2009 - 2010
Calendrier des conférences / Conference Calendar
TRIMESTRE D'AUTOMNE 2009 / FALL 2009 SEMESTERDate Heure/Time : 04/16/2010
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Panagiota Daskalopoulos, Columbia University
Titre/Title : TBA
Resume/Abstract :
À venir / Coming soon
Date Heure/Time : 04/09/2010
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Nigel Hitchin, Oxford University
Titre/Title : TBA
Resume/Abstract :
À venir / Coming soon
Date Heure/Time : 03/19/2010
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Michael Larsen, Indiana University
Titre/Title : TBA
Resume/Abstract :
À venir / Coming soon
Date Heure/Time : 03/12/2010
Lieu/Venue : CRM, Pavillon André Aisenstadt, Université de Montréal, salle 6214
Conférencier/Speaker : Winnie Li, Penn State University
Titre/Title : Recent progress on the arithmetic of noncongruence modular forms
Resume/Abstract :
After more than one century's effort, the arithmetic of congruence modular forms is well-understood. Contrary to this, the understanding for the arithmetic of noncongruence forms is quite primitive. A main obstacle is the lack of efficient Hecke operators. However, Atkin and Swinnerton-Dyer have come up with a conjecture which is meant to play the role of Hecke operators. Further, Scholl has attached to the space of noncongruence forms a compatible family of l-adic Galois representations. In this talk we'll survey recent progress on the arithmetic of noncongruence forms and modularity of Scholl representations.
Date Heure/Time : 02/26/2010
Lieu/Venue : CRM, Pavillon André Aisenstadt, Université de Montréal, salle 6214
Conférencier/Speaker : John Coates, University Cambridge
Titre/Title : TBA
Resume/Abstract :
À venir / Coming soon
Date Heure/Time : 02/19/2010
Lieu/Venue : UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214
Conférencier/Speaker : Jeremy Quastel, University of Toronto
Titre/Title : Large scale behaviour of the continuum random polymer and KPZ
Resume/Abstract :
About 30 years ago it was observed that a large class of one dimensional random systems have highly anomalous fluctuations. We will describe some of these models and survey recent progress in proving some of the conjectured scalings and limiting distributions.
Date Heure/Time : 02/12/2010
Lieu/Venue : CRM, Pavillon André Aisenstadt, Université de Montréal, salle 6214
Conférencier/Speaker : Frank Sottile, Texas A&M University
Titre/Title : Orbitopes
Resume/Abstract :
An orbitope is the convex hull of an orbit of a compact group acting linearly on a vector space. Instances of these highly symmetric conex bodies have appeared in many areas of mathematics and its applications, including protein reconstruction, symplectic geometry, and calibrations in differential geometry. In this talk, I will discuss Orbitopes from the perpectives of classical convexity, algebraic geometry, and optimization with an emphasis on ten motivating problems and concrete examples. This is joint work with Raman Sanyal and Bernd Sturmfels.
Date Heure/Time : 02/05/2010
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Robert McCann, University of Toronto
Titre/Title : Optimal multidimensional pricing facing informational asymmetry
Resume/Abstract :
The monopolist's problem of deciding what types of products to manufacture and how much to charge for each of them, knowing only statistical information about the preferences of an anonymous field of potential buyers, is one of the basic problems analyzed in economic theory. The solution to this problem when the space of products and of buyers can each be parameterized by a single variable (say quality X, and income Y) garnered Mirrlees (1971) and Spence (1974) their Nobel prizes in 1996 and 2001. The multidimensional version of this question is a largely open problem in the calculus of variations (see Basov's book "Multidimensional Screening".) I plan to describe recent work with A Figalli and Y-H Kim, identifying structural conditions on the value b(X,Y) of product X to buyer Y which reduce this problem to a convex program in a Banach space--- leading to uniqueness and stability results for its solution, confirming robustness of certain economic phenomena observed by Armstrong (1996) such as the desirability for the monopolist to raise prices enough to drive a positive fraction of buyers out of the market, and yielding conjectures about the robustness of other phenomena observed Rochet and Chone (1998), such as the clumping together of products marketed into subsets of various dimension. The passage to several dimensions relies on ideas from differential geometry / general relativity, optimal transportation, and nonlinear PDE.
