(CRM-, Joint-) Colloquium Fridays 3:30pm, Room B005, Department of Mathematics and Statistics, University of Ottawa Supported by

Coffee: Common Room, before the colloquium at 3pm.

(Carleton-uOttawa shuttle information)

Schedule:

Aug. 30 (UOttawa) - CRM Distinguished Lecture Series

• Speaker: Alexander Merkurjev (UCLA)
• Title: Cohomological invariants of algebraic groups
• Abstract: The notion of a cohomological invariant of an algebraic group was introduced by J.P. Serre. A survey of old a new results will be given in the talk.
• Short bio: The work of Merkurjev focuses on algebraic groups, quadratic forms, Galois cohomology, algebraic K-theory and central simple algebras. In the early 1980s he proved a fundamental result about the structure of central simple algebras of period dividing 2, which relates the 2-torsion of the Brauer group with Milnor K-theory. In subsequent work with Suslin this was extended to higher torsion as the Merkurjev–Suslin theorem, recently generalized in the norm residue isomorphism theorem (previously known as the Bloch-Kato conjecture), proven in full generality by Rost and Voevodsky. In the late 1990s Merkurjev gave the most general approach to the notion of essential dimension, introduced by Buhler and Reichstein, and made fundamental contributions to that field. In particular Merkurjev determined the essential p-dimension of central simple algebras of degree p^2 (for a prime p) and, in joint work with Karpenko, the essential dimension of finite p-groups.
  In 1982 Merkurjev won the Young Mathematician Prize of the Petersburg Mathematical Society for his work on algebraic K-theory. In 1986 he was an invited speaker at the International Congress of Mathematicians in Berkeley, California, and his talk was entitled "Milnor K-theory and Galois cohomology". In 1995 he won the Humboldt Prize, an international prize awarded to renowned scholars. In 1994 Merkurjev gave a plenary talk at the 2nd European Congress of Mathematics in Budapest, Hungary. In 2012 he won the Cole Prize in Algebra for his work on the essential dimension of groups.

Oct. 2 (Carleton) - Special colloquium (3:00-4:00 pm, coffee starting at 2:30, Room HP 4351)

• Speaker: Peter Glynn (Stanford University)
• Title: Monte Carlo Methods for Stochastic Differential Equations
• Abstract: Stochastic differential equations (SDEs) and associated jump-diffusion processes are widely used as models within the physical sciences, biology, engineering, economics, and finance. In this survey talk, we will discuss the use of Monte Carlo sampling methods as a means of numerically solving such models. As for deterministic differential equations, time-stepping methods are typically used to generate approximate solutions to SDEs. Not surprisingly, the bias induced by the approximation leads to slow convergence of the numerical scheme. We will then discuss several recent developments in this area. Surprisingly (and unlike the deterministic case), it turns out that we can frequently sample such paths without any approximation error/bias. We will conclude the talk by discussing some of the challenges that remain in this area.
  The talk is aimed at the general audience and will be followed by a reception sponsored by the Laboratory for Research in Statistics and Probability. Everyone is welcome.
• Short bio: Peter W. Glynn is the current Chair of the Department of Management Science and Engineering at Stanford University. He received his B.Sc. (Hon) in Mathematics from Carleton University in 1978, and a Ph.D in Operations Research from Stanford University in 1982. He then joined the faculty of the University of Wisconsin at Madison, where he held a joint appointment between the Industrial Engineering Department and Mathematics Research Center, and courtesy appointments in Computer Science and Mathematics. In 1987, he returned to Stanford, where he joined the Department of Operations Research. He is now the Thomas Ford Professor of Engineering in the Department of Management Science and Engineering, and also holds a courtesy appointment in the Department of Electrical Engineering. From 1999 to 2005, he served as Deputy Chair of the Department of Management Science and Engineering, and was Director of Stanford's Institute for Computational and Mathematical Engineering from 2006 until 2010. In addition, he is an Adjunct Research Professor at Carleton University, and also a Co-Director of the Laboratory for Research in Statistics and Probability at Carleton. He is a Fellow of INFORMS and a Fellow of the Institute of Mathematical Statistics, has been co-winner of Best Publication Awards from the INFORMS Simulation Society in 1993 and 2008, was a co-winner of the Best (Biannual) Publication Award from the INFORMS Applied Probability Society in 2009, and was awarded the John von Neumann Theory Prize from INFORMS in 2010. In 2012, he was elected to the National Academy of Engineering. His research interests lie in simulation, computational probability, queueing theory, statistical inference for stochastic processes, and stochastic modeling.

