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Showing 1 to 20 of 23 for “"Settore MAT/02 - Algebra"”.
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FROM DG-CATEGORIES OVER K TO K-LINEAR STABLE INFINITY-CATEGORIES
… This result is a meeting point between algebraic topology and algebraic geometry. In 2013 L. Cohn proved it in a preprint, and in 2016, he updated the preprint to its latest version. Since then the ∞-category theory and the spectral algebraic geometry theory have made progress: …
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On algebraic and statistical properties of AES-like ciphers
… other modern block ciphers) presents a highly algebraic structure, which led researchers to exploit it for novel algebraic attacks. These tries have been unsuccessful, except for academic reduced versions. Starting from an intuition by I. Toli, we have developed a mixed algebraic-statistical …
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Differential attacks using alternative operations and block cipher design
… can be proven secure against a well-known algebraic attack, based on the action of the permutation group generated by the round functions of the cipher.
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Gluing silting objects along recollements of well generated triangulated categories
… of silting modules over the Kronecker algebra and the classification of non-compact tilting sheaves over a weighted noncommutative regular projective curve of genus 0.
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Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras
… multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.
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Formal Proofs of Security for Privacy-Preserving Blockchains and other Cryptographic Protocols
… chapters, distinguishing between the hardness of algebraic problems and the strength of cryptographic primitives. Once that the bases are given, the first protocols are analysed in chapter 3, where two Attribute Based Encryption schemes are proven secure. First context and motivation are …
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Optimal Codes and Entropy Extractors
… true also for nonlinear codes. In case of systematic codes, a class of codes including linear codes, we can derive stronger results on the relationship between the Griesmer bound and optimal codes. We also construct a family of optimal binary systematic codes contradicting the Griesmer bound. …
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Cyclic Codes: Low-Weight Codewords and Locators
Error correcting codes has become an integral part of the design of reliable data transmissions and storage systems. They are also playing an increasingly important role for other applications such as the analysis of pseudorandom sequences and the design of secure cryptosystems. Cyclic codes form a …
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Component Groups of Stabilizers in Algebraic Groups: Computational Methods and Applications
… of nilpotent elements in complex semisimple Lie algebras have been a relevant topic of research over the last century. The works of Alekseevskii (1979) and Sommers (1998) contributed significantly to the determination of such groups for exceptional Lie algebras, while Jantzen (2004) provided …
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Classifying semisimple orbits of theta-groups
I consider the problem of classifying the semisimple orbits of a theta-group. For this purpose, once a preliminary presentation of the theoretical subjects where my problem arises from, I first give an algorithm to compute a Cartan subspace; subsequently I describe how to compute the little Weyl …
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HOMOTOPY SETOIDS AND GENERALIZED QUOTIENT COMPLETION
In this thesis, we deal with some categorical structures arising from the Martin-Löf Intuitionistic Type Theory. In the first part, we introduce the homotopy setoids, considering ideas from the homotopy type theory, and we study their categorical properties. In order to do that, we use the …
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OVERCONVERGENT MODULAR AND DE RHAM SHEAVES AND P-ADIC ITERATION OF THE GAUSS-MANIN CONNECTION
We construct p-adic iteration of the Gauss-Manin connection on overconvergent sheaves of de Rham classes on Hilbert modular varieties in the case p is unramified in the totally real field. This is a generalization of the work of Andreatta-Iovita in the case of elliptic curves, using a technique …
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A DOCTRINAL VIEW OF LOGIC
… particular first-order theories — using the same mathematical structure. The thesis begins with a thorough analysis of Henkin’s Theorem for first-order logic (“every consistent theory has a model”), with the aim of interpreting it in the language of existential implicational doctrines. The thesis …
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On Boolean functions, symmetric cryptography and algebraic coding theory
… into account the index coding with side information (ICSI) problem. Firstly we investigate the optimal length of a linear index code, that is equal to the min-rank of the hypergraph related to the instance of the ICSI problem. In particular we extend the the so-called Sandwich Property from …
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A CATEGORICAL-ALGEBRAIC EXPLORATION OF MODELS FOR MANY-VALUED LOGIC
In this thesis, we study from a categorical-algebraic point of view the structures of lattice-ordered groups and MV-algebras, which are used in modeling logic with many truth values. In the first part, we show that the semi-abelian category of lattice-ordered groups satisfies several important …
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SEMISTABLE MODELS OF HYPERELLIPTIC CURVES IN THE WILD CASE & DIFFERENTIAL OPERATORS ON P-ADIC MODULAR FORMS
… my PhD, until completing it during summer 2022. The second part of this thesis discusses some research findings related to a completely unrelated topic proposed to me by my PhD advisor Fabrizio Andreatta, namely the one of geometric constructions of differential operators on sheaves of …
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A COMPARISON BETWEEN GEOMETRIC QUASI-FUNCTORS AND FOURIER-MUKAI FUNCTORS
… del suo nucleo, dando così risposta affermativa ad una congettura di Toën.
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On semiseparability, semifunctors and conditions up to retracts
L'abstract è presente nell'allegato / the abstract is in the attachment
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