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"David, Joseph"
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Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity-Topoi
We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their
derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise
as the functor of points of such objects. We choose to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with
a structure sheaf, thus naturally generalizing the work of Lurie (2004), but our approach applies not only to different settings of
algebraic geometry such as classical algebraic geometry, derived algebraic geometry, and the algebraic geometry of commutative ring
spectra as in Lurie (2004), but also to differential topology, complex geometry, the theory of supermanifolds, derived manifolds etc.,
where it produces a theory of higher generalized orbifolds appropriate for these settings. This universal framework yields new insights
into the general theory of Deligne-Mumford stacks and orbifolds, including a representability criterion which gives a categorical
characterization of such generalized Deligne-Mumford stacks. This specializes to a new categorical description of classical
Deligne-Mumford stacks, a result sketched in Carchedi (2019), which extends to derived and spectral Deligne-Mumford stacks as well.
eBook
The magic of thinking big
First published in 1959, David J. Schwartz's classic teachings are as powerful today as they were then. Practical, empowering and hugely engaging, this book not only inspires, it gives you the tools to change your life for the better - starting from now. His step-by-step approach shows you how to: defeat disbelief and the negative power it creates; make your mind produce positive thoughts; plan a concrete success-building programme; do more and do it better by turning on your creative power; and capitalise on the power of now! Revised for today's reader, it offers a go-to guide to a better life - starting with the way you think.
Book
Transitioning organizations to post-quantum cryptography
Quantum computers are expected to break modern public key cryptography owing to Shor’s algorithm. As a result, these cryptosystems need to be replaced by quantum-resistant algorithms, also known as post-quantum cryptography (PQC) algorithms. The PQC research field has flourished over the past two decades, leading to the creation of a large variety of algorithms that are expected to be resistant to quantum attacks. These PQC algorithms are being selected and standardized by several standardization bodies. However, even with the guidance from these important efforts, the danger is not gone: there are billions of old and new devices that need to transition to the PQC suite of algorithms, leading to a multidecade transition process that has to account for aspects such as security, algorithm performance, ease of secure implementation, compliance and more. Here we present an organizational perspective of the PQC transition. We discuss transition timelines, leading strategies to protect systems against quantum attacks, and approaches for combining pre-quantum cryptography with PQC to minimize transition risks. We suggest standards to start experimenting with now and provide a series of other recommendations to allow organizations to achieve a smooth and timely PQC transition.
Standards and recommendations for transitioning organizations to quantum-secure cryptographic protocols are outlined, including a discussion of transition timelines and the leading strategies to protect systems against quantum attacks.
Journal Article