Oct. 4 (UOttawa) - Joint colloquium

• Speaker: David B. Leep (University of Kentucky)
• Title: Zeros of quadratic forms and higher degree forms
• Abstract: Many fields have the property that a homogeneous form with coefficients from the field has a nontrivial zero over the field if the number of variables is large enough compared to the degree of the form. Two important questions arise. Which fields have this property? Given a field with this property, exactly how many variables are needed for a given degree to guarantee a nontrivial zero over the field? This talk will survey some fascinating answers to these questions. We will consider algebraically closed fields, finite fields, p-adic fields, totally imaginary number fields, as well as function fields and power series fields over these fields. A special emphasis will be given to quadratic forms. Open questions and conjectures will be presented. This survey talk will be accessible to all faculty and graduate students.

Oct. 25 (Carleton) - Joint colloquium (3:30-4:30, coffee starting at 3:00, HP 4351 (MacPhail Room)

• Speaker: Yuri Bahturin (Memorial University of Newfoundland)
• Title: Growth of subalgebras and subideals in free Lie algebras
• Abstract: This is a joint work with A. Olshanskii. We investigate subalgebras in free Lie algebras, the main tool being relative growth and cogrowth functions. Our study reveals drastic differences in the behavior of proper finitely generated subalgebras and nonzero subideals. For instance, the growth of a proper finitely generated subalgebra H of a free Lie algebra L, with respect to any fixed free basis X, is exponentially small compared to the growth of the whole of L. Quite opposite, the cogrowth of any nonzero subideal S is exponentially small compared to the growth of L.

Nov. 1 (UOttawa) - Joint colloquium

• Speaker: Lionel Nguyen Van Thé (Université d'Aix-Marseille, France)
• Title: Dynamique des groupes polonais non-archimédiens et combinatoire finie
• Abstract: Au cours des dernières années, plusieurs travaux ont montré que certaines propriétés dynamiques d'une classe de groupes topologiques appelés "polonais non-archimédiens" étaient intimement liées à des phénomènes remarquables en combinatoire finie. Le but de cet exposé sera de présenter quelques résultats relatifs à cette interaction.

Nov. 15 (Carleton) - Joint colloquium

• Speaker: Laurent Marcoux, University of Waterloo
• Title: Non-selfadjoint double commutant theorems
• Abstract: Let H be a complex, separable Hilbert space. The celebrated von Neumann Double Commutant Theorem states that if \N is a unital and selfadjoint subalgebra of the set B(H) of continuous linear operators acting on H, then (\N)' := {T in B(H) : TN = NT for all N in \N} coincides with the closure of \N in the strong operator topology. The beauty of this result lies in the fact that for such algebras, it equates a purely algebraic notion - that of belonging to the second commutant of the algebra - with a purely topological notion - that of belonging to the closure of the algebra in a given topology. In this talk, we shall discuss extensions of this result to not necessarily selfadjoint algebras of operators in B(H). Even in finite-dimensions, it is an interesting problem to completely classify the set of matrix algebras which are equal to their second commutants. This is joint work with Mitja Mastnak (St Maryʼs University, Halifax)

Jan. 15 at 4:00pm room B015 (UOttawa) - Joint colloquium

• Speaker: Ugo Bruzzo (SISSA)
• Title: The shape of moduli space
• Abstract: In geometry, a moduli space is a space whose points parameterise geometric objects (varieties of a given dimension, vector bundles on a given variety, etc). Moduli spaces not only answer the mathematician's proclivity to classification, but are also widely used in theoretical physics, for instance to parameterise possible models of a physical theory. They tend to have a rather complicated geometry. In some cases the fact that they carry group actions (for instance, by an algebraic torus) allows one to get information about their topology (e.g., compute their Betti numbers). My talk will be a general introduction to this subject with some examples.

