Seminars and Colloquiums
for the week of February 4, 2008
Speakers:
Professor Wenbo Li, Monday
Professor Fernando Schwartz , Monday
Professor J. Douglas Birdwell & Professor Tsewei Wang, Tuesday
Dr. P. Vassilevski, Thursday
Dr. Sergey Melikhov, Friday
Monday, February 4
PROBABILITY SEMINAR
TIME: 10:10 – 11:00 a.m.
ROOM: Ayres 309A
SPEAKER: Professor Wenbo Li (University of Delaware)
TITLE: “Fourier Transforms with Only Real Zeros and Probability”
ABSTRACT: The study of Fourier transforms with only real zeros has significant impacts in analysis, combinatorics and probability. We will provide several examples to demonstrate the usefulness in probability. In particular, we will present recent joint work with Y. Leung and Rakesh on the spectral analysis of Browian motion with jump boundary.
DIFFERENTIAL GEOMETRY COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 214
SPEAKER: Professor Fernando Schwartz
TITLE: “On the topology of black holes”
ABSTRACT: 3+1 dimensional black holes have spherical topology, but in higher dimensions this is no longer true. In this talk I will explain the preceding statement and show a construction, in terms of Riemannian geometry, of outermost apparent horizons with nonspherical topology.
Tuesday, February 5
JUNIOR COLLOQUIUM
TIME: 3:40 – 4:30 p.m.
ROOM: Ayres 214
SPEAKERS: Professor J. Douglas Birdwell, Professor, Electrical Engineering and Computer Science &
Professor Tsewei Wang, Associate Professor, Chemical and Biomolecular Engineering
TITLE: “Catching Bad Guys Using Mathematics: The Mathematics of Using DNA Profiles in Human Identification
ABSTRACT: Law enforcement agencies have used DNA typing of individuals and crime stains since the mid 1990s to help identify perpetrators of crimes. US federal and States all have laws that permit the collection and storage of DNA profiles of offenders convicted of felonies, and this is gradually being extended to arrestees. This talk will briefly review the characteristics of DNA evidence and the roles that mathematics can play in human identification. An overview of three applications will be presented: a method for efficiently indexing large populations of DNA profiles to enable rapid search and retrieval of profiles matching forensic evidence, the mathematics that enables the analysis of DNA mixtures to determine likely contributors, and the use of population statistics and likelihood ratios to determine probable genetic relationships between individuals. A brief overview of some recent cases will also be presented to highlight the relevance of these applications to current events.
Thursday, February 7
MATHEMATICS COLLOQUIUM
TIME: 3:40 p.m.
ROOM: Ayres 214
SPEAKER: Dr. P. Vassilevski
TITLE: “Exact De Rham Sequences of Finite Element Spaces on Agglomerated Elements”
ABSTRACT: In this talk we introduce new ?nite element spaces that can be constructed for agglomerates of standard elements in 3-d. The agglomerates are assumed to have certain regular structure in the sense that they share faces with closed boundaries composed of 1-d edges. The spaces are subspaces of a originally given de Rham sequence of respective H1-conforming, H(curl)-conforming, H(div)-conforming and piecewise constant spaces. The procedure can be recursively applied so that a sequence of nested de Rham complexes can be constructed. As an application, we use the sequence of nested counterparts of the respective piecewise linears, the lowest order Nédélec, and the lowest order Raviart-Thomas spaces, to construct V-cycle multigrid as preconditioners in the conjugate gradient method. The resulting element agglomeration AMG (algebraic multigrid) methods appear to perform very similarly to the geometric MG in the case of uniformly re ?ned meshes.
This talk is based on a joint work with Joseph E. Pasciak, Texas A&M University.
Friday, February 8
TOPOLOGY SEMINAR
TIME: 2:30-3:20 p.m.
ROOM: Ayres Hall 209A
SPEAKER: Dr. Sergey Melikhov
TITLE: “Realizing Steenrod homotopy classes by spheroids”
ABSTRACT: A study of actions of p-adic integers on ANRs motivates comparison of Steenrod and singular homotopy groups of non-ANRs (which arise as potential orbit spaces).
By a result due essentially to W. Hurewicz and K. Borsuk, singular (i.e. "usual"), Steenrod (=strong shape) and Cech (=shape) homotopy groups (pointed sets for n=0) \hat\pi_n(X), \pi_n(X) and \check\pi_n(X) are isomorphic for any locally n-connected compactum X, where "local n-connectedness" is with respect to your favorite of the three theories.
We prove that for n>1 and a locally n-connected compactum X which is also simply connected, the homomorphism \hat\pi_{n+1}(X) -> \pi_{n+1}(X) is onto. The condition of simply-connectedness cannot be dropped.
Interested in giving or arranging a talk? Check out our calendar.
Previous Announcements:
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Seminars from 2006-2007 academic year