Seminars & Events for 2007-2008

February 26, 2008
4:30pm - 6:30pm
Metric and kernel learning
Operations Research and Financial Engineering

Many problems in data mining and machine learning, both in supervised and unsupervised learning, depend crucially on the choice of an appropriate distance or similarity measure. The appropriateness of such a measure can ultimately dictate the success or failure of the learning algorithm, but its choice is highly problem and application dependent.

Speaker: Inderjit Dhillon, University of Texas
Location:
February 27, 2008
12:30pm - 2:30pm
Robust statistical techniques for financial modeling
Operations Research and Financial Engineering

A Series of Eight Lectures Mondays & Wednesdays at the Bendheim Center for Finance (BCF)

Speaker: Elvezio Ronchetti, University of Geneva
Location:
BCF 106
February 27, 2008
4:30pm - 6:30pm
Integral Apollonian circle packings
Department Colloquium

Apollonian circle packings are infinite packings of circles, constructed recursively from an initial configuration of four mutually touching circles by adding circles externally tangent to triples of such circles. Configurations of four mutually touching circles were studied by Descartes in 1643. If the initial four circles have integer curvatures, so do all the circles in the packing.

Speaker: Jeff Lagarias, University of Michigan
Location:
Fine Hall 314
February 28, 2008
12:30pm - 2:30pm
Hyperbolic 3-Manifolds and Arithmetic

Thurston's geometrisation program tells us that we can understand all closed 3-manifolds if we can understand those with a finite volume hyperbolic structure. This is not easy, however, and it is not even clear at the outset that there exist more than a few such manifolds.

Speaker: Simon Marshall, Princeton University
Location:
Fine Hall 214
February 28, 2008
2:00pm - 4:00pm
The bilinear Hardy-Littlewood function for the tail
Ergodic Theory & Statistical Mechanics
Speaker: Idris Assani, University of North Carolina
Location:
Fine Hall 401
February 28, 2008
2:15pm - 4:15pm
Run time bounds for a model related to sieving
Discrete Mathematics Seminar

The following problem is very close to one arising in factorization algorithms.

Generate random numbers in the interval $[1,N]$ until some subset has a product which is a square. How long does this take (and how can you tell when you're done)?

Speaker: Robin Pemantle, Tel-Aviv University and IAS
Location:
Fine Hall 314
February 28, 2008
4:30pm - 6:30pm
Invariants of Legendrian knots in Heegaard Floer homology
Topology Seminar

A new invariant of Legendrian knots will be defined, taking values in the knot Floer homology of the underlying null-homologous knot. With the aid of this invariant we find transversely non-simple knots in many overtwisted contact structures, and show that the Eliashberg-Chekanov twist knots (in particular the $7_2$ knot in Rolfsen's table) are not transversely simple.

Speaker: Andras Stipsicz, Columbia University
Location:
Fine Hall 314
February 28, 2008
4:30pm - 6:30pm
Stochastic convex optimization using mirror averaging algorithms
Operations Research and Financial Engineering

Several statistical problems where the goal is to minimize an unknown convex risk function, can be formulated in the general framework of stochastic convex optimization.

Speaker: Philippe Rigollet, Georgia Institute of Technology
Location:
February 28, 2008
4:30pm - 6:30pm
Hilbert Spaces of Entire Functions and Automorphic L-Functions
Princeton University/IAS Number Theory Seminar

We review the de Branges theory of Hilbert spaces of entire functions. This theory gives a canonical form for a class of operators as multiplication operator together with a generalized Fourier transform taking such an operator to a generalized differential operator.

Speaker: Jeff Lagarias, University of Michigan
Location:
IAS - Simonyi Hall Seminar Room SH-101
February 29, 2008
12:00pm - 2:30pm
Noncommutative differential operators, unparametrized paths and Hodge structures
Algebraic Geometry Seminar

Joint Columbia-Courant-Princeton Algebraic Geometry Seminar at Columbia

Speaker: Mikhail Kapranov, Yale University
Location:
417 Mathematics Hall, Columbia
February 29, 2008
2:00pm - 4:00pm
(Conjectural) triply graded link homology groups of the Hopf link and Hilbert schemes of points on the plane
Joint PU/IAS Symplectic Geometry Seminar

Gukov et al. suggested triply graded link homology groups via refined BPS counting on the deformed conifold. Through large N duality they identify their Poincaré polynomials as refined topological vertices. I further apply the geometric engineering to interpret them as holomorphic Euler characteristics of natural vector bundles over Hilbert schemes of points on the affine plane.

