## Scientific General Events

Since Gaspard Monge formulated the problem of finding an optimal transportation plan for piles of soil in his 1781 "Memoire sur les deblais et remblais," the problem of transporting a given distribution of mass from one location to another distribution of mass in a different location, while minimizing a certain cost of research. Following the seminal results of Brenier, optimal transportation has received a lot of attention in the last 15 years, leading to a very active field of research in applied mathematics. That it also provides a powerful and versatile tol for a wide range of economic applications is now becoming apparent. Mass transportation duality is useful in formulating the problem of existence, uniqueness and purity fo equilibrium in hedonic models. It has natural connections with multidimensional screening and urban economics that deserve to be better explored. In econometrics, it lies at the heart of improvements of estimates of monotone functions (such as cumulative distribution and quantile functions), and of the problem of testing economic model specification, to name only a few applications.

In order to gather researchers at the forefront of developments of these economic applications, to increase their awareness of each other's work, to identify the most important unexplored problems and pave the way for collaborations, a first one day meeting ("Transportation Day") has been organized at Columbia University on june 25th 2007 (participants: Guillaume Carlier (Paris Dauphine), Victor Chernozhukov (MIT), Pierre-André Chiappori (Columbia), Ivar Ekeland (UBC and PIMS), Alfred Galichon (Ecole polytechnique), Marc Henry (Columbia), Robert McCann (UToronto), Lars Nesheim (UCL), Heleno Pioner (Chicago) and Jay Sethuraman (Columbia)). Due to the numerous potential applications of mass transportation methods to economics, the Columbia meeting was also intended to become the first of a long series of annual meetings in rotating venues.

The aim of the workshop "Transport, optimization, equilibrium in economics" is to bring together economists and mathematicians with common interests in subjects related to the mathematics of transportation in a broad sense. On the mathematical side, the goal will be to present a wide spectrum of techniques and models of transportation (optimal transportation, networks, congestion modeling, optimal location) both from the theoretical and numerical point. On the economic side, recent works of Ekeland, Chiappori, McCann and Nesheim have shown that optimal transportation techniques are powerful tools for the analysis of matching problems and hedonic equilibria. Transportation theory has a wide range of potential applications in econometrics, urban economics, adverse selection problems and nonlinear pricing, topics which naturally fall in the scope of the meeting.

The workshop will last 5 working days. To benefit from the pluridisciplinary character of this workshop, we plan an alternance of lectures (4 per day) and of open sessions (1 per day).

The Pacific Institute for the Mathematical Sciences (PIMS) cordially invites you to attend the Ekeland Banquet, recognizing the contributions of Professor Ivar Ekeland.

**Mini-course 1**

*The Nash-Moser method and applications (Massimiliano Berti and Philippe Bolle)*

*Lecture 1:*

Periodic and quasiperiodic solutions near an elliptic equilibrium for Hamiltonian PDEs: presentation of the problem. We shall specially focus on periodic solutions of nonlinear wave equations.

Lyapunov-Schmidt reduction: the range and the bifurcation equations.

Small denominator problem and statement of a Nash Moser implicit function theorem for the range equation.

Variational structure of the bifurcation equation.

*Lecture 2:*

Nash Moser-type iterative scheme. Convergence proof, under appropriate weak invert-ibility assumptions on the linearized problems.

*Lectures 3-4:*

Inversion of the linearized equations in presence of small divisors for periodic solutions in any spatial dimensions.

*Reference Material*

1. M. Berti, P. Bolle, Cantor families of periodic solutions for completely resonant nonlinear wave equations, Duke Math. J. 134 (2006) 359-419.

2. M. Berti, P. Bolle, Cantor families of periodic solutions for wave equations via a variational principle, Advances in Mathematics. 217 (2008) 1671-1727.

3. M. Berti, P. Bolle, Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions, preprint 2008.

4. J. Bourgain , Green's function estimates for lattice Schodinger operators and applications, Annals of Mathematics Studies 158, Princeton University Press, Princeton, 2005.

5. W. Craig, Problemes de petits diviseurs dans les equations aux derivees partielles, Panoramas et Syntheses, 9, Societe Mathematique de France, Paris, 2000.

