(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 transportation information)

Schedule:

Sept. 5 (UOttawa) - CRM Distinguished Lecture Series.

• Speaker: Yuri Tschinkel (Courant Institute)
• Title: Quadratic forms and geometry of numbers
• Abstract: I will survey some classical and recent ideas in higher-dimensional arithmetic geometry.
• Short bio: Yuri Tschinkel received his doctorate in mathematics from the Massachusetts Institute of Technology in 1992. From 1992-95 he was Junior Fellow of the Harvard Society of Fellows, and from 1995-96 he was a Leibniz fellow at the Ecole Normale Superieure in Paris. Yuri Tschinkel was a faculty member at the University of Illinois at Chicago, a visiting associate professor at Princeton University, the Gauss chair of mathematics at the University of Gottingen, and professor and chair of the mathematics department at the Courant Institute, New York University.
  He was also a member of the Institute for Advanced Study in Princeton and held visiting fellowships at the Isaac Newton Institute for Mathematical Sciences in Cambridge, University of Tokyo, Max Planck Institute in Bonn, Institut des Hautes Etudes Scientifiques in Paris, Eidgenossische Technische Hochschule Zurich, and Research Institute for Mathematical Sciences at Kyoto University. He was an invited speaker at the International Congress of Mathematicians in Madrid in 2006.
  He serves on the editorial boards of Algebraic Geometry, Experimental Mathematics, the Bulletin of the American Mathematical Society, the European Journal of Mathematics, and the Progress in Mathematics series from Birkhauser. He is a member of the Scientific Council of the Fondation Sciences Mathematiques de Paris and has served on several other advisory boards.
  Tschinkel's research is at the interface of algebraic geometry and number theory. He studies higher-dimensional algebraic varieties, their hidden symmetries and rational points. He is the author of 100 papers and editor of 14 books.

Sept. 19 (UOttawa) - CRM Distinguished Lecture Series

• Speaker: David Vogan (MIT)
• Title: Matrices almost of order two
• Abstract: Langlands' conjectures about automorphic forms suggest that infinite-dimensional irreducible representations of GL(n,R) (something quite subtle) correspond more or less to conjugacy classes of elements of order 2 in GL(n,C) (something extremely simple). I'll explain where this statement comes from, and how Langlands made precise the "more or less" so that the statement is actually true. I'll explain further how to use the same point of view to address other interesting problems, like Cartan's classification of real semisimple Lie groups.
• Short bio: David Vogan received the B.A. and S.M. degrees from the University of Chicago in 1974, and the Ph.D. from MIT in 1976 under the direction of Bertram Kostant. He continued as an Instructor, and Member of the Institute for Advanced Study, before joining the MIT mathematics faculty in 1979.
  His research interests include group representations and Lie algebras. He is a member of the research group Atlas of Lie groups and representations, which in 2007 computed the character table of the Lie group E8, attracting a great deal of international press.
  He was selected by the MIT Department Faculty as the Robert E. Collins Distinguished Scholar in 2007. In 2011, he received the AMS Levi L. Conant Prize for his article, "The Character Table for E8". He is a Fellow of the American Academy of Arts & Sciences (1996). He has given many distinguished lectures, including a plenary address at the ICM in Berkeley in 1986. He is President of the American Mathematical Society (2013-15).

Oct. 3 (UOttawa) - CRM Colloquium

• Speaker: Laurent Manivel (CRM, University of Montreal)
• Title: An algebraic version of the P vs NP problem: how to compare the permanent and the determinant
• Abstract: In order to attack the P vs NP problem with the full force of mathematics, Leslie Valiant developped an algebraic (slightly weaker) version called the VP vs VNP problem. This problem can ultimately be translated into the question of understanding how different are the determinant and the permanent (the determinant without signs). I will present the mathematical problem in detail as well as the state of the art, including the program elaborated by Mulmuley and Sohoni, which involves deep ideas from algebraic geometry and representation theory.
• Short bio: A former student of the Ecole Normale Superieure in Paris, Laurent Manivel received his PhD from the University of Grenoble in 1992. He has been a CNRS researcher at the Institut Fourier in Grenoble from 1989 to 2014 and he is currently a member of the Centre de Recherches Mathematiques in Montreal. He has received the Jacques Herbrand prize from the French Academy of Sciences. His research interests lie in complex algebraic geometry and representation theory.

