s of lectures for Banff meeting, Groups and Geometries, May 4-8, 2015 Michael Aschbacher: Quaternion fusion packets Abstract I’ll discuss work on a fusion theoretic version of the so-called Classical Involution Theorem for groups. The project is part of a program to simplify part of the proof of the theorem classifying the finite simple groups.I’ll discuss work on a fusion theoretic version of ...

We begin this paper with a discussion of n-dimensional algebraic Vector bundles. Vector bundles of rank n may be identified with locally free Ox-modules of rank n. Several sections are dedicated to reviewing the basic notions of scheme-theory. We show how to construct the projectization of arbitrary rings. This construction corresponds to the construction of the tautological line bundle over an...

Parapolar spaces are point-line geometries introduced as a geometric approach to (exceptional) algebraic groups. We characterize wide class of Lie parapolar satisfying simple intersection property. In particular many the exceptional incidence occur. {In an appendix, we extend our result locally disconnected case and discuss some other well known characterizations.

Let G be a non-connected reductive algebraic group over an algebraically closed field K and let D connected component of G. We investigate the Jordan classes we obtain description regular part closure class in terms induction G∘-orbits. use this result to show that Lusztig strata are locally closed.

Locally repairable codes, or locally recoverable codes (LRC for short) are designed for application in distributed and cloud storage systems. Similar to classical block codes, there is an important bound called the Singleton-type bound for locally repairable codes. In this paper, an optimal locally repairable code refers to a block code achieving this Singleton-type bound. Like classical MDS co...

Identify a string x over f0; 1g with the positive integer whose binary representation is 1x. We say that a self-reduction is k-local if on input x all queries belong to fx ? 1; : : :; x ? kg. We show that all k-locally self-reducible sets belong to PSPACE. However, the power of k-local self-reductions changes drastically between k = 2 and k = 3. Although all 2-locally self-reducible sets belong...

We generalize the construction of locally recoverable codes on algebraic curves given by Barg, Tamo and Vlăduţ [4] to those with arbitrarily many recovery sets by exploiting the structure of fiber products of curves. Employing maximal curves, we create several new families of locally recoverable codes with multiple recovery sets, including codes with two recovery sets from the generalized Giuli...