The Mod-2 Cohomology Ring of the Third Conway Group is Cohen-Macaulay

By explicit machine computation we obtain the mod-2 cohomology ring of the third Conway group Co_3. It is Cohen-Macaulay, has dimension 4, and is detected on the maximal elementary abelian 2-subgroups.Comment: 12 pages; writing style now more concis

MARACAS: a real-time multicore VCPU scheduling framework

This paper describes a multicore scheduling and load-balancing framework called MARACAS, to address shared cache and memory bus contention. It builds upon prior work centered around the concept of virtual CPU (VCPU) scheduling. Threads are associated with VCPUs that have periodically replenished time budgets. VCPUs are guaranteed to receive their periodic budgets even if they are migrated between cores. A load balancing algorithm ensures VCPUs are mapped to cores to fairly distribute surplus CPU cycles, after ensuring VCPU timing guarantees. MARACAS uses surplus cycles to throttle the execution of threads running on specific cores when memory contention exceeds a certain threshold. This enables threads on other cores to make better progress without interference from co-runners. Our scheduling framework features a novel memory-aware scheduling approach that uses performance counters to derive an average memory request latency. We show that latency-based memory throttling is more effective than rate-based memory access control in reducing bus contention. MARACAS also supports cache-aware scheduling and migration using page recoloring to improve performance isolation amongst VCPUs. Experiments show how MARACAS reduces multicore resource contention, leading to improved task progress.http://www.cs.bu.edu/fac/richwest/papers/rtss_2016.pdfAccepted manuscrip

Endotrivial modules for the sporadic simple groups and their covers

In a step towards the classification of endotrivial modules for quasi-simple groups, we investigate endotrivial modules for the sporadic simple groups and their covers. A main outcome of our study is the existence of torsion endotrivial modules with dimension greater than one for several sporadic groups with $p$-rank greater than one.Comment: in Journal of Pure and Applied Algebra, published online 19th February 201

O'NAN MOONSHINE AND ARITHMETIC

Answering a question posed by Conway and Norton in their seminal 1979 paper on moonshine, we prove the existence of a graded infinite-dimensional module for the sporadic simple group of O'Nan, for which the McKay--Thompson series are weight $3/2$ modular forms. The coefficients of these series may be expressed in terms of class numbers, traces of singular moduli, and central critical values of quadratic twists of weight 2 modular $L$-functions. As a consequence, for primes $p$ dividing the order of the O'Nan group we obtain congruences between O'Nan group character values and class numbers, $p$-parts of Selmer groups, and Tate--Shafarevich groups of certain elliptic curves. This work represents the first example of moonshine involving arithmetic invariants of this type

Coxeter and crystallographic arrangements are inductively free

AbstractUsing the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type E8. With little extra work we prove that also all Coxeter arrangements are inductively free