasinghage Tharindu Dasun Perera, Yi Wang

The rapid growth of urban areas and concerns over climate change make it vital to improve the energy sustainability of cities. Understanding the complex interactions within different sectors (sectoral) and localities (spatial) of cities plays a crucial rol ...

2021

Fourier uniqueness in even dimensions

Maryna Viazovska

In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness results in several key dimensions (d = 1, 8, 24), in which a function could be uniquely reconstructed from the values of it and its Fourier transform on a discr ...

National Academy of Sciences2021

Fourier interpolation on the real line

Maryna Viazovska

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,+/- 1,+/- ...

2019

SU(4) topological resonating valence bond spin liquid on the square lattice

Olivier Clément Romain Gauthé

We generalize the construction of the spin-1/2 SU(2) resonating valence bond (RVB) state to the case of the self-conjugate 6 representation of SU(4). As for the case of SU(2) [J.-Y. Chen and D. Poilblanc, Phys. Rev. B 97, 161107(R) (2018)], we use the proj ...

2019

Petersson inner products of weight-one modular forms

Maryna Viazovska

In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that ...

2019

En route to CO2-containing renewable materials: catalytic synthesis of polycarbonates and non-isocyanate polyhydroxyurethanes derived from cyclic carbonates

Paul Joseph Dyson, Felix Daniel Bobbink, Antoine Philippe Van Muyden

Combining CO2-chemistry with biomass conversion allows renewable polymeric materials including polycarbonates and polyhydroxyurethanes (PHUs) to be generated. The demand for robust materials with modular properties that can be prepared on an industrial sca ...

Royal Society of Chemistry2019

A modular low-complexity ECG delineation algorithm for real-time embedded systems

David Atienza Alonso, Francisco Javier Rincon Vallejos, Roman Hermida Correa

This work presents a new modular and lowcomplexity algorithm for the delineation of the different ECG waves (QRS, P and T peaks, onsets and end). Involving a reduced number of operations per second and having a small memory footprint, this algorithm is int ...

2018

Some applications of smooth bilinear forms with Kloosterman sums

Philippe Michel

We revisit a recent bound of I. Shparlinski and T. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earlier resul ...

Maik Nauka/Interperiodica/Springer2017

Elliptic curves over a finite field and the trace formula

Ian Nicholas Petrow

We prove formulas for power moments for point counts of elliptic curves over a finite field k such that the groups of k-points of the curves contain a chosen subgroup. These formulas express the moments in terms of traces of Hecke operators for certain con ...

Wiley2017

On Moments Of Twisted L-Functions

Philippe Michel

We study the average of the product of the central values of two L-functions of modular forms f and g twisted by Dirichlet characters to a large prime modulus q. As our principal tools, we use spectral theory to develop bounds on averages of shifted convol ...

Johns Hopkins Univ Press2017

Analytic twists of modular forms and applications

Alexandre François Peyrot

We are interested in the study of non-correlation of Fourier coefficients of Maass forms against a wide class of real analytic functions. In particular, the class of functions we are interested in should be thought of as some archimedean analogs of Frobeni ...

EPFL2017

Colloidal nanocrystals for photoelectrochemical and photocatalytic water splitting

Raffaella Buonsanti, Anna Loiudice, Chethana Janardhana Gadiyar

Colloidal nanocrystals (NCs) are among the most modular and versatile nanomaterial platforms for studying emerging phenomena in different fields thanks to their superb compositional and morphological tunability. A promising, yet challenging, application in ...

2017