Oct. 17 (Carleton) - Joint colloquium (3:30-4:30, coffee after the talk at 4:30, HP 4351 (MacPhail Room)

• Speaker: Nassif Ghoussoub, UBC
• Title: On the Hardy-Schrodinger operator with a singularity on the boundary
• Short Bio: Nassif Ghoussoub is currently a Professor of Mathematics, a "Distinguished University Scholar", and an elected member of the Board of Governors of the University of British Columbia. He was the founding Director of PIMS (Pacific Institute for the Mathematical Sciences) for the period 1996-2003, a co-founder of the MITACS Network of Centres of Excellence and a member of its Board of Directors for the periods 1998-2003 and 2008-12. He is also the founder of BIRS (Banff International Research Station) and has been its Scientific Director since 2004. For more information please see http://www.birs.ca/~nassif/
  The talk is aimed at the general (mathematical) audience. Everyone is welcome.
  After the talk refreshments and coffee will be provided in the faculty lounge.

Oct. 24 (UOttawa) - Joint colloquium

• Speaker: Mayer Alvo
• Title: Bridging the gap: A likelihood function approach for the analysis of ranking data
• Abstract: In the parametric setting, the notion of a likelihood function forms the basis for the development of tests of hypotheses and estimation of parameters. Tests in connection with the analysis of variance stem entirely from considerations of the likelihood function. On the other hand, non- parametric procedures have generally been derived without any formal mechanism and are often the result of clever intuition. In this talk, we propose a more formal approach for deriving tests involving the use of ranks. Specifically, we define a likelihood function motivated by characteristics of the ranks of the data and demonstrate that this leads to well-known tests of hypotheses. We also point to various areas of further exploration.

Nov. 28 (Ottawa) - Joint colloquium

• Speaker: Frithjof Lutscher
• Title: Biological Invasions, Random Walks, and Interfaces.
• Abstract: The spatial spread of non-native biological populations is one of the greatest risks to biodiversity worldwide. Prevention and clean-up efforts cost millions of dollars annually. For example, the invasion of the Emerald Ash borer starting in Detroit in the early 2000s was detrimental to ash trees in Michigan, Ontario and beyond. Efforts to replant are ongoing. Mathematical models are indispensable to understand these processes of invasion that occur on large temporal and spatial scales. One modeling approach is based on reaction-diffusion equations that result as scaling limits from random walks. A particular challenge is to include natural landscape heterogeneity into these models of individual movement and population growth. In this talk, I will begin with an introduction and overview of reaction-diffusion models for biological invasions, and then report on recent extensions of these models to include the patchy structure that most natural landscapes show. The resulting equations are coupled systems of reaction-diffusion equations with a novel type of matching conditions at interfaces between patches. These interface conditions represent individual movement behavior in response to landscape features. I will show that the spread rate in a heterogeneous domain depends critically on the assumptions of how individuals behave at patch interfaces. One option for managing invasive species is to partially remove their main resources, for example Ash trees for the Emerald Ash borer. One surprising result that I will explain is that the spread rate of a population may increase in response to such management actions.

