| |
|
| FEBRUARY 2011 |
Department Colloquium
|
Topic:
|
Multiple mixing and short polynomials
|
Presenter:
|
David Masser,
University of Basel, Switzerland
|
Date:
|
Wednesday, February 9, 2011, Time: 4:30 p.m.,
Location: Fine Hall 314
|
Abstract:
|
In dynamical systems the notion of multiple mixing
seems to strengthen that of mixing for an action n a probability space.
Whether it actually does is a long-standing open question. After Ledrappier's unexpected 1978 confirmation for two
commuting actions the theory for general compact abelian groups has been studied, and several problems
have been posed by Klaus Schmidt. In this context the speaker in
2004 proved that when multiple mixing fails it does so in an orderly
fashion thanks to the so-called “non-mixing sets", and in 2006 with
Harm Derksen that the size of the smallest such
set could be effectively determined. Last year we gave a finiteness
result for these smallest sets. It is closely related to the problem of
finding all “shortest" elements of a given ideal in a polynomial
ring. To display the effectivity we tested a
simple ideal in F_2[x; y; z]; it turned out to have 137 shortest elements
modulo a natural equivalence relation.
|
|
|
Ergodic Theory and Statistical Mechanics Seminar
|
Topic:
|
Discrete Schrodinger operators with periodic and
almost periodic potentials
|
Presenter:
|
Mira Shamus, IAS
|
Date:
|
Thursday, February 10, 2011, Time: 2:00 p.m.,
Location: Fine Hall 801 (note change of room #)
|
Abstract:
|
The first half of the talk will be a survey; I will
start from general facts about discrete Schrodinger operators with
periodic potentials, and then discuss operators with almost periodic
potentials, focusing on the almost Mathieu operator. In the second half,
I will state and prove some results connecting the absolutely continuous
spectrum of almost periodic operators to the spectra of their periodic
approximations.
|
|
|
Princeton University and IAS Number Theory
Seminar
|
Topic:
|
Impossible intersections for elliptic curves
|
Presenter:
|
David Masser,
University of Basel, Switzerland
|
Date:
|
Thursday, February 10, 2011, Time: 4:30 p.m.,
Location: Fine Hall 214
|
Abstract:
|
See http://www.math.princeton.edu/~seminar/2010-11-sem/MasserAbstract02-10-2011.pdf
|
|
|
Discrete Mathematics Seminar
|
Topic:
|
Phase Transitions of Achlioptas Processes
|
Presenter:
|
Will Perkins, NYU
|
Date:
|
Thursday, February 10, 2011, Time: 2:15 p.m.,
Location: Fine Hall 224
|
Abstract:
|
Achlioptas processes are a class of modifications of the Erdős–Rényi random graph. At each step of an Achlioptas process we add one of two randomly selected edges to the graph according
to a fixed rule. We present new results on the phase transitions of a
group of Achlioptas processes called
'bounded-size rules' and show that qualitatively, these processes belong
to the same class as the Erdős–Rényi process.
The results include the size and structure of small components in the
barely sub- and supercritical time periods. We will also discuss another
type of Achlioptas process that seems to
exhibit markedly different behavior at the phase transition.
|
|
|
Topology Seminar
|
Topic:
|
Bordered Floer homology and
the contact category
|
Presenter:
|
Rumen Zarev, Columbia
|
Date:
|
Thursday, February 10, 2011, Time: 4:30 p.m.,
Location: Fine Hall 314
|
Abstract:
|
Bordered Heegaard Floer homology is a verison of Heegaard Floer homology for 3-manifolds with boundary, developed by Lipshitz, Ozsvath, and Thurston. A key component of the
theory is a DG-algebra associated to a parametrized surface F. I will discuss how the homology of this algebra can be
naturally identified with a full subcategory of the category of contact
structures on Fx[0,1], with convex boundary conditions.