Jan. 24 (Carleton) - Joint colloquium

• Speaker: S. Ejaz Ahmed (Brock University)
• Title: Perspectives on Human Bias versus Machine Bias: Big Data Analysis
• Abstract: In high-dimensional data settings where number of variables is greater than observations, many penalized regularization approaches were studied for simultaneous variable selection and estimation. However, with the existence of covariates with weak effect, many existing variable selection methods, including Lasso and its generations, cannot distinguish covariates with weak and no contribution. Thus, prediction based on a submodel of selected covariates may not be trust worthy. In this talk, we propose a high-dimensional shrinkage estimation strategy to improve the prediction performance of a submodel. Such a high-dimensional shrinkage estimator (HDSE) is constructed by shrinking a weighted ridge estimator in the direction of a predefined candidate submodel. Under an asymptotic distributional quadratic risk criterion, its prediction performance is explored analytically. We show that the proposed HDSE performs better than the weighted ridge estimator. More importantly, it improves the prediction performance of any candidate submodel generated from most existing Lasso-type variable selection methods significantly. The relative performance of the proposed HDS strategy is demonstrated by both simulation studies and the real data analysis.

Feb. 7 (UOttawa) - Joint colloquium

• Speaker: Zinovy Reichstein (University of British Columbia)
• Title: Quadratic forms and their Pfister numbers
• Abstract: Quadratic forms and their use in geometry and number theory have a long and distinguished history going back to ancient times. The algebraic theory is more recent. It originated in the work of Ernst Witt in the 1930s, who organized the non-degenerate quadratic forms over a field $K$ into what we now call the Witt ring of $K$. In the 1960s Albrecht Pfister introduced the basic building blocks of this ring, which we now call Pfister forms. The smallest number of $d$-fold Pfister forms required to represent a quadratic form $q$ is called the $d$th Pfister number of $q$. These numbers may be viewed as a measure of complexity of quadratic forms.

  In this talk I will give an informal introduction to the theory of quadratic forms, then discuss a theorem, proved jointly with Patrick Brosnan and Angelo Vistoli, which shows that there exist quadratic forms with surprisingly large Pfister numbers.

Feb. 28 (UOttawa) - Joint colloquium

• Speaker: Michael C Wolfson and Geoff Rowe (University of Ottawa)
• Title: HealthPaths – Using Health Trajectories to Estimate and Simulate the Relative Importance of Determinants of Health Adjusted Life Expectancy (HALE), a Statistical Analysis
• Abstract: Background There is broad agreement that a summary measure of population health such as HALE is fundamental. While HALE is strongly correlated with income, multivariate analyses ascribing relative importance to a range of socioeconomic determinants are relatively rare.

  Methods This analysis combines very detailed statistical analysis of Statistics Canada’s longitudinal National Population Health Survey (NPHS), with the HealthPaths dynamic microsimulation model. Microsimulation is used to synthesize a realistic base-case representative longitudinal population sample, and then a series of carefully constructed counterfactual populations, each cutting a link in the “web of causality” estimated from the NPHS. Comparisons of the distributions of health-adjusted life lengths and summary HALE measures between counterfactuals and the base case are then used to estimate the quantitative importance of the determinants being analysed. Replicate simulations plus underlying replicate regressions further enable sophisticated measures of uncertainty in model results.

  Findings This analysis extends an earlier version which focused on four factors -- obesity, smoking, education, and Antonovsky’s Sense of Coherence (SoC). In that analysis, surprisingly, SoC had the largest potential impact, while education and smoking each accounted for about half as many years of (cause-deleted) HALE, and obesity accounted for relatively little. This analysis extends these results to encompass a broader range of factors, including household income, leisure and daily physical activity, employment, sense of mastery, family membership, and institutional residence. These additions change the rank order and magnitudes of the factors somewhat, reflecting omitted variable biases. The statistical analysis has had to confront a number of challenges with the main data set, including “inertia” in health states, missing data, and errors in variables.

