Abstract: Fourier transform estimates for $\|\widehat
f\,\|_{L_{q,\widetilde w}}$ via $\|f\|_{L_{p,w}}$ from above and from
below are studied. For $p=q$, equivalence results, i.e.,
$$C_1\|f\|_{L_{p,w}}\le \|\widehat f\,\|_{L_{p,\widetilde w}}\le
C_2\|f\|_{L_{p,w}},\qquad {\widetilde w}(x)=w(1/x)x^{p-2},\qquad 1\le
p<\infty,$$ where $C_1, C_2$ are constants, are shown to be valid for
functions from certain classes under the Muckenhoupt conditions: $w\in
A_p$ or $w\in A_{2p}$. Sharpness of these conditions is proved. Some
multidimensional extensions are given. This is a joint work with S.
Tikhonov (dimension one) and S. Tikhonov and D. Gorbachev
(multidimensional case).
Sept. 24 (UOttawa) - CRM Distinguished Lecture
Speaker: Nolan Wallach (UCSD)
Title: Levels of entanglement.
Abstract: One of the ways that quantum theory differs from classical
physics is through the notion of entanglement. Which has become one of
the main resources in the theoretical development of quantum information
and quantum computing. In this lecture we will discuss several
mathematical tools for the measurement of levels of multiparticle
entanglement of a quantum state. Although most of the literature on
entanglement is in the physics journals the concept of entanglement is
mathematical and in its simplest form it is very elementary. The lecture
will discuss techniques coming from invariant theory and algebraic
geometry that are used in the measurement of entanglement.
About the speaker: Nolan Wallach received his Ph.D. in 1966 from the
University of Washington.
After spending three years at the University of California, Berkeley, he
moved to Rutgers University where we became a Full Professor in 1972.
In 1989 he moved to the University of California, San Diego, where has
been ever since.
Professor Wallach has made numerous significant contributions to a broad
range of areas of mathematics,
including global differential geometry, noncommutative harmonic
analysis, cohomology of locally symmetric spaces,
representations of infinite dimensional Lie algebras, invariant theory,
and the theory of symmetric functions.
He is known for the proof of the Casselman - Wallach theorem on the
uniqueness of globalization of Harish-Chandra modules.
Professor Wallach was also among the pioneers in applying derived
functor modules to the study of unitary representations.
Professor Wallach has published five books. His book with Armand Borel,
titled "Continuous cohomology, discrete subgroups,
and representations of reductive groups", and his two-volume book on
real reductive groups,
are two main references for experts in the areas of representation
theory and automorphic forms.
Professor Wallach has received several awards and fellowships, including
an Alfred P. Sloan Fellowship (1972-1974)
and a Linback Award for Research Excellence (1977). In 2004 he was
elected to be a Fellow of the American Academy of Arts and Sciences.
He worked as an Associate Editor of Annals of Mathematics (1997-2003)
and an Editor for the Bulletin of American Mathematical Society,
and was an invited speaker at the International Congress of
mathematicians in Helsinki (1978).
Oct. 1 (UOttawa)
Speaker: Raluca Balan (Ottawa)
Title: Recent advances on the stochastic heat and wave equations with Gaussian noise
Abstract: I will begin this talk with a brief introduction to
the theory of stochastic partial differential equations
(s.p.d.e.'s) initiated by John Walsh in his Saint-Flour Lecture Notes
(1986).
The focus will be on the stochastic heat and wave equations.
In the classical theory, such equations are perturbed by a space-time
white noise,
and a random-field solution exists only in spatial dimension 1. If one
replaces the white noise with a ``colored noise'',
a random field solution exists in any spatial dimension, provided one
considers an appropriate ``color spectrum''.
The most interesting case is when the noise enters the equation in a
multiplicative way.
In this case, some progress has been made using the Wiener-chaos
decomposition of the solution, but there are still many open questions
left.
This talk is based partially on joint work with Ciprian Tudor (Lille).