|
|
|
Differential Geometry and Geometric
Analysis Seminar
|
Topic:
|
The logarithmic singularities of the
Green functions of the conformal powers of the Laplacian
|
Presenter:
|
Raphael Ponge, University
of Tokyo
|
Date:
|
Friday, February 11, 2011, Time: 3:00 p.m., Location:
Fine Hall 314
|
Abstract:
|
Green functions play an important role
in conformal geometry. In this talk, we shall explain how to compute
explicitly the logarithmic singularities of the Green kernels of the
conformal powers of the Laplacian, including
the Yamabe and Paneitz operators. The results are formulated in terms of explicit conformal
invariants arising from the ambient metric of Fefferman-Graham.
As applications we obtain a new characterization of locally conformally flat manifolds and a spectral-theoretic
characterization of the conformal class of
the round sphere.
|
|
|
PACM Colloquium
|
Topic:
|
A few computational and applied math problems in
density functional theory related calculations
|
Presenter:
|
Lin-Wang Wang, Lawrence Berkeley
National Lab
|
Date:
|
Monday, February 14, 2011, Time: 4:00 p.m., Location:
Fine Hall 214
|
Abstract:
|
Density functional theory (DFT) has become the most
widely used quantum mechanical method in material science simulations.
Due to the change of computer architectures, and the corresponding change
in the scope of problems amenable by the DFT method, the algorithms used
in the DFT calculations are also changing. In this talk, I will discuss a
few commonly used ground state based algorithms for large scale DFT
calculations. I will also discuss what it will take to speed up the DFT
molecular dynamics simulations by a thousand times, and the
self-consistent problems often encountered in large system simulations.
Some of our recent effort in implementing our planewave DFT code in GPU will also be discussed. Finally, I will present a method
using auxiliary periodic boundary conditions to solve an open boundary
condition scattering state problem in quantum transport calculations.
|
|
|
Algebraic Geometry Seminar
|
Topic:
|
TBA
|
Presenter:
|
Tom Graber, Caltech & IAS
|
Date:
|
Tuesday, February 15, 2011, Time: 4:30 p.m., Location:
Fine Hall 322
|
|
|
Department Colloquium
|
Topic:
|
Modular representations of p-adic groups
|
Presenter:
|
Florian Herzig, IAS
|
Date:
|
Wednesday, February 16, 2011, Time: 4:30 p.m.,
Location: Fine Hall 314
|
Abstract:
|
The Langlands program
relates complex representations of GL_n(Q_p)
to n-dimensional Galois representations. For n = 1 this is explained by
class field theory and for n = 2 this is closely related to the theory of
modular forms. For general n, this is now understood by the work of
Harris-Taylor and Henniart. In the last decade,
a mod-p (as well as a p-adic) version of the Langlands program have been emerging, and they have
already played an important role in some recent progress in number
theory. But so far understanding has been limited to n = 1 and 2. We
survey some of the known story for n = 2, and then discuss some recent
progress on the classification of mod p representations of GL_n(Q_p).
|
|
|
Ergodic Theory and Statistical Mechanics Seminar
|
Topic:
|
Effective Limit Distribution of the Frobenius Numbers
|
Presenter:
|
Han Li, Yale University
|
Date:
|
Thursday, February 17, 2011, Time: 3:00 p.m. (note special time)
Location: Fine Hall 801 (note change of room
number)
|
Abstract:
|
The Frobenius number of a
lattice point $\bf{a}$ with positive coprime coordinates, is the largest integer which can
NOT be expressed as a non-negative integer linear combination of the
coordinates of $\bf{a}$. Marklof showed in 2010
that the limit distribution of the Frobenius numbers is given by the distribution for the covering radius function of
a random unimodular lattice. The aim of the
talk is to discuss the reason of this phenomenon, and indicate how to
obtain the rate of the convergence of the corresponding distribution
functions.
|
|
|
Princeton University and IAS Number Theory
Seminar (please note different location)
|
Topic:
|
Heuristics for lambda invariants
|
Presenter:
|
Sonal Jain, NYU
|
Date:
|
Thursday, February 17, 2011, Time: 4:30 p.m., Location:
IAS - S-101
|
Abstract:
|
The $\lambda$-invariant is an invariant of an
imaginary quadratic field that measures the growth of class numbers in cyclotomic towers over the field. It also
measures the number of zeroes of an associated $p$-adic L-function. In this talk, I will discuss the following
question: How often is the p-adic $\lambda$-invariant of an imaginary quadratic field equal to $m$?