  Interpretation Widely observed socioeconomic gradients in health, when examined in greater detail, are the culmination of myriad co-evolving dynamic processes, where their interacting and joint effects, alone, are each small. It is essential to employ an analytical framework that combines robust estimates of individual multivariate health status dynamics with health determinants dynamics in order to assess realistically the sources of health inequalities.

March 28 - booked

April 4 (UOttawa) - Joint Colloquium at 11:30, room FTX315 (Different time and place)

• Speaker: Camille Male (Paris 5)
• Title: The spectrum of large random matrices, the non commutative random variables and the distribution of traffics.
• Abstract: The purpose of this talk is to give an introductory presentation of a notion of distributions, which generalizes the notion of law of complex random variables and is useful to understand the spectrum of large random matrices. Free probability theory has been introduced by Voiculescu in the 80's for the study of the von Neumann algebras of the free groups. It consists in an algebraic setting of non commutative probability, where one encodes "non commutative random variables" in abstract (non commutative) algebras endowed with linear forms (which satisfies properties in order to play the role of the expectation). In this context, Voiculescu introduce the notion of freeness which is the analogue of the classical independence. A decade later, he realized that a family of independent random matrices invariant in law by conjugation by unitary matrices are asymptotically free. This phenomenon is called asymptotic freeness. This approach had a deep impact in operator algebra and probability and has been generalized in many directions. A simple particular case of Voiculescu's theorem gives an estimate, for N large, of the spectrum of an N by N Hermitian matrix H_N = A_N + 1/\sqrt N X_N, where A_N is a given deterministic Hermitian matrix and X_N has independent gaussian standard sub-diagonal entries. Nevertheless, it turns out that asymptotic freeness does not hold in certain situations. For instance, in the problem of computing the asymptotic spectrum of H_N = A_N + 1/\sqrt N X_N as above when the entries of X_N can grow with N, one need more information on A_N that its non commutative distribution. To answer this question, I mimic Voiculescu's approach introducing the distributions of traffics and their free product. This notion of distribution is richer than Voiculescu's notion of distribution of non commutative random variables. The notion of freeness for traffics is an intriguing mixing between the classical independence and Voiculescu's notion of freeness. Thanks to these concepts, we prove an asymptotic freeness theorem for independent random matrices invariant in law by conjugation by permutation matrices. These notions are very related to the notion of convergence of large graphs introduced by Benjamini and Schramm. The free product of traffics reduces in this context to a natural notion of free product of random graphs and random groups.

April 4 (Carleton) - Joint Colloquium

• Speaker: Uffe Haagerup (University of Copenhagen)
• Title: Approximation properties for groups and C*-algebras
• Abstract: It is a classical result in Fourier analysis that the Fourier series of a continuous function may fail to converge uniformly or even pointwise to the given function. However, if one uses a summation method as, e.g., Cesaro mean convergence, one actually gets uniform convergence of the Fourier series. This result can easily be generalized first to all abelian LC (= locally compact) groups, and next to all amenable (LC) groups, where in the non-abelian case, the continuous functions on the dual group should be replaced by the reduced group C*-algebra of the group. In 1994 Jon Kraus and I introduced a new approximation property (AP) for locally compact groups. The groups having (AP) form the largest class of LC groups for which a generalized Cesaro mean convergence theorem can hold. The group SL(2,R) has this property, but it was only proven recently by Vincent Lafforgue and Mikael de la Salle that SL(n,R) fails to have (AP) for n = 3,4,... In joint work with Tim de Laat we extend their result by proving that Sp(2,R) and, more generally, all simple connected Lie groups of real rank at least 2 and with finite centre do not have the (AP). In the talk I will give an introduction to amenability, weak amenability and the property (AP) for locally compact groups, and the corresponding properties for C*-algebras will also be discussed. Weak amenability is another approximation property for LC groups.

