Institute for Computational Engineering and Mathematics, Stanford University

Tue 9 Feb 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Towards an efficient, distributedmemory library for (arbitraryprecision) linear algebra, conic optimization, and lattice reduction

ESB 4133 (PIMS Lounge)
Tue 9 Feb 2016, 12:30pm1:30pm
Abstract
While large numbers of researchers have investigated efficient distributedmemory schemes for dense and sparsedirect linear algebra, relatively little work has been performed on extensions into the important fields of conic optimization and lattice reduction. (Perhaps surprising) performance barriers for distributed sparse Secondorder Cone Programs will be discussed, and a case will be made for defaulting to explicitly storing quasiconstant edgedegree plus lowrank decompositions of the sparse KKT systems and then solving said systems via applying the iterativelyrefined inverse of an a priori regularized, Symmetric QuasiSemidefinite factorization as a preconditioner for Flexible GMRES(k). Recent work towards highperformance variants of lattice reduction schemes (LLL and BKZ 2.0) will also be briefly discussed to help make the case for the importance of highprecision arithmetic. Some practical issues related to the implementation of these techniques within the open source library Elemental (https://github.com/elemental/Elemental) will also be discussed.
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Wed 10 Feb 2016, 10:00am
Math Education Research Reading
Math 126

"PeerAssisted Reflection: A DesignBased Intervention for Improving Success in Calculus"

Math 126
Wed 10 Feb 2016, 10:00am11:00am
Abstract
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Bernardo Villarreal Herrera
University of British Columbia

Wed 10 Feb 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

Cosimplicial groups and spaces of homomorphisms

ESB 4133 (PIMS Lounge)
Wed 10 Feb 2016, 3:15pm4:15pm
Abstract
In this talk I will give some relations between spaces of homomorphisms when the target group G is a real linear algebraic group, through homotopy stable decompositions of simplicial spaces. To obtain a simplicial space Hom(L,G) out of spaces of homomorphisms we think of L, a (suitable) family of finitely generated groups, as a cosimplicial group.
Also, if G=U, the colimit of the unitary groups U(m), I will show when the geometric realization of Hom(L,U) has an "Einfinityringspace" structure.
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Institute for Advanced Study, Princeton

Thu 11 Feb 2016, 3:30pm
Discrete Math Seminar
MATH 126

Random walk on unipotent groups

MATH 126
Thu 11 Feb 2016, 3:30pm4:30pm
Abstract
Random walk on a group is an established but stillgrowing field. I discuss aspects of recent work, alone and joint with Persi Diaconis, on random walks on unipotent groups. Among our results, we have a new local limit theorem for random walk on the Heisenberg group, which applies to arbitrary centered measures of compact support and obtains an optimal rate. There is also a mixing time bound of degree times diameter squared for the mixing time of random walk on some Cayley graphs of cyclic groups.
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Fri 12 Feb 2016, 1:00pm
Probability Seminar
MATH 126

Thermodynamic limit on the graph of Zigzag diagrams

MATH 126
Fri 12 Feb 2016, 1:00pm2:00pm
Abstract
In this talk, I will first introduce the notions of Gibbs measures and thermodynamic limit on graded graphs, as they were defined by the Russian school (Vershik, Kerov, Olshanski,...). Then, I will present some results related to the thermodynamic limit on the graph of Zigzag diagrams: the latter is a graded graph whose set of vertices of degree n consists of words of length n1 in two letters, and such that the edge structure is given by a simple combinatorial relation between words of consecutive lengths. This graph is related to the Young graph, and I will explain this relation by mapping paths on the graph of Zigzag diagrams to paths on the Young graph. "
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Institute for Advanced Study, Princeton

Fri 12 Feb 2016, 3:00pm
Department Colloquium
MATX 1100

Covering systems of congruences and the Lovasz Local Lemma

MATX 1100
Fri 12 Feb 2016, 3:00pm4:00pm
Abstract
The Lov\'{a}sz Local Lemma is a powerful technique from probabilistic combinatorics for treating many rare events with localized dependence structure. I discuss the local lemma and its application in my negative solution to the following problem of Erd\H{o}s.
A distinct covering system of congruences is a collection of arithmetic progressions
a_i \bmod m_i, \qquad 1 < m_1 < m_2 < ... < m_k
whose union is the integers. Can m_1 be arbitrarily large?
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Note for Attendees
Sushi lunch will be served at 12:25 p.m.