Hermitian Forms over Algebras with Involution and Hermitian Categories

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Dense Packings via Lifts of Codes to Division Rings

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obtain algorithmically effective versions of the dense lattice sphere packings constructed from orders in Q-division rings by the first author. The lattices in question are lifts of suitable codes from prime characteristic to orders O in Q-division rings a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Conditional Flatness, Fiberwise Localizations, And Admissible Reflections

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We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localizatio ...

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Hierarchy of quasisymmetries and degeneracies in the CoSi family of chiral crystal materials

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In materials, certain approximated symmetry operations can exist in a lower-order approximation of the effective model but are good enough to influence the physical responses of the system, and these approximated symmetries were recently dubbed "quasisymme ...

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Tangent functional connectomes uncover more unique phenotypic traits

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Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projecti ...

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Positive Definite Completions and Continuous Graphical Models

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This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

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Nonlinear optical frequency conversion is of fundamental importance in photonics and underpins countless of its applications: Sum- and difference-frequency generation in media with quadratic nonlinearity permits reaching otherwise inaccessible wavelength r ...

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Small-angle scattering tensor tomography algorithm for robust reconstruction of complex textures

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The development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. It is of great value to have reconstruction methods that can handle many different nanostructural symmetries. For s ...

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Byzantine consensus is Θ(n^2): the Dolev-Reischuk bound is tight even in partial synchrony!

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The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with n processes and at most f < n/3 failures, any solution t ...

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On the Grothendieck-Serre conjecture for classical groups

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We prove some new cases of the Grothendieck-Serre conjecture for classical groups. This is based on a new construction of the Gersten-Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue ...

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Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

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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

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