Publication
Diagonal Quartic Surfaces And Transcendental Elements Of The Brauer Group
Publications associées (32)
Multiplicity-free Representations of Algebraic Groups
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Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...
Amer Mathematical Soc2024Some Mordell-Weil lattices and applications to sphere packings
We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields.In some cases, these families of elliptic curves ...
EPFL2024Algebraic twists of GL(2) automorphic forms
In this thesis we consider the problem of estimating the correlation of Hecke eigenvalues of GL2 automorphic forms with a class of functions of algebraic origin defined over finite fields called trace functions. The class of trace functions is vast and inc ...
EPFL2023Moments of the number of points in a bounded set for number field lattices
Maryna Viazovska, Vlad Serban, Nihar Prakash Gargava
We examine the moments of the number of lattice points in a fixed ball of volume for lattices in Euclidean space which are modules over the ring of integers of a number field . In particular, denoting by the number of roots of unity in , we ...
arXiv2023Lattice packings through division algebras
In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...
SPRINGER HEIDELBERG2023Distributed Lossy Computation with Structured Codes: From Discrete to Continuous Sources
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This paper considers the problem of distributed lossy compression where the goal is to recover one or more linear combinations of the sources at the decoder, subject to distortion constraints. For certain configurations, it is known that codes with algebra ...
2023Almost cyclic regular semisimple elements in irreducible representations of simple algebraic groups
Let G be a simple linear algebraic group defined over an algebraically closed field of characteristic p ≥ 0 and let φ be a nontrivial p-restricted irreducible representation of G. Let T be a maximal torus of G and s ∈ T . We say that s is Ad-regular if α(s ...
2023Asymmetric phase modulation of light with parity-symmetry broken metasurfaces
Karim Achouri, Jean-Yves Duboz
The design of wavefront-shaping devices is conventionally approached using real-frequency modeling. However, since these devices interact with light through radiative channels, they are by default non-Hermitian objects having complex eigenvalues (poles and ...
Washington2023Coxeter Combinatorics For Sum Formulas In The Representation Theory Of Algebraic Groups
Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...
AMER MATHEMATICAL SOC2022Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity
Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...
EPFL2022