Feb. 6 (UOttawa) - CRM Distinguished Lecture

• Speaker: Stanislaw Lech Woronowicz (University of Warsaw)
• Title: Categories of C-star algebras subject to an action of a quantum group.
• Abstract: Given C*-algebras X and Y one may consider the C*-algebra X\otimes Y. If X and Y are equipped with actions of a locally compact quantum group G, then there exists unique action of G on X\otimes Y such that the natural embeddings of X and Y into X\otimes Y intertwine the actions of G. In the categorical language: tensor product \otimes defines a monoidal structure on the category C*_G of all C^*-algebras equipped with the action of G. This is no longer the case if G is a quantum group. Let G be a locally compact quantum group. It turns out that the category of C*_G admits a monoidal structure satisfying certain natural conditions if and only if G is quasitriangular. The monoidal structures are in bijective correspondence with unitary R-matrices. In general the monoidal structure is not given by \otimes.
• Short Bio: Stanislaw Lech Woronowicz received M.S. and Ph.D. both the degrees in theoretical physics from the University of Warsaw in 1962 and in 1968 respectively. He continued as an adjunct (1968-72), an associate professor (1972-77), and a professor (1977-2011) at the faculty of Physics, University of Warsaw. He is the founder of the theory of compact quantum groups. His research interests also include non-compact quantum groups and C*-algebras. He also became vice dean (1977-78), and the dean (1982-84) of the Faculty of Physics, University of Warsaw. He received Alfred Jurzykowski Foundation (New York) Prize for distinguished achievements in mathematical physics in 1989, Foundation for Polish Science Prize in exact sciences for the series of papers on quantum groups and C*-algebras in 1993. He was awarded Humboldt Research Prize in 2008, and Stefan Banach Medal in 2009. He was invited twice as an invited speaker at ICMs in Warsaw in 1983, and in Kyoto in 1990. He is a full member of Polish Academy of Science since 2002, and Towarzystwo Naukowe Warszawskie since 2004.

Feb. 27 (UOttawa) - Joint Colloquium

• Speaker: Aaron Smith (UOttawa)
• Title: Mixing time of the constrained Ising process on the lattice at low density
• Abstract: The kinetically constrained Ising process (KCIP) was introduced by Fredrickson and Andersen to study liquid near the glass transition. Since then, it has been proposed as a model for `local' computer networks by Aldous and appears in various guises in other areas of combinatorics and computer science. This talk presents recent work on the mixing properties of the KCIP in the low density limit, where the average number of particles present does not grow with the graph size; this is the natural limit to consider for the network model. We point out that Aldous' conjecture for the mixing time of this process requires a simple correction term, and show that this corrected version of the conjecture is true up to logarithmic factors for the lattice in dimensions $d \neq 2$. We will introduce the model, mention some fantastic recent work on the model by Chleboun, Faggionato, Martinelli, Toninelli and others, and give a short proof sketch that emphasizes the relationship between the KCIP and other interacting particle systems.

Mar. 5 (UOttawa) - Joint Colloquium (2:30pm B005)

• Speaker: Paul Bourgade
• Title: From the mesoscopic to microscopic scale in random matrix theory.
• Abstract: Eugene Wigner has envisioned that the distributions of the eigenvalues of large Gaussian random matrices are new paradigms for universal statistics of large correlated quantum systems. These random matrix eigenvalues statistics supposedly occur together with delocalized eigenstates. In this lecture, I will explain recent developments proving this paradigm, for both eigenvalues and eigenvectors of random matrices. This is achieved by bootstrap on scales, from mesoscopic to microscopic. Random walks in random environments, homogenization and the coupling method play a key role.

Mar. 6 (Carleton) - Joint Colloquium (HP 4351 MacPhail Room)

• Speaker: Peter Glynn (Stanford University)
• Title: Convergence to Equilibrium for Queueing Models
• Abstract: We will discuss, in some detail, the rate of convergence to equilibrium for one-dimensional reflected Brownian motion (RBM) with negative drift. This model is widely used as an approximation to heavily loaded queues. As part of this discussion, we will consider the spectral representation for RBM, and the related eigenstructure of the infinitesimal generator of RBM. The talk will discuss the implications of these results for performance analysis of queues, as well as the planning of steady-state queueing simulations. Finally, we will briefly contrast the theory with that associated with the Ornstein-Uhlenbeck process, which acts as an approximation to many-server queues (e.g. call centers). This is joint work with Rob Wang. 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) from Carleton in 1978, and his 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. 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. 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 the co-winner of the John von Neumann Theory Prize from INFORMS in 2010. In 2012, he was elected to the National Academy of Engineering, and in 2014 was the Markov Lecturer for INFORMS. His research interests lie in simulation, computational probability, queueing theory, statistical inference for stochastic processes, and stochastic modeling.

