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 Events
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, distributed-memory library for (arbitrary-precision) linear algebra, conic optimization, and lattice reduction
ESB 4133 (PIMS Lounge)
Tue 9 Feb 2016, 12:30pm-1:30pm

Abstract

While large numbers of researchers have investigated efficient distributed-memory schemes for dense and sparse-direct 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 Second-order Cone Programs will be discussed, and a case will be made for defaulting to explicitly storing quasi-constant edge-degree plus low-rank decompositions of the sparse KKT systems and then solving said systems via applying the iteratively-refined inverse of an a priori regularized, Symmetric Quasi-Semidefinite factorization as a preconditioner for Flexible GMRES(k). Recent work towards high-performance variants of lattice reduction schemes (LLL and BKZ 2.0) will also be briefly discussed to help make the case for the importance of high-precision 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.

Note for Attendees

Sushi lunch will be served at 12:25 p.m.
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Wed 10 Feb 2016, 10:00am
Math Education Research Reading
Math 126
"Peer-Assisted Reflection: A Design-Based Intervention for Improving Success in Calculus"
Math 126
Wed 10 Feb 2016, 10:00am-11:00am

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, 3:15pm-4:15pm

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 "E-infinity-ring-space" structure.

Note for Attendees

 The seminar is back to the regular time!
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Bob Hough
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, 3:30pm-4:30pm

Abstract

Random walk on a group is an established but still-growing 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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Pierre Tarrago
Fri 12 Feb 2016, 1:00pm
Probability Seminar
MATH 126
Thermodynamic limit on the graph of Zigzag diagrams
MATH 126
Fri 12 Feb 2016, 1:00pm-2:00pm

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 n-1 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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Bob Hough
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, 3:00pm-4:00pm

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?

Note for Attendees

Refreshments will be served in MATH 125 before the colloquium.
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