6. S. Kuksin, Analysis of Hamiltonian PDEs, Oxford Lecture series in Mathematics and its applications 19, Oxford University Press, 2000.

**Mini-course 2**

**Symmetries and collisions in the n-body problem 9 (Davide Ferrario and Susanna Terracini)**

Davide L. Ferrario

Lecture 1:

*Lecture 2:*Susanna Terracini

*Lecture 3:*Davide L. Ferrario

*Lecture 4:*Susanna Terracini

1. Symmetries and the variational formulation of the n-body problem.

2. Equivariant minimization

3. Planar symmetry groups

4. Collisions

5. McGehee coordinates and total collisions

6. Asymptotic estimates

7. Averaged variations

8. Local equivariant variations

9. Transitive decomposition of symmetry groups

10. Collisions and singularities.

*Reference Material*

1. D. L. Ferrario: Transitive decomposition of symmetry groups for the $n$-body problem: Adv. in Math. 213 (2007) 763-784.

2. D. L. Ferrario: Symmetry groups and non-planar collisionless action-minimizing solutions of the three-body problem in three-dimensional space. Arch. Rational Mech. Anal. 179 (2006), 389--412.

3. D. L. Ferrario and S. Terracini: On the existence of collisionless equivariant minimizers for the classical n-body problem. Inventiones Mathematicae, Vol. 155 N. 2 (2004), 305--362.

4. V.Barutello, D. L. Ferrario and S. Terracini: On the singularities of generalized solutions to $n$--body type problems: math.DS/0701174 (to appear in IMRN)

5. V. Barutello, D. L. Ferrario and S. Terracini: Symmetry groups of the planar 3-body problem and action-minimizing trajectories (to appear in Arch. Rational Mech. Anal..

*All papers can be downloaded from*http://www.matapp.unimib.it/~ferrario/papers/index.html**Theme**: Quantitative Methods for Environmental Sustainability**Conference technical topics include**:

* Agro-climate risk

* Analysis of extremes

* Assessing status and trends

* Design and analysis of computer experiments

* Environmental reporting and indicators

* Environmental risk assessment

* Environmental standards

* Monitoring, modelling and managing environmental systems

* Network design and efficient data collection

* Space-time modelling**Applications to**:

* biodiversity, climate change, sustainable agriculture, air quality, water quality, soil contamination, energy, environmental economics, ecosystem and human healthAndrew Chesher: Instrumental variable models for discrete outcomes

Shinichi Sakata: On Long-Run Covariance Matrix Estimation with the Truncated Flat Kernel

**One Hour Talks**Anton Alekseev, University of Geneva

Title:*The Kashiwara-Vergne conjecture and Drinfeld's associators*Michel Brion, University of Grenoble

Title:*Counting points of homogeneous varieties over finite fields*

Pavel Etingof, MIT

Title:*Parabolic induction and restriction functors for rational Cherednik algebras and their applications*Victor Ginzburg, University of Chicago

Title:*Quantization of del Pezzo surfaces*Iain Gordon, University of Edinburgh

Title:*The Shapiro-Shapiro Conjecture and Calogero-Moser space*Victor Guillemin, MIT

Title:*Asymptotic properties of spectral measures*

J.-S. Huang, Hong Kong University of Science and Technology

Title:*Dirac operators and Lie algebra cohomologies*Anthony Joseph, Weizmann Institute

Title:*The Borcherds Character Formula, the Littelmann Path Model and n homology*Victor Kac, MIT

Title:*Classification of simple linearly compact generalized Jordan superalgebras*

Allen Knutson, UCSD

Title:*The totally nonnegative Grassmannian and juggling patterns*James Lepowsky, Rutgers

Title:*Tensor product theory for vertex operator algebra modules, and applications*Hiraku Nakajima, Kyoto University

Title:*Quiver varieties and double affine Grassmannian*

Andrei Okounkov, Princeton University

Title:*The mystical powers of eta*Dale Peterson, UBC

Title:*The Toda lattice and small quantum cohomology of homogeneous spaces*Konstanze Rietsch, King's College

