Orientable manifolds can only have an odd Euler characteristic in dimensions divisible by 4. I will prove the analogous result for spin and string manifolds, where the dimension can only be a multiple of 8 and 16 respectively. The talk will require very little background. I'll go over the definition of spin and string structures, discuss cohomology operations and Poincare duality.

Structure-preserving signatures are an important cryptographic primitive that is useful for the design of modular cryptographic protocols. In this work, we show how to bypass most of the existing lower bounds in the most efficient Type-III bilinear group setting. We formally define a new variant of structure-preserving signatures in the Type-III setting and present a number of fully secure schemes with signatures half the size of existing ones. We also give different constructions including constructions of optimal one-time signatures. In addition, we prove lower bounds and provide some impossibility results for the variant we define. Finally, we show some applications of the new constructions.

In the context of surplus models of insurance risk theory, 
some rather surprising and simple identities are presented. This 
includes an
identity relating level crossing probabilities of continuous-time models 
under (randomized) discrete and continuous observations, as well as
reflection identities relating dividend payments and capital injections. 
Applications as well as extensions to more general underlying processes are
discussed.

 

We focus on the mathematical structure of systemic risk measures as proposed by Chen, Iyengar, and Moallemi (2013). In order to clarify the interplay between local and global risk assessment, we study the local specification of a systemic risk measure by a consistent family of conditional risk measures for smaller subsystems, and we discuss the appearance of phase transitions at the global level. This extends the analysis of spatial risk measures in Föllmer and Klϋppelberg (2015).

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