Oct. 15 (Carleton) - Joint colloquium
Speaker: Grace Y. Yi (University of Waterloo )
Title: Analysis of Incomplete Data: Some Issues and Methods
Abstract: Standard statistical analysis is often challenged by new emerging issues and
various complex features of data arising in practice.
We are frequently faced with incomplete data that can not be analyzed directly with standard methods.
It is well known that simply ignoring missingness could lead to severely misleading results.
Although there has been rapid development in the analysis of such data in recent years, many challenging problems still remain.
In this talk, I will first give a brief review in this direction, and
then discuss some modeling and analysis methods concerning data with missing observations.
Biographical Sketch:
Professor Grace Yi is a Full Professor at the University of Waterloo.
She obtained her Ph.D. degree in 2000 from the University of Toronto.
Her research interests cover a wide range of areas related to biostatistics,
including survival analysis, recurrent events, longitudinal data analysis, missing responses and or covariates,
measurement errors and inference using composite likelihoods.
She has published more than 40 papers since receiving Ph.D. in 2000.
In recognition of her outstanding research achievements she received the 2010 CRM-SSC Prize.
She is co-editor of the Canadian Journal of Statistics and the Journal of Applied Probability and Statistics.
Nov. 5 (UOttawa) - CRM afternoon
Lecture 1. 3:00pm - 4:00pm
Speaker: Sergey Bezuglyi (Institute for Low Temperature Physics, Ukraine)
Title: Aperiodic Cantor dynamics
Abstract: A homeomorphism T of a Cantor set X is called
aperiodic if for every point x the orbit (T^n(x)) is infinite. The pair
(X,T) represents a Cantor aperiodic dynamical system. In my talk I will
first discuss the topological properties of the set of all aperiodic
homeomorphisms considered as a subset of Homeo(X).
Every aperiodic homeomorphism admits a realization as a Vershik map
acting on a path space of a Bratteli diagram. The second part of my talk
will be focused on aperiodic homeomorphisms whose Bratteli-Vershik
models are represented by the diagrams of simplest form: stationary and
finite rank diagrams. For such diagrams one can explicitly describe the
set of ergodic invariant measures.
Coffee: 4:00pm - 4:30pm
Lecture 2. 4:30pm - 5:30pm
Speaker: Patrick Brosnan (UBC)
Title: Admissible normal functions and the Hodge conjecture
Abstract: Normal functions are objects introduced by Poincare and
used by Lefschetz in his proof of the Hodge conjecture for surfaces.
Unfortunately Lefschetz's proof does not generalize from surfaces to
higher dimensional varieties. However, several years ago Mark Green
and Phillip Griffiths introduced a
formulation of the general Hodge conjecture that involves
singularities of normal functions on a higher dimensional base. I
will discuss work with H. Fang, Z. Nie and G. Pealstein on the
Green-Griffiths program and on normal functions in general. One of
the key features is the tendency of admissible normal functions, which
are by definition analytic objects, to behave like algebraic objects.
Title: Gauge theory: from physics to mathematics and back
Abstract:
I shall review, also from a historical viewpoint, how the mathematical
foundation of gauge theory turned out to be the theory of connections on
fibre bundles. In recent times the mathematical picture of gauge
theories has become much richer, also as a consequence of the
interactions with string theory. The application of powerful
mathematical techniques has produced results that in turn have
interesting physical applications.
Dec. 3 (Carleton) - Joint colloquium
Speaker: J. N. K. Rao (Carleton)
Title: Coping with Nonresponse and Missing Data in Surveys
Abstract: Total nonresponse and item nonresponse are major sources of non-sampling errors in
surveys. In this introductory talk, I will discuss several issues related to nonresponse, including factors causing nonresponse and statistical tools for coping with nonresponse. I will demonstrate the effects of bias due to total nonresponse on survey estimates through examples. I will present some methods to handle total nonresponse at the design stage as well as at the estimation stage. Item nonresponse is generally handled through imputation or filling in missing item values, using auxiliary information. I will present some imputation methods for survey data and discuss difficulties associated with statistical
inferences using imputed data and methods to get around those difficulties.