March 13 (Carleton) - Joint Colloquium

• Speaker: Anton Izosimov (University of Toronto)
• Title: Free multidimensional rigid body and algebraic curves
• Abstract: It is a classical result of Euler that the rotation of a torque-free three-dimensional rigid body about the short or the long axis is stable, while the rotation about the middle axis is unstable. I will talk about a multidimensional generalization of this result. It turns out that the stability criterion for the multidimensional rigid body is naturally formulated in terms of relative position of certain quadrics and straight lines on the plane. I will also explain how to prove this result using simple ideas from classical algebraic geometry.

April 10 (Carleton) - Joint Colloquium

• 2:00-3:00 Don Dawson (Carleton University) Random walk, percolation and interacting diffusions in an ultrametric setting
• 3:00-3:30 Coffee break (Reception)
• 3:30-4:30 Garth Dales (Lancaster University) Norming the infinitesimals of large fields

  Please see below for more details on both talks and speakers:

  TITLE: Random walk, percolation and interacting diffusions in an ultrametric setting.

  SPEAKER: Don Dawson, Carleton University

  ABSTRACT: Spatial stochastic models have been intensively studied in Euclidean spaces for many years. Recently the analogous questions have arisen naturally in a class of ultrametric spaces and the question of the relations between these two settings have been investigated. In this lecture we introduce these ideas and briefly describe recent joint research projects with Luis Gorostiza and Andreas Greven in this area. This includes a brief outline of a program motivated by some open problems on the scaling limits of a class of interacting diffusions.

  SHORT BIO: Donald Dawson received his B.Sc.(Hon.) in Mathematics and Physics from McGill University in 1958 and his doctorate from MIT in 1963. He taught at McGill from 1963-1970. He has been a member of the School of Mathematics and Statistics at Carleton since 1970 and was appointed Professor Emeritus and Distinguished Research Professor in 1999. He served as Director of the Fields Institute from 1996-2000 and as the President of the Bernoulli Society for Mathematical Statistics and Probability for 2003-2005.

  He is a Fellow of the Royal Society of Canada, Institute of Mathematical Statistics, International Statistical Institute, Royal Society (London) and American Mathematical Society. He received a Gold Medal from the Statistical Society of Canada in 1991, a Max Planck Award of the for International Cooperation from the Humboldt Foundation in 1996, the CRM-Fields prize in 2004 and Dr. Sci. from McGill University in 2005.

  His research interests include probability and stochastic processes and their applications to complex systems, statistical physics, genetics and evolutionary biology. He has published over 100 scientific papers and 8 monographs and has supervised 27 Ph.D. students and 30 postdoctoral fellows.

  TITLE: Norming the infinitesimals of large fields

  SPEAKER: H. G. Dales, Lancaster, England

  ABSTRACT: We introduce some large ordered fields and ask whether one can put an algebra norm on the subalgebra of infinitesimals of the field. In particular we shall introduce a 'grown-up version of the real line'. We shall explain a connection with a the following question of Kaplansky: Let K be a compact space, and let C(K) denote the Banach algebra of all continuous functions on K. Are all homomorphisms from C(K) into a Banach algebra automatically continuous? To answer this we shall discuss prime ideals in the algebras C(K), and the 'super-real fields' that are built from them.

  In fact Kaplansky's question is independent of ZFC; we shall explain what this means. Indeed many innocuous-looking queries about the family of prime ideals in algebras of continuous functions turn out to be tangled with questions within set theory.

  Full details of the proofs are contained in the following books: H. G. Dales, Banach algebras and automatic continuity, OUP, 2000; H. G. Dales and W. H. Woodin, Super-real fields: totally ordered fields with additional structure, OUP, 1996.

  SHORT BIO: Prof. H.G. Dales is among the world's leading researchers in functional analysis, in particular Banach algebra theory, and related disciplines. He has more than 80 publications to his record, counting well over 1,000 citations.