Date Heure/Time : 01/29/2010
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Kumar Murty, University of Toronto
Titre/Title : The Euler-Kronecker constant of a number field
Resume/Abstract :
Ihara has defined an invariant of a number field that for the rational numbers is Euler's constant and for imaginary quadratic fields is related to Kronecker's limit formula. In this talk, we will discuss various properties of this invariant and its relation to zeros of L-functions.
Date Heure/Time : 01/15/2010
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Jim Bryan, UBC
Titre/Title : The orbifold vertex: counting curves on orbifolds by counting piles of colored boxes
Resume/Abstract :
Over the last few decades, sophisticated theories, often inspired by string theory, have been developed for counting curves on Calabi-Yau threefolds. For the particularly nice class of toric threefolds, these theories reduce to a beautiful combinatorial problem: how many different ways are there of piling boxes in a corner? When the curve counting is considered for toric orbifolds, the combinatorial problem transforms into counting colored boxes. We will assume no knowledge of Calabi-Yau threefolds, toric geometry, orbifolds, or string theory. Experience stacking boxes in a moving van is helpful, but not necessary.
Date Heure/Time : 01/08/2010
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Henri Darmon, McGill University
Titre/Title : Diophantine equations: what numbers reveal about shape and structure
Resume/Abstract :
This talk will be a survey of a few of the most classical Diophantine equations, and of the insights they give into mathematical structures arising in algebra, geometry and topology. Since this lecture is primarily aimed at the students participating in the McGill winter school, no prior background in mathematics at the graduate level will be assumed (at least, consciously.)
Date Heure/Time : 12/18/2009
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : François Lalonde, Université de Montréal
Titre/Title : La nouvelle géométrie algébrique réelle
Resume/Abstract :
Je présenterai les travaux récents en topologie symplectique réelle, et notamment les travaux de Jean-Yves Welschinger sur les invariants de Gromov-Witten en géométrie algébrique réelle. Ces résultats, maintenant connus sous le nom de Gromov-Witten-Welschinger constituent une révolution et ouvrent la voie de la géométrie algébrique réelle énumérative qui stagnait depuis son enfance il y a quatre siècles.
Date Heure/Time : 12/04/2009
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Erez Boas, Université de Bordeaux
Titre/Title : Galois modules in arithmetic and geometry
Resume/Abstract :
At first, Galois module theory was about describing the algebraic structure of classical arithmetical objects like rings of algebraic integers and their groups of units. The theory acquired more interest when it appeared that the Galois structure of such modules is related to the behaviour of L-functions. In the 1990s it was shown that these relations could be generalised to "higher dimensional number theory", namely to relations among analogous objects arising from algebraic varieties equipped with a group action. In this talk we shall go over the basic results of the classical theory, present the geometric set-up and give indications on some current directions of research."
Date Heure/Time : 11/27/2009
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Shing-Tung Yau, Harvard University
Titre/Title : Canonical metrics on Kähler manifolds
Resume/Abstract :
We will give a brief tour of the beautiful role played by canoncial metrics in the modern developments in the study of Kâhler manifolds and in algebraic geometry. We will end with some new results that illustrate the current vitality and importance of this area of research and indicate its future directions.
Date Heure/Time : 11/20/2009
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : James Lewis, University of Alberta
Titre/Title : New Invariants on Algebraic Cycles
Resume/Abstract :
I will explain the intertwining role of Hodge theory and algebraic cycles, beginning from the classical constructions in the 1960's to the more recent developments using arithmetical normal functions.
