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APRIL 19 - 21, 2006 |
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| Discrete Mathematics Seminar |
| Topic: |
Shannon capacity and privileged users |
| Presenter: |
Noga Alon, Tel Aviv University and IAS |
| Date: |
Wednesday, April 19, 2006, Time: 2:15 p.m., Location: Fine 224 |
| Abstract: |
See http://www.math.princeton.edu/~bsudakov/alon2005-2006.pdf |
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| Special Seminar |
| Topic: |
Huygens' principle and hyperplane configurations |
| Presenter: |
A.P. Veselov, Loughborough, UK |
| Date: |
Wednesday, April 19, 2006, Time: 2:15 p.m., Location: Fine Hall 314 |
| Abstract: |
Huygens' principle (in the narrow Hadamard's sense) for a
second-order hyperbolic equation means that its fundamental solution is
located on the characteristic conoid. Physically this implies that a
localised disturbance will have an effect localised in time at any point.
This remarkable property holds in particular for the wave
equations in the Euclidean spaces of odd dimension starting from 3. The
description of the hyperbolic equations satisfying Huygens' principle is
known as Hadamard's problem, which still remains largely open.
The development of the theory of quantum integrable systems in the
last two decades led to a substantial progress in this old problem, which
turned out to be closely related to a new special class of hyperplane
configurations, generalizing the Coxeter arrangements. I will discuss what
is currently known about these configurations and some related
geometric structures, appeared in the theory of Frobenius manifolds and
WDVV equation. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
Quivers and singularities |
| Presenter: |
Martijn Wijnholt, Princeton University |
| Date: |
Wednesday, April 19, 2006, Time: 3:00 p.m., Location: Fine Hall 214 |
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| Geometric Analysis Seminar ***Please note NEW special time, date, and location |
| Topic: |
Evolution of minimal tori in Riemannian manifolds |
| Presenter: |
Weiyue Ding, Beijing University |
| Date: |
Wednesday, April 19, 2006, Time: 3:30 p.m., Location: Fine Hall 322 |
| Abstract: |
In a joint work with Jiayu Li, Qingyue Liu, we propose to study the existence of minimal surfaces of gengus p>=1 in Riemannian manifolds using a L^2 gradient flow of the energy E(u, g), where g denotes conformal structures in the Teichmuller space T_p. The problem is much simpler when p=1, i.e. the surfaces are tori. In this case, we obtain results on the solvability of the Cauchy problem, blow-up of the map u(t) and degeneration of the conformal structure g(t), energy identities when blow-up or degeneration occurs, and convergence at time infinity, etc. |
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| Department Colloquium |
| Topic: |
Point Processes, Repulsion, and Fair Allocation |
| Presenter: |
Yuval Peres, University of California, Berkeley |
| Date: |
Wednesday, April 19, 2006, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
A random collection of points in space is called a "point
process". Recently, there has been increasing interest in processes that
exhibit "repulsion", such as zeros of random polynomials, noncolliding
particles and Eigenvalues of random matrices. I will describe the class of
determinantal point processes, which exhibit perfect repulsion, and
discuss the dynamical meaning of repulsion, see the movie at
http://stat-www.berkeley.edu/~peres/GAF/dynamics/dynamics.html .
In the second part of the talk, based on joint work with C. Hoffman and
A. Holroyd, I will discuss the problem of "fair allocation": allocating
the same area to every point of an isometry-invariant point process. Given
such a point process M in the plane, the Voronoi tesselation assigns a
polygon (of different area) to each point of M. Fair allocations, see
http://stat-www.berkeley.edu/~peres/stable/stable.html have a richer
geometry. For any Isometry-invariant point process, we show that there is
a unique fair allocation that is "stable" in the sense of the Gale-Shapley
stable marriage problem. It turns out that repelling point processes have
allocations that are better localized than the Poisson process. |
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| Algebraic Topology Seminar |
| Topic: |
Homotopy groups of toric spaces |
| Presenter: |
Martin Bendersky, CUNY |
| Date: |
Thursday, April 20, 2006, Time: 3:00 p.m., Location: Fine Hall 401 |
| Abstract: |
I will lecture on the work of David Allen. Unstable spectral sequences will be used to determine the homotopy groups of some toric spaces through a range. |
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| Analysis Seminar |
| Topic: |
Weak-strong uniqueness for the Navier-Stokes equation |
| Presenter: |
Pierre Germain, Ecole Polytechnique, Palaiseau |
| Date: |
Thursday, April 20, 2006, Time: 4:00 p.m., Location: Fine Hall 322 |
| Abstract: |
There exist classes of strong solutions of the Navier-Stokes equation such that: if a weak solution belongs to them, it is unique. We say then that weak-strong uniqueness holds. Serrin criterion is the first example of such a result. We will discuss new results which generalize Serrin criterion. |
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| Algebraic Geometry Seminar *** Please note special date and location |
| Topic: |
Freedom Conjecture |
| Presenter: |
Fedor Bogomolov, New York University |
| Date: |
Thursday, April 20, 2006, Time: 4:30 p.m., Location: Fine 214 |
| Abstract: |
The conjecture states that the commutator of the Sylow subgroup of the Galois group $Gal(\bar k(X)/k(X))$( k- closed, X-algebraic variety) is cohomologically free pro-$l$-group. It has many applications in algebraic geometry (like Bloch-Kato) and I will discuss why it should be true. |
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| Topology Seminar |
| Topic: |
Mom Technology and Low-Volume Hyperbolic 3- Manifolds |
| Presenter: |
Robert Meyerhoff, IAS and Boston College |
| Date: |
Thursday, April 20, 2006, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
In the late 1970's, W. Thurston proved that the set of volumes of complete hyperbolic 3-manifolds (of finite volume) is well-ordered and of order type omega^omega. In particular, there is a smallest volume v(1), a second smallest volume v(2), and so on; and that this sequence v(1) < v(2) < v(3) < ... has a limit point v(omega) which is the smallest volume of a one-cusped hyperbolic 3-manifold. And so on after that. D. Gabai, P. Milley, and I have developed a new method, the "Mom technology," which holds considerable promise for finding a reasonable collection of parent manifolds from which the low-volume manifolds can be obtained by hyperbolic Dehn surgery. |
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| Geometric Analysis Seminar |
| Topic: |
Some positivity results of quasi-local mass |
| Presenter: |
Mu-Tao Wang, Columbia University |
| Date: |
Friday, April 21, 2006, Time: 3:00 p.m., Location: Fine Hall 314 |
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APRIL 24 - 28, 2006 |
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| PACM Seminar |
| Topic: |
Coherence in stochastic dynamical systems |
| Presenter: |
Lee Deville, Courant Institute of Mathematical Sciences, New York University |
| Date: |
Monday, April 24, 2006, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
It is known that random perturbations to dynamical systems can be small and irrelevant, or, alternately, so large as to overwhelm the dynamics. More interesting are cases where small random perturbations introduce qualitative changes in a system without introducing significant randomness. In effect, these are generating noise-induced, yet coherent, dynamics. We will show that this phenomenon is present in a large class of dynamical systems and describe several examples in detail. The examples will include stochastically-forced ODEs and PDEs, and Markov chains. |
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| Graduate Student Seminar |
| Topic: |
TBA |
| Presenter: |
Corinna Ulcigrai, Princeton University |
| Date: |
Tuesday, April 25, 2006, Time: 12:30 p.m., Location: Fine 224 |
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| Algebraic Topology Seminar