I'll explain how one can model this question by statistics of $p$-adic random matrices, and show one can test this
model by computing $\lambda$-invariants rapidly. This is joint work
with Jordan Ellenberg and Akshay Venkatesh.
|
|
|
Differential Geometry and Geometric
Analysis Seminar
|
Topic:
|
Compactness and Quantization phenomena in conformal
geometry: Some recent results and open problems
|
Presenter:
|
Luca Martinazzi, Pisa
|
Date:
|
Friday, February 18, 2011, Time: 3:00 p.m., Location:
Fine Hall 314
|
Abstract:
|
I will briefly introduce the GJMS operators,
Q-curvature and their basic properties, then I will describe the possible behaviours of a given sequence of metrics (on a
closed Riemannian manifold or on a domain in R^n or similar) having prescribed Q-curvatures which converge to a given
function. If the sequence is not-precompact various blow-up phenomena appear, only in part well understood. I will
complete the talk with a few open questions.
|
|
|
Analysis Seminar
|
Topic:
|
Explicit formula for the solution of the cubic Szego equation on the real line and its applications
|
Presenter:
|
Oana Pocovnicu, Universite Paris-Sud, Orsay
|
Date:
|
Monday, February 21, 2011, Time: 4:00 p.m., Location:
Fine Hall 314
|
Abstract:
|
In this talk we consider the cubic Szego equation: i u_t = Pi
(|u|^2u) on the real line, where Pi is the Szeg? projector on non-negative frequencies.
This equation was introduced as a model of a non-dispersive Hamiltonian
equation. Like 1-d cubic NLS and KdV, it
is known to be completely integrable in the
sense that it possesses a Lax pair structure. As a consequence, it turns
out that a whole class of finite dimensional manifolds, consisting of
rational functions, is invariant under the flow of the Szeg? equation.
First, we present an explicit formula for the solutions. Then, as
an application, we prove soliton resolution in
H^s, s>0, for "generic" data. Namely, we show that
solutions with generic rational functions as initial data can be
decomposed in H^s, for all s>0, into a sum of solitons plus a remainder, as time tends to infinity. As for non-generic data, we
construct an example for which soliton resolution holds only in H^s, 0< s < 1/2, while the high Sobolev norms grow to infinity over time. As a second
application, we construct explicit generalized action-angle coordinates
on the manifolds of generic rational functions. In particular, this shows
that most trajectories of the Szeg? equation spiral around Lagrangian toroidal cylinders (the non-compact
generalizations of the Lagrangian tori in the Liouville-Arnold
theorem).