Title:*A mirror symmetric approach to Kostant's quantum Toda lattice*

Jean-Pierre Serre, College de France

Title:*Lie Groups and Prime Numbers*Birgit Speh, Cornell

Title:*TBA*David Vogan, MIT

Title:*The orbit method for reductive groups*Nolan Wallach, UCSD

Title:*Hidden subgroup problems in quantum computing.***45 Minute Talks**Ivan Losev, Belarusian State University

Title:*Quantized symplectic actions and W-algebras*Alessandra Pantano, University of California at Irvine

Title:*Unitarity of Nonspherical Minimal Principal Series*Nicholas Ressayre, Université Montpellier 2

Title:*Restricting representations to a reductive subgroup.*Alistair Savage, University of Ottawa

Title:*Moduli spaces of sheaves and the boson-fermion correspondence*Wai Ling Yee, University of Windsor

Title:*Kazhdan-Lusztig Polynomials and Signature Computations*Since their inception in 1994, the bi-annual ANTS meetings have become the premier international forum for the dissemination of new research in algorithmic number theory. The aim is to bring together leading experts in the field, as well as young researchers and graduate students for the purpose of exchanging ideas and presenting their work. The conference proceedings will be published in Springer's prestigious

*Lecture Notes in Computer Science*series. Other highlights include the award of the*Selfridge Prize in Computational Number Theory*, sponsored by the*Number Theory Foundation*, to the best contributed paper, as well as a poster session.The Canadian Young Researchers Conference in Mathematics and Statistics (CYRC) is an annual event that provides a unique forum for young mathematicians across Canada to present their research and to collaborate with their peers.

All young academics involved in research in the mathematical sciences are invited to give a scientific talk describing their work and to attend talks on a host of current research topics in mathematics and statistics. Participants will have the opportunity to build and strengthen lasting personal and professional relationships, to develop and improve their communication skills, and to gain valuable experience in the environment of a scientific conference.

All graduate students, senior undergraduate students, and post-doctoral fellows studying mathematics and statistics at a Canadian university are invited to participate in this conference. Students from Canadian PIMS universities will be strongly encouraged to attend and present at this conference.

All participants are encouraged to deliver a thirty-minute presentation describing their research (or a general interest talk related to their research interests). Those interested in presenting will be required to submit an abstract outlining the content of their proposed talk. Since the body of conference participants will have a wide range of research interests and knowledge, all presentations should be aimed at an audience with a broad knowledge base in mathematics and statistics, but must be tailored to those without a depth of knowledge in any particular area of research.

Presentations will be scheduled for Friday evening (May 9), Saturday (May 10), and Sunday (May 11) morning. The presentations will be open, in the sense that anyone interested, such as undergraduate students, faculty members, and visitors, may attend.

Number theory was coined the "Queen of Mathematics" by Gauss. It is one of the oldest branches of mathematics. Over the years, it has extended its roots into a variety of other domains such as probability, combinatorics, analysis, algebra, and geometry. We hope that this one day conference will give a glimpse into the

diverse aspects of modern number theory.Dr. Igor Burstyn.

Occupational Medicine, University of Alberta.

Title: A vignette from occupational epidemiology: Stitching evidence from tattered fabricDr. Mahyar Etminan.

Centre for Clinical Epidemiology & Evaluation, Vancouver.

Title: TBADr. Adrian Levy. Centre for Health Evaluation and Outcome Sciences;

Department of Health Care and Epidemiology, UBC.

Title: TBADr. Bill Leslie.

Department of Internal Medicine, University of Manitoba.

Title: TBADr. Malcolm Maclure.

Pharmaceutical Services Division, BC Ministry of Health.

Title: You randomize. We Analyze.Dr.Ed Mills.

Faculty of Health Sciences, SFU.

Title: TBADr. Carl Phillips.

Department of Public Health Sciences, University of Alberta.

Title: Can quantitative methods help detect and reduce "publication bias in situ"?Dr. Jat Sandhu.

Vancouver Coastal Health.

Title: TBA**The Mahler measure of curves and surfaces**

by Marie José Bertin Université Pierre et Marie Curie (Paris 6), Institut de Mathématiques de JussieuI report on some new examples of explicit logarithmic Mahler measures of multivariate polynomials.

