Department of Mathematics, University of South Carolina

Fri 24 Oct 2014, 3:00pm
Department Colloquium
MATX 1100

A new asymptotic enumeration technique: the Lovasz Local Lemma

MATX 1100
Fri 24 Oct 2014, 3:00pm4:00pm
Abstract
The lopsided version of the Lovasz Local Lemma gives asymptotically tight lower boundsfor a number of enumeration problems. In the configuration model matching upper bounds are available. In this way a number of asymptotic enumeration results, mostly due to Wormald and McKay, can be proved in an alternative way. A new result is asymptotic enumeration of graphs with respect to degree sequence and girth. A classical probabilistic result of Paul Erdos showed the existence of graphs with arbitrary large girth and chromatic number. If the degree sequence satisfies some mild conditions, we show that almost all graphs with this degree sequence and prescribed girth have high chromatic number.
This is joint work with Lincoln Lu.
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Univeristy of Michigan

Fri 31 Oct 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)

Imaging with waves in complex environments (PIMSIAMUBC distinguished colloquium)

ESB 2012 (PIMS)
Fri 31 Oct 2014, 3:00pm4:00pm
Abstract
The talk is concerned with the application of sensor array imaging in complex environments. The goal of imaging is to estimate the support of remote sources or strong reflectors using time resolved measurements of waves at a collection of sensors (the array). This is a challenging problem when the imaging environment is complex, due to numerous small scale inhomogeneities and/or rough boundaries that scatter the waves. Mathematically we model such complexity (which is necessarily uncertain in applications) using random processes, and thus study imaging in random media. I will focus attention on the application of imaging in random waveguides, which exhibits all the challenges of imaging in random media. I will present a quantitative study of cumulative scattering effects in such waveguides and then explain how we can use such a study to design high fidelity imaging methods.
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UC Berkeley

Fri 14 Nov 2014, 3:00pm
Department Colloquium
MATX 1100

The fundamental theorem of arithmetic for metric measure spaces

MATX 1100
Fri 14 Nov 2014, 3:00pm4:00pm
Abstract
A metric measure space (mms) is simply a complete, separable metric space equipped with a probability measure that has full support. A fundamental insight of Gromov is that the space of such objects is much ``tamer'' than the space of complete, separable metric spaces per se because mms carry within themselves a canonical family of approximations by finite structures: one takes the random mms that arises from picking some number of points independently at random and equipping it with the induced metric and uniform probability measure. A natural (commutative and associative) binary operation on the space of mms is defined by forming the Cartesian product of the two underlying sets equipped with the sum of the two metrics and the product of the two probability measures. There is a corresponding notion of a prime mms and an analogue of the fundamental theorem of arithmetic in the sense that any mms has a factorization into countably many prime mms which is unique up to the order of the factors. Moreover, a rich Fourier theory enables one to analyze convolutions of probability measures on the space of mms and obtain counterparts of classical results in the theory of infinitely divisible and stable probability measures on Euclidean spaces due to L\'evy, It\^o, Hin\u{c}in, and LePage. This is joint work with Ilya Molchanov (Bern).
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The University of Auckland

Fri 21 Nov 2014, 3:00pm
Department Colloquium
Math Annex 1100

Reducing lectures, making students responsible, and offering semiauthentic mathematical experiences.

Math Annex 1100
Fri 21 Nov 2014, 3:00pm4:00pm
Abstract
In the Mathematics Department of The University of Auckland a major research project into undergraduate mathematics learning outcomes has required the development of three innovative ways to deliver undergraduate mathematics. One of these involves reducing lectures to less than one per week, handing responsibility for most of their mathematical learning to students using web or text resources. We then use the staff time saved to provide semiauthentic mathematical experiences in which students work in small groups for up to two hours at a time guided by a lecturer on openended mathematical situations. Such sessions require new teaching skills and new learning orientations. There is some evidence that we have made progress on the development of mathematical process skills.
Our research shows that, with our small trial groups, students perform at similar levels on the conventional assessments as do the students in the standard courses.
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Caltech

Fri 30 Jan 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS) TBA (time and date to be confirmed)

PIMSUBC distinguished colloquium

ESB 2012 (PIMS) TBA (time and date to be confirmed)
Fri 30 Jan 2015, 3:00pm4:00pm
Abstract
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UCLA

Fri 6 Mar 2015, 3:00pm
Department Colloquium
MATX 1100

TBA

MATX 1100
Fri 6 Mar 2015, 3:00pm4:00pm
Abstract
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Brown University

Fri 13 Mar 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS)

PIMSUBC Distinguished Colloquium, TitleTBA

ESB 2012 (PIMS)
Fri 13 Mar 2015, 3:00pm4:00pm
Abstract
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Note for Attendees
Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.