|
|
|
PACM Colloquium
|
Topic:
|
TBA
|
Presenter:
|
Robert Ghrist,
University of Pennsylvania
|
Date:
|
Monday, February 21, 2011, Time: 4:00 p.m., Location:
Fine Hall 214
|
|
|
Algebraic Geometry Seminar
|
Topic:
|
Symplectic deformation invariance of rationally connected 3-folds
|
Presenter:
|
Zhiyu Tian, Stony Brook
|
Date:
|
Tuesday, February 22, 2011, Time: 4:30 p.m., Location:
Fine Hall 322
|
|
|
Department Colloquium
|
Topic:
|
TBA
|
Presenter:
|
Gautam Chinta, The City University of New
York
|
Date:
|
Wednesday, February 23, 2011, Time: 4:30 p.m.,
Location: Fine Hall 314
|
|
|
Princeton University and IAS Number Theory
Seminar
|
Topic:
|
Whittaker Functions and Demazure Characters
|
Presenter:
|
Daniel Bump, Stanford University
|
Date:
|
Thursday, February 24, 2011, Time: 4:30 p.m.,
Location: Fine Hall 214
|
Abstract:
|
It is well-known that there are connections between
the representation theory of a reductive p-adic
group and the topology of the flag variety of the Langlands L-group. We will discuss Whittaker functions in this light. The Casselman-Shalika formula shows that the values of
the spherical Whittaker function are the same as the characters of
irreducible representations of the L-group. The Borel-Weil-Bott theorem identifies these same characters as cohomology groups of line bundles on the flag
variety. Generalizing the Borel-Weil-Bott theorem, cohomology groups of line bundles on Schubert varieties are "Demazure characters". We will show how Demazure characters also appear in Iwahori Whittaker functions. This is joint work with
Ben Brubaker and Anthony Licata.
|
|
|
Topology Seminar
|
Topic:
|
Right-angledness, flag
complexes, asphericity
|
Presenter:
|
Mike Davis, Ohio State and IAS
|
Date:
|
Thursday, February 24, 2011, Time: 4:30 p.m.,
Location: Fine Hall 314
|
Abstract:
|
I will discuss three related constructions of spaces
and manifolds and then give necessary and
sufficient conditions for the resulting spaces to be aspherical.
The first construction is the polyhedral product functor.
The second construction involves applying the reflection group trick to a
"corner of spaces". The third construction involves
pulling back a corner of spaces via a coloring of a simplicial complex. The two main sources of examples of corners which yield aspherical results are: 1) products of aspherical manifolds with (aspherical)
boundary and 2) the Borel-Serre bordification of torsion-free arithmetic groups which
are nonuniform lattices.
|
|
|
Discrete Mathematics Seminar
|
Topic:
|
TBA
|
Presenter:
|
Robin Thomas, Georgia Tech
|
Date:
|
Thursday, February 24, 2011, Time: 2:15 p.m.,
Location: Fine Hall 224
|
|
|
Differential Geometry and Geometric
Analysis Seminar
|
Topic:
|
TBA
|
Presenter:
|
Luis Silvestre, Chicago
|
Date:
|
Friday, February 25, 2011, Time: 3:00 p.m., Location:
Fine Hall 314
|
|
|
Joint Analysis Seminar and PACM Colloquium
|
Topic:
|
TBA
|
Presenter:
|
Roman Vershynin,
University of Michigan
|
Date:
|
Monday, February 28, 2011, Time: 4:00 p.m., Location:
Fine Hall 214
|
|
|
MARCH
2011
|
|
|
Algebraic Geometry Seminar
|
Topic:
|
TBA
|
Presenter:
|
Karen Smith, Univ. of Michigan
|
Date:
|
Tuesday, March 1, 2011, Time: 4:30 p.m., Location:
Fine Hall 322
|
|
|
Department Colloquium
|
Topic:
|
New theory of hypergeometric functions
|
Presenter:
|
Ivan Cherednik,
University of North Carolina
|
Date:
|
Wednesday, March 2, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
|
Abstract:
|
The lecture will be devoted to the new
vintage in the theory of special functions, a unification of the Bessel, hypergeometric, spherical and Whittaker functions,
their p-adic and difference counterparts, and
of course the theta-functions (associated with root systems) in one
definition. The latter was suggested 13 years ago, but a reasonably
complete analytic theory of such "global spherical
functions" was created only recently, including the Harish-Chandra
asymptotic formula and many more. These global functions generalize the
classical q-hypergeometric (basic) series
introduce by Heine in 1846, but the new approach is very
different even for one variable. Algebraically, the global functions
are actually similar to the Bessel functions. For instance, the
corresponding Fourier transform is essentially involutive (like for the classical Hankel transform),
which is broken in the Harish-Chandra theory and its p-adic counterpart. The construction is based on DAHA,
q-deformations of the classical Heisenberg-Weyl algebras. The Lie theory was expected to provide such unification
(the Gelfand program) but it did
not materialize. The new theory actually begins with "nonsymmetric" global spherical functions (eigenfunctions of first order opertators)
and their counterparts everywhere (including "nonsymmetric" Schur functions), which is generally beyond the Lie
theory. It clarifies why we need to go "back" to
the Heisenberg algebras and their deformations. The case of rank one will
be mainly considered; no special knowledge of representation
theory is assumed.