  Biographical information: Professor Haagerup is among the world's leading mathematicians, having made ground-breaking contributions in a variety of areas ranging from operator algebras and operator theory to free probability, random matrices and applications in mathematical physics. Modern functional and harmonic analysis even reflects his tremendous influence through fundamental concepts bearing his name that have entered the mathematical lexicon, such as the Haagerup tensor product and the Haagerup property. His many honours include an invited lecture at the ICM 1986 (Berkeley) as well as plenary lectures at both the ICM 2002 (Beijing) and the ICMP 2012 (Aalborg). He received the 14th European Latsis Prize from the European Science Foundation in 2012, and presently holds an Advanced Grant from the European Research Council. He is a member of the Royal Danish Academy of Sciences and Letters, as well as the Norwegean Academy of Science and Letters.

April 25 (UOttawa) - CRM Distinguished Lecture

• Speaker: Philippe Biane (Paris-Est)
• Title: Gog and Magog triangles
• Abstract: These are two species of triangles, made of positive integers, which appear in many combinatorial problems. For some mysterious reasons it turns out that there is the same number of Gog and Magog triangles. I will describe some recent progress on understanding this mystery. The talk will be completely elementary.
• Short Bio: Philippe Biane a été professeur à l'université Paris VI et à l'École normale supérieure (ENS) de Paris. Il est directeur de recherche au Centre national de la recherche scientifique, à l'Institut Gaspard-Monge de l'université Paris-Est de Marne-la-Vallée. Il se consacre surtout aux probabilités libres (de) à la suite de Dan Voiculescu, ainsi qu'à la théorie des probabilités pour des variables non commutatives. En outre, il développe les connaissances sur les liens entre le mouvement brownien, la fonction zêta de Riemann et les fonctions apparentées à la théorie des nombres. Il a obtenu en 1994 le prix Rollo Davidson. Il a été invité référent au Congrès international des mathématiciens de 2002 à Pékin, sur le thème des probabilités libres. Philippe Biane est coéditeur de la revue spécialisée Probability Theory and Related Fields.

May 1 (UOttawa) - CRM Distinguished Lecture

• Speaker: Jianhong Wu (York University)
• Title: Measuring Climate Impact on Tick Expansion and Lyme Disease Spread
• Abstract: The extent to which climate change may affect human health by increasing risk from vector-borne diseases has been under considerable debate, resolution of which requires well defined and validated metrics and standards. In a series of collaborative projects, we develop and analyze stage-structured periodic deterministic models parametrized by the North American geographical landscape and projected temperature. The model analysis provides quantified potential effects of future climate change on /R/_0 of the tick vector of Lyme disease /Ixodes scapularis/ and explore their significance for Lyme disease risk in particular, and for vector-borne diseases in general. Increased temperatures due to projected climate change increased /R/_0 by factors (2-5 fold in Canada and 1.5-2 fold in the US) comparable to observed ranges of /R/_0 for pathogens and parasites due to variations in strains, geographic locations, epidemics, host and vector densities, and control. We conclude that a warming climate may have co-driven Lyme disease emergence in North America, and in the future will likely drive substantial disease spread into new geographic regions and may increase tick-borne disease risk where climate is currently suitable.
• Short Bio: Prof. Jianhong Wu is a University Distinguished Research Professor, Canada Research Chair in Industrial and Applied Mathematics and Director of the Center for Disease Modeling. He is an internationally recognized specialist in the mathematical theory and applications of differential equations, infinite dimensional dynamical systems, non-linear analysis, data analysis, population biology and neural dynamics. He leads a national research team of mathematicians, epidemiologists, virologists, infectious disease experts and leading public health scientists to map the spread of diseases such as SARS, influenza and West Nile virus. Wu’s research uses mathematical models and computer simulations to track and predict disease spread patterns, from which recommendations can be made to evaluate and improve public health policy in Canada and elsewhere.