Speaker: Hiraku Nakajima, Kyoto University and IAS
Location:
Fine Hall 314
February 29, 2008
2:30pm - 4:00pm
The cone theorem revisited
Algebraic Geometry Seminar

Joint Columbia-Courant-Princeton Algebraic Geometry Seminar at Columbia

Speaker: James McKernan, MIT
Location:
417 Mathematics Hall, Columbia
February 29, 2008
3:00pm - 5:00pm
The Structure of Shrinking Solitons
Differential Geometry & Geometric Analysis Seminar

We discuss a handful of structure theorems for shrinking solitons with bounded curvature. In particular we prove a priori injectivity radi.

Speaker: Aaron Naber, Princeton University
Location:
Fine Hall 314
February 29, 2008
4:00pm - 6:00pm
Measuring wild ramification using rigid geometry
Algebraic Geometry Seminar

Joint Columbia-Courant-Princeton Algebraic Geometry Seminar at Columbia

Speaker: Kiran Kedlaya, MIT
Location:
417 Mathematics Hall, Columbia
March 3, 2008
4:00pm - 6:00pm
Closing the optimality gap using affinity propagation
PACM/Applied Mathematics Colloquium

An important problem in science and engineering is how to find and associate constituent patterns or motifs in large amounts of high-dimensional data. Examples include the identification and modeling of object parts in images, and the detection and association of RNA motifs that regulate tissue-dependent gene splicing in mammals.

Speaker: Brendan Frey, University of Toronto
Location:
Fine Hall 214
March 3, 2008
4:00pm - 6:00pm
Null structure and almost optimal local well-posedness of the Maxwell-Dirac system
Analysis Seminar

In this talk I will present recent joint work with P. D'Ancona and D. Foschi on the classical Maxwell-Dirac system, which is the fundamental PDE in quantum electrodynamics. We show that the system has some special structural properties ("null" structure) which improve the regularity of solutions.

Speaker: Sigmund Selberg, Norwegian University of Science and Technology
Location:
Fine Hall 110
March 4, 2008
4:30pm - 6:30pm
Generalized eigenfunctions and spectrum for Dirichlet forms
Mathematical Physics Seminar

How existence of certain solutions determines the spectrum is a classical issue for Schrödinger operators. We will discuss such results in the context of Dirichlet forms. The framework of Dirichlet forms covers in particular rather general elliptic operators on manifolds as well as (suitable) quantum graphs.

Speaker: Daniel Lenz, Chemnitz University of Technology
Location:
March 4, 2008
4:30pm - 6:30pm
Moduli of polarized symplectic manifolds
Algebraic Geometry Seminar

In many ways irreducible symplectic manifolds behave similar to K3-surfaces, although it is known that the global Torelli theorem fails in general. Nevertheless, it is possible to relate moduli spaces of polarized irreducible symplectic manifolds to quotients of type IV domains by an arithmetic group.

Speaker: Klaus Hulek, Gottfried Wilhelm Leibniz Universität, Hannover
Location:
Fine Hall 322
March 5, 2008
4:30pm - 6:30pm
The harmonic mean curvature flow of a 2-dimensional hypersurface
Department Colloquium

The harmonic mean curvature flow is the flow that moves a hypersurface embedded in $R^3$ by the speed given by a ratio of the Gauss and the mean curvature of the given surface in the direction of its normal. It is a fully nonlinear, weakly parabolic equation, degenerate at the points at which our hypersurface changes its convexity and fast diffusion when the mean curvature tends to zero.

Speaker: Natasa Sesum, Columbia University
Location:
Fine Hall 314
March 6, 2008
12:30pm - 2:30pm
Prime Splitting Laws
Algebraic number theory seeks to understand and somehow classify all Galois extensions of a number field $K$. One perspective on this basic classification problem emerges from the Cebotarev density theorem, which implies that such extensions $L/K$ are determined by the primes of $K$ that split completely in $L$.