|
|
|
Ergodic Theory and Statistical Mechanics Seminar
|
Topic:
|
TBA
|
Presenter:
|
Ivan Corwin, New York University
|
Date:
|
Thursday, March 3, 2011, Time: 2:00 p.m., Location:
Fine Hall 801 (note change in room #)
|
|
|
Discrete Mathematics Seminar
|
Topic:
|
TBA
|
Presenter:
|
Zeev Dvir, Princeton University
|
Date:
|
Thursday, March 3, 2011, Time: 2:15 p.m., Location:
Fine Hall 224
|
|
|
Princeton University and IAS Number Theory
Seminar
|
Topic:
|
TBA
|
Presenter:
|
Kartik Prasanna, University of Michigan, Ann
Arbor
|
Date:
|
Thursday, March 3, 2011, Time: 4:30 p.m., Location:
Fine Hall 214
|
|
|
Topology Seminar
|
Topic:
|
Nondistorted subgroups of Out(F_n), via Lipschitz retraction in spaces of trees (joint work with M. Handel)
|
Presenter:
|
Lee Mosher, Rutgers University
|
Date:
|
Thursday, March 3, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
|
Abstract:
|
We prove that various subgroups of Out(F_n) --- the outer automorphism group of a free group of rank n --- such as the stabilizer of the conjugacy class of a rank n-1 free factor, are
undistorted in Out(F_n). The method of proof is
to show that these subgroups are Lipschitz retracts of the ambient group, in fact we
construct these retractions in appropriate spaces of trees on which F_n acts.
|
|
|
Differential Geometry and Geometric
Analysis Seminar
|
Topic:
|
An Aronsson type approach to extremal quasiconformal mappings
|
Presenter:
|
Luca Capogna, University
of Arkansas
|
Date:
|
Friday, March 4, 2011, Time: 3:00 p.m., Location: Fine
Hall 314
|
Abstract:
|
Quasiconformal mappings $u:\Omega\to
\Omega'$ between open domains in $\R^n$,
are $ W^{1,n}$ homeomorphisms whose dilation $K=|du|/ (det du)^1/n$ is in $L^\infty$.
A classical problem in geometric function theory consists in finding QC minimizers for the dilation within
a given homotopy class or with
prescribed boundary data. In a joint work with A. Raich we study $C^2$ extremal quasiconformal mappings in space and establish necessary
and sufficient conditions for a `localized' form of extremality in the spirit of the work of G. Aronsson on
absolutely minimizing Lipschitz extensions. We
also prove short time existence for smooth solutions of a gradient flow
of QC diffeomorphisms associated to the extremal problem.
|
|
|
PACM Colloquium
|
Topic:
|
Generalized Markov models in population genetics
|
Presenter:
|
Joshua Plotkin,
University of Pennsylvania
|
Date:
|
Monday, March 7, 2011, Time: 4:00 p.m., Location: Fine
Hall 214
|
|
|
Algebraic Geometry Seminar
|
Topic:
|
TBA
|
Presenter:
|
Kyungyong Lee, U.