When the polynomial defines a parametrizable curve, its Mahler measure is expressed in terms of Bloch-Wigner dilogarithms of an element of the Bloch group of an imaginary quadratic field ( Thus a link with hyperbolic varieties). When the polynomial defines a singular K3-surface, I give several examples of the Mahler measure expressed in terms of the L-series of the K3-surface for s=3. Dedekind zeta motives for totally real fields by Francis Brown CNRS, Institut de Mathématiques de Jussieu, IHES**On singular Bott-Chern classes**

by José Ignacio Burgos Gil Universidad de BarcelonaThe singular Bott-Chern classes measure the failure of an exact Riemann-Roch theorem for closed immersions at the level of currents. They are the key ingredient in the definition of direct images of hermitian vector bundles under closed immersions and in the proof of the arithmetic Riemann-Roch theorem in Arakelov geometry for closed immersions. There are two definitions of singular Bott-Chern classes. The first due to Bismut, Gillet and Soulé uses the formalism of super connections. The second, due to Zha, is an adaptation of the original definition of Bott-Chern classes by Bott and Chern.In this talk we will give an axiomatic characterization of singular Bott-Chern classes, which is similar to the characterization of Bott-Chern forms, but that depends on the choice of an arbitrary characteristic class. This characterization allow us to give a new definition of singular Bott-Chern forms by means of the deformation to the normal cone technique and to compare the previous definitions of singular Bott-Chern forms. Moreover we will give an explicit computation of the characteristic class associated to Bismut-Gillet-Soulé definition of singular Bott Chern currents.

**Generic p-rank of semi-stable fibration**

by Junmyeong Jang Purdue UniversityIn this presentation, I will be concerned with two pathological phenomenons of positive characteristic, the failure of Miyaoka-yau inequality and the failure of semi-positivity theorem. Szpiro showed that a Frobenius base change of non-isotrivial smooth fibration violates Miyaoka-Yau inequality. For such a fibration, if the p-rank of the generic fiber is maximal, the dimension of the Lie algebra of Picard scheme is stable after the Frobenius base change. Using this fact and a reduction argument we can construct a counter example of Miyaoka-Yau inequality with smooth Picard scheme, which is a counterexample of Parshin's expectation. And we will see for a semi-stable fibration p : X ? C of a proper smooth surface to a proper smooth curve, if the p-rank of the generic fiber is maximal, the semi-positivity theorem holds and if the p-rank of the generic fiber is 0, some Frobenius base change of p violates the semi-positivity theorem. This result may be applied to a problem of the distribution of p-ranks of reductions of a certain non-closed point in the moduli space of curves over Q¯.

**The Abel-Jacobi map on the Einsestein symbol**

by Matthew Kerr Durham UniversityIn this talk we consider two different constructions of motivic cohomology classes on families of toric hypersurfaces and on Kuga varieties. Under certain modularity conditions on the former we say how the constructions "coincide", obtaining a complete explanation of the phenomenon observed by Villegas, Stienstra, and Bertin in the context of Mahler measure. (This is where the AJ computation on the Kuga varieties, done using our formula with J. Lewis and S. Mueller-Stach, will be summarized). We also look at an application of the toric construction in the non-modular case, to limits of normal functions for families of Calabi-Yau 3-folds.

**Moduli of polarized logarithmic Hodge structures and period maps**

by Sampei Usui Osaka University**Height and GIT weight**

by Xiaowei Wang The Chinese University of Hong KongIn this talk, we will establish a new connection between the weight in the geometric invariant theory and the height introduced by Cornalba and Harris CH and Zhang Z. Then I will explains two applications of this connection.

*Talks will be held at CAB 269 (April 12, 14, 15, 16) and ETL E1 008 (April 13). We have booked the computer lab at CAB 341. map*

This workshop will bring together scientists working on mathematical modeling of viral disease with a focus on viral evolution and epidemiology, and with particular application to influenza and HIV.

Please note: People registering after March 25th will not be registered for the dinner on Friday, April 4th. Please inquire at the meeting about the availability of space at the dinner, if you wish to attend.

Waves, Vortices, and Climate Modelling