Date Heure/Time : 11/06/2009
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Christopher Sogge, Johns Hopkins
Titre/Title : Kakeya-Nikodym averages and Lp norms of eigenfunctions
Resume/Abstract :
On any compact Riemannian manifold $(M, g)$ of dimension $n$, the $L^2$-normalized eigenfunctions ${\phi_{\lambda}}$ satisfy $||\phi_{\lambda}||_{\infty} \leq C \lambda^{\frac{n-1}{2}}$ where $-\Delta \phi_{\lambda} = \lambda^2 \phi_{\lambda}.$ The bound is sharp in the class of all $(M, g)$ since it is obtained by zonal spherical harmonics on the standard $n$-sphere $S^n$. But of course, it is not sharp for many Riemannian manifolds, e.g. flat tori $\R^n/\Gamma$. We say that $S^n$, but not $\R^n/\Gamma$, is a Riemannian manifold with maximal eigenfunctiongrowth. The problem which motivates us is to determine the $(M, g )$ with maximal eigenfunction growth. In an earlier work, two of us showed that such an $(M, g)$ must have a point $x$ where the set ${\mathcal L}_x$ of geodesic loops at $x$ has positive measure in $S^*_x M$. We strengthen this result here by showing that such a manifold must have a point where the set ${\mathcal R}_x$ of recurrent directions for the geodesic flow through x satisfies $|{\mathcal R}_x|>0$. We also show that if there are no such points, $L^2$-normalized quasimodes have sup-norms that are $o(\lambda^{n-1)/2})$, and, in the other extreme, we show that if there is a point blow-down $x$ at which the first return map for the flow is the identity, then there is a sequence of quasi-modes with $L^\infty$-norms that are $\Omega(\lambda^{(n-1)/2})$.
Date Heure/Time : 10/30/2009
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Glenn Stevens, Boston University
Titre/Title : p-adic variation in the theory of automorphic forms
Resume/Abstract :
Automorphic forms provide powerful analytic tools for investigating subtle arithmetic properties of elliptic curves and other algebraic varieties. Nowadays this principle has been turned on its head, allowing us to apply arithmetic tools to gain insight into the existence and nature of associated automorphic forms. Wiles' proof of the modularity conjecture (from which Fermat's Last Theorem was derived) is just one well known example. In this talk we will explore the theme of p-adic variation through an investigation of simple concrete examples, and will discuss some of the unifying aspects this theme brings to arithmetic, geometry and analysis.
Date Heure/Time : 10/09/2009
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Ravi Ramakrishna, Cornell University
Titre/Title : What is a Galois Representation?
Resume/Abstract :
In introductory graduate classes we learn about the Galois correspondance for finite extensions of fields. It is often useful to study infinite Galois groups. It turns out that many of the important arithmetic questions of the last 30 years, such as the Weil Conjectures, Fermat's Last Theorem, Serre's Conjecture and the Sato-Tate Conjecture involve studying representations of these infinite Galois groups. This talk will be a leisurely tour of Galois representations and their applications to a breadth of problems.
Date Heure/Time : 09/25/2009
Lieu/Venue : UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Conférencier/Speaker : Svetlana Katok, Pennsylvania State University
Titre/Title : Structure of attractors for (a,b)-continued fraction transformations
Resume/Abstract :
I will discuss one-dimensional maps related to a family of (a,b)-continued fractions, suggested for consideration by Don Zagier, and give a sufficient condition for validity of the Reduction theory conjecture that states that the associated natural extension maps have attractors with finite rectangular structure where every point of the plane is mapped after finitely many iterations. I will show how the structure of these attractors can be ``computed" from the data $(a,b)$, and give a dynamical interpretation of the ``reduction theory" that underlines these constructions. The set of parameter pairs $(a,b)$ for which the conjecture is not valid is also well-understood; in particular, the points for which the attractors do not have finite rectangular structure is a non-empty nowhere dense subset of the boundary $b=a+1$ of the set of parameters . If time permits, I will also explain how these continued fractions can be used for coding of geodesics on the modular surface. This is a joint work with Ilie Ugarcovici.