Conn.
|
Date:
|
Tuesday, March 8, 2011, Time: 4:30 p.m., Location:
Fine Hall 322
|
|
|
Department Colloquium (joint with ORFE)
|
Topic:
|
TBA
|
Presenter:
|
Alice Guionnet,
Lyon, France
|
Date:
|
Wednesday, March 9, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
|
|
|
Topology Seminar
|
Topic:
|
TBA
|
Presenter:
|
Matt Hedden, Michigan
State
|
Date:
|
Thursday, March 10, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
|
|
|
Differential Geometry and Geometric
Analysis Seminar
|
Topic:
|
CR moduli spaces on a
contact 3-manifold
|
Presenter:
|
Jih-Hsin Cheng,
Academia Sinica, Taiwan
|
Date:
|
Friday, March 11, 2011, Time: 3:00 p.m., Location:
Fine Hall 314
|
Abstract:
|
We study low-dimensional problems in topology and
geometry via a study of contact and Cauchy-Riemann ($CR$) structures. In
particular, we consider various $CR$ moduli spaces on a contact 3-manifold. A contact structure is called spherical
if it admits a compatible spherical $CR$ structure. We will talk about
spherical contact structures and our analytic tool, an evolution equation
of $CR$ structures. We argue that solving such an equation for the
standard contact 3-sphere is related to the Smale conjecture in 3-topology. Furthermore, we propose a contact analogue of
Ray-Singer's analytic torsion. This ''contact torsion'' is expected to be
able to distinguish among ''spherical space forms'' $\{\Gamma\backslash
S^{3}\}$ as contact manifolds. Positivity of the $CR$ Paneitz operator becomes an important property in the study of recent years. We
will investigate the relation between this property and the embeddability of $CR$ structures if we have enough
time.
|
|
|
Ergodic Theory and Statistical Mechanics Seminar
|
Topic:
|
Diffusion in a periodic Lorentz gas with narrow
tunnels (P. Balint, N. Chernov,
and D. Dolgopyat)
|
Presenter:
|
Nikolai Chernov, University
of Alabama at Birmingham
|
Date:
|
Friday, March 11, 2011 (note
special day), Time: 2:00 p.m.
Location: Fine Hall 801 (note change in room
number)
|
Abstract:
|
In a periodic Lorentz gas a particle moves bouncing
off a regular array of fixed convex obstacles (scatterers),
like in a pinball machine. When the horizon is finite, one observes a
classical diffusion law. When the obstacles are so large that the tunnels
between them become narrow (of width $\epsilon \to 0$) then the diffusion
matrix scales with $\epsilon$. In the limit, when $\epsilon=0$, the
particle is trapped in a compact region with cusps in the boundary. In
that case the system ceases to be uniformly hyperbolic and develops
anomalies. Correlations decay slowly, as $1/n$, and the classical central
limit theorem fails. Instead, a non-classical limit law holds, with a
scaling factor of $\sqrt{n\log n}$ replacing the standard $\sqrt{n}$. However, for a special observables whose average values at the cusps vanish, the
classical central limit law still holds.
|
|
|
PACM Colloquium
|
Topic:
|
Brother, can you spare a compacton?
|
Presenter:
|
Philip Rosenau, Tel
Aviv University
|
Date:
|
Monday, March 21, 2011, Time: 4:00 p.m., Location:
Fine Hall 214
|
Abstract:
|
Unlike certain personal or national tragedies which
may extend indefinitely, patterns observed in nature are of finite
extent. Yet, as a rule, the solitary patterns predicted by almost all
existing mathematical models extend indefinitely with their tails being a by product of their analytical nature. Rather then viewing such tails as a manifestation of the
inherent limitation of math to model physics in detail, we adopt the
opposite view: the persistence of tails in a large variety of solitary patterns
points to a missing mechanism capable to constrain the pattern. Clearly,
to induce a compact pattern one has to escape the curse of analyticity.