  Dales was a scholar at Queens' College, Cambridge, England, obtaining a PhD in 1970. He spent most of his career at the University of Leeds, England, interspersed with several year-long visits to the University of California at Berkeley and Los Angeles, where he worked with Bill Bade and Phil Curtis. He is now semi-retired and holds a part-time sinecure at the University of Lancaster in north-west England.

  Dales is the author of the 900+ pages book "Banach algebras and automatic continuity" (2000), which has quickly become a standard reference in the field, and of two books with W.H. Woodin, now of Harvard, that seek to persuade analysts of the great importance of set theory.

  Dales is currently Vice-Chair of the Ethics Committee of the European Mathematical Society, and has written articles on "Open access".

May 1 (UOttawa) - CRM Distinguished Lecture

• Speaker: Jeffrey Rosenthal (University of Toronto)
• Title: Adaptive MCMC For Everyone
• Abstract: Markov chain Monte Carlo (MCMC) algorithms, such as the Metropolis Algorithm and the Gibbs Sampler, are an extremely useful and popular method of approximately sampling from complicated probability distributions. Adaptive MCMC attempts to automatically modify the algorithm while it runs, to improve its performance on the fly. However, such adaption often destroys the ergodicity properties necessary for the algorithm to be valid. In this talk, we first illustrate basic MCMC algorithms using simple Java applets. We then discuss adaptive MCMC, and present results and examples concerning its ergodicity and efficiency. We close with some recent ideas which make adaptive MCMC more widely applicable for all users in broader contexts.
• Short Bio: Jeffrey Rosenthal is a professor in the University of Toronto's Department of Statistics, cross-appointed with Department of Mathematics. He received his B.Sc. (in mathematics, physics, and computer science) from the University of Toronto in 1988, and his Ph.D. in mathematics from Harvard University in 1992 (supervised by Persi Diaconis). He is a recipient of the CRM-SSC Prize in 2006, the COPSS Presidents' Award in 2007 and the Statistical Society of Canada Gold Medal in 2013. He was elected a Fellow of the Royal Society of Canada in 2012.

May 21 (UOttawa) - Joint Colloquium (2:30pm B005)

• Speaker: Ralf Meyer (Goettingen)
• Title: Noncommutative C*-tensor products and C*-quantum groups with projection
• Abstract: The usual spatial tensor product combines two C*-algebras so that they commute. Actions of C*-quantum groups on both factors that are suitably linked give another tensor product where the two factors no longer commute; the easiest case are the skew-commutative tensor products of Z/2-graded C*-algebras. This construction is crucial to understand an analogue of semidirect product groups for C*-quantum groups. We model these by C*-quantum groups with a projection (idempotent endomorphism). In the classical case, a projection is equivalent to a semidirect product decomposition. In general, it allows to split a C*-quantum group into two factors; one of them is an ordinary C*-quantum group, the other is only a braided C*-quantum group: the comultiplication takes values in a noncommutative tensor product. This is joint work with Sutanu Roy and Lech Woronowicz.

May 22 (UOttawa) - Joint Colloquium (3:30pm B005)

• Speaker: Cristian Lenart (SUNY Albany)
• Title: Affine Lie algebras, quantum $K$-theory, and combinatorics
• Abstract: Kirillov-Reshetikhin (KR) modules are certain finite-dimensional modules for affine Lie algebras. The (symmetric) Macdonald polynomials are Weyl group invariant polynomials with rational function coefficients in $q,t$, which specialize to the irreducible characters of semisimple Lie algebras upon setting $q=t=0$. Quantum $K$-theory is a $K$-theoretic generalization of quantum cohomology. Braverman and Finkelberg related the Macdonald polynomials specialized at $t=0$ to the quantum $K$-theory of flag varieties. With S. Naito, D. Sagaki, A. Schilling, and M. Shimozono, I proved that the same specialization of Macdonald polynomials equals the graded character of a tensor product of (one-column) KR modules. I will discuss the combinatorics underlying these connections. The talk is largely self-contained.