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• Yaghoub Sharifi, Ph.D. Thesis Defence, Mathematics
  11:00 AM - 1:00 PM
  August 6, 2013
  (Senior Supervisor: Jason Bell) Title: Centralizers in Associative Algebras Abstract: This thesis is divided into two parts. The subject of the first part is the structure of centralizers in associative algebras. We prove that, over an algebraically closed field of characteristic zero, the centralizer of a non-constant element in the second Weyl algebra has GK dimension one, two or three. Those centralizers of GK dimension one or two are commutative and those of GK dimension three are not locally PI. We show that for each n 2 f1; 2; 3g there exists a centralizer of GK dimension n. We will also find explicit forms of centralizers for some elements of the second Weyl algebra. Some algebras such as the first Weyl algebra, quantum planes and finitely generated graded algebras of GK dimension two can be viewed as subalgebras of some skew Laurent polynomial algebra over a ?eld. We prove that if K is a ?eld, ? 2 Aut(K) and the ?xed ?eld of ? is algebraically closed in K, then the centralizer of a non-constant element of a subalgebra of K[x; x??1; ?] is commutative and a free module of finite rank over some polynomial algebra in one variable. In the last chapter, which is the second part of this thesis, we first prove a new version of Shirshov's theorem. We then use this theorem to prove an analogue of Kaplansky's theorem, i.e. if D is a central division k-algebra which is left algebraic of bounded degree d over some subfield, which is not necessarily central, then [D : k] ? d2.
• Sergey Blagodurov, PhD Defence, Comp Sci
  2:00 PM - 4:00 PM
  August 6, 2013
  Ph.D. Thesis DEFENSE SERGEY BLAGODUROV Diploma with Honors (M.Sc.), Moscow Engineering Physics Institute (State University), Moscow, Russia, 2008. Tuesday, August 6th, 2013 2:00 p.m. TASC1 9204 WEST ADDRESSING SHARED RESOURCE CONTENTION IN DATACENTER SERVERS Servers are major energy consumers in modern datacenters. Much of that energy is wasted because applications compete for shared resources and suffer severe performance penalties due to resource contention. Contention for shared resources remains an unsolved problem in existing datacenters despite significant research efforts dedicated to this problem in the past. The goal of this work is to investigate how and to what extent contention for shared resource can be mitigated via workload scheduling. Scheduling is an attractive tool, because it does not require extra hardware and is relatively easy to integrate into the system. I have designed and implemented multiple Open Source and proprietary schedulers during my work on this dissertation. Most notably, I introduced the Distributed Intensity Online (DIO) scheduler to target the shared resource contention in the memory hierarchy of Uniform Memory Access (UMA) systems, followed by the Distributed Intensity NUMA Online (DINO) scheduler that I designed to improve performance and decrease power consumption on Non Uniform Memory Access (NUMA) servers. As part of my internship in HP Labs, I designed a work conserving scheduler that prioritizes access to the multiple CPU cores on an industry level multicore server, thus managing contention for CPU and improving server power efficiency. Finally, the Clavis2D framework extends the contention awareness to the datacenter level and provides a comprehensive cluster scheduling solution that simultaneously takes into account multiple performance- and power-related goals. My dissertation work utilizes state-of-the-art industry level datacenter infrastructure, does not require any modification or prior knowledge about the workload and provides significant performance and energy benefits on-the-fly. Key words: multicore processors, scheduling, shared resource contention, performance evaluation. Ph.D. Examining Committee: Dr. Alexandra Fedorova, Senior Supervisor Dr. Jian Pei, Supervisor Dr. Arrvindh Shriraman, Internal Examiner Dr. Diwakar Krishnamurthy, External Examiner Dr. Greg Mori, Chair
• O. Arda Cien PhD Education Thesis Examination
  10:00 AM - 1:30 PM
  August 7, 2013
  No Description

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