Differently stated, one has to supplement the existing models with a
mechanism(s) which may beget a local singularity. When this is done the
resulting local loss of solution's uniqueness
enables to connect a smooth part of the solution with the trivial ground
state and thus to form an entity with a compact support: the compacton. We shall describe a variety of singularity
inducing mechanisms that beget compact solutions of dispersive or
dissipative uni and multi-dimensional
phenomena. Compactified variants of the K-dV, Klein-Gordon and Schroedinger equations will be surveyed. In Part two of the lecture we shall discuss
the intriguing nature of these (weakly strong or strongly weak)
solutions, the underlying singularities and their relation with a
discrete antecedent where a sharp fronts are replaced with tails decaying
at a doubly exponential rate.
|
|
|
Ergodic Theory and Statistical Mechanics Seminar
|
Topic:
|
TBA
|
Presenter:
|
Corinna Ulcigrai, University of Bristol
|
Date:
|
Thursday, March 24, 2011, Time: 2:00 p.m., Location:
Fine Hall 801 (note change in room #)
|
|
|
Differential Geometry and Geometric
Analysis Seminar
|
Topic:
|
TBA
|
Presenter:
|
Min-Chun Hong, University of
Queensland Brisbane
|
Date:
|
Friday, March 25, 2011, Time: 3:00 p.m., Location:
Fine Hall 314
|
|
|
Department Colloquium
|
Topic:
|
TBA
|
Presenter:
|
Yuri Tschinkel, NYU
|
Date:
|
Wednesday, March 30, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
|
|
|
APRIL
2011
|
|
|
Differential Geometry and Geometric
Analysis Seminar
|
Topic:
|
Geometrical variational problems in economics
|
Presenter:
|
Robert McCann, University of Toronto
|
Date:
|
Friday, April 1, 2011, Time: 3:00 p.m., Location: Fine
Hall 314
|
|
|
Joint Analysis Seminar and PACM Colloquium
|
Topic:
|
TBA
|
Presenter:
|
Peter Jones, Yale University
|
Date:
|
Monday, April 4, 2011, Time: 4:00 p.m., Location: Fine
Hall 214
|
|
|
PACM Colloquium - Distinguished Lecture
Seminar ***Please note special date
|
Topic:
|
TBA
|
Presenter:
|
Ray Goldstein, Cambridge University
|
Date:
|
Wednesday, April 6, 2011, Time: 4:00 p.m., Location:
Fine Hall 214
|
|
|
Department Colloquium
|
Topic:
|
TBA
|
Presenter:
|
Thomas Haines, University of
Maryland
|
Date:
|
Wednesday, April 6, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
|
|
|
Topology Seminar
|
Topic:
|
Geometric structures on moment-angle manifolds
|
Presenter:
|
Taras Panov, Moscow State University
|
Date:
|
Thursday, April 7, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
|
Abstract:
|
Moment-angle complexes are spaces acted
on by a torus and parametrised by finite simplicial complexes. They are central objects in toric topology, and currently are gaining much
interest in the homotopy theory. Due the their combinatorial origins, moment-angle
complexes also find applications in combinatorial geometry and
commutative algebra. Moment-angle complexes corresponding to simplicial subdivision of spheres are topological
manifolds, and those corresponding to simplicial polytopes admit smooth realisations as intersection of real quadrics in C^m.
After an introductory part describing
the general properties of moment-angle complexes we shall concentrate on
the complex-analytic and Lagrangian aspects of
the theory. We show that the moment-angle manifolds corresponding to
complete simplicial fans admit nonKaehler complex-analytic structures. This generalises the known construction of
complex-analytic structures on polytopal moment-angle manifolds, coming from identifying them as LVM-manifolds. We
proceed by describing the Dolbeault cohomology and certain Hodge numbers of moment-angle
manifolds by applying the Borel spectral
sequence to holomorphic principal bundles over toric varieties.
A new wide family of minimal Lagrangian submanifolds N
in C^m or CP^m can be
constructed from intersections of real quadrics. These submanifolds have the following topological
properties: every N embeds in the corresponding moment-angle manifold Z,
and every N is the total space of two different fibrations,
one over the torus T^{m-n} with fibre a real moment-angle manifold R, and another
over a small cover with fibre a torus. These
properties are used to produce new examples of Lagrangian submanifolds with quite complicated topology.
Different parts of this talk are based on joint works with Victor Buchstaber, Andrei Mironov and Yuri Ustinovsky.
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Differential Geometry and Geometric
Analysis Seminar
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Topic:
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TBA
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Presenter:
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Dmitri Burago, Penn
State
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Date:
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Friday, April 8, 2011, Time: 3:00 p.m., Location: Fine
Hall 314
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PACM Colloquium
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Topic:
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From (basic) image denoising to surface evolution
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Presenter:
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Antonin Chambolle, CMAP -- Ecole Polytechnique
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Date:
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Monday, April 11, 2011, Time: 4:00 p.m., Location:
Fine Hall 214
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Abstract:
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It is relatively easy to make a connection between the
implicit time-discrete approaches for the mean curvature flow and the
"Rudin-Osher-Fatemi" total variation
based approach for image denoising. This
connection has interesting consequences, allowing to
build explicit solutions for the flow of the total variation or study regularity issues, up to showing the existence of the crystalline
curvature flow of convex sets or building up efficient algorithms. The
talk will explain the relationship between all these problems. (Joint
works with V. Caselles, M. Novaga,
J. Darbon, T. Pock, D. Cremers)
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Algebraic Geometry Seminar
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Topic:
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TBA
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Presenter:
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Mircea Mustaţă, U. of Michigan
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Date:
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Tuesday, April 12, 2011, Time: 4:30 p.m., Location:
Fine Hall 322
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Department Colloquium
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Topic:
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TBA
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Presenter:
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Steve Zelditch,
Northwestern University
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Date:
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Wednesday, April 13, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
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Differential Geometry and Geometric
Analysis Seminar
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Topic:
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TBA
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Presenter:
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Richard Bamler, Princeton
University
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Date:
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Friday, April 15, 2011, Time: 3:00 p.m., Location:
Fine Hall 314
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PACM Colloquium
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Topic:
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TBA
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Presenter:
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Gregory Rempala,
Medical College of Georgia
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Date:
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Monday, April 18, 2011, Time: 4:00 p.m., Location:
Fine Hall 214
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Department Colloquium
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Topic:
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TBA
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Presenter:
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Alexander Bufetov, Rice
University
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Date:
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Wednesday, April 20, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
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Princeton University and IAS Number Theory
Seminar
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Topic:
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TBA
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Presenter:
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Henri Darmon,
McGill University
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Date:
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Thursday, April 21, 2011, Time: 4:30 p.m., Location:
Fine Hall 214
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Ergodic Theory and Statistical Mechanics Seminar
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Topic:
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TBA
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Presenter:
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Alexander Bufetov, Rice
University
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Date:
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Thursday, April 21, 2011, Time: 2:00 p.m., Location:
Fine Hall 801 (note change in room number)
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PACM Colloquium
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Topic:
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TBA
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Presenter:
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Boaz Nadler, Weizmann Institute --
Israel
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Date:
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Monday, April 25, 2011, Time: 4:00 p.m., Location:
Fine Hall 214
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Topology Seminar
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Topic:
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TBA
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Presenter:
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Peter Ozsvath, MIT
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Date:
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Thursday, April 28, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
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Differential Geometry and Geometric
Analysis Seminar
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Topic:
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TBA
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Presenter:
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Artem Pulemotov, Chicago
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Date:
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Friday, April 29, 2011, Time: 3:00 p.m., Location:
Fine Hall 314
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MAY
2011
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Differential Geometry and Geometric
Analysis Seminar
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Topic:
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TBA
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Presenter:
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Yannick Slre, Universite de Aix-Marseille III
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Date:
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Friday, May 6, 2011, Time:
3:00 p.m., Location: Fine Hall 314
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Department Colloquium
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Topic:
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TBA
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Presenter:
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Balazs Szegedy, University of Toronto
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Date:
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Wednesday, May 11, 2011, Time: 4:30 p.m., Location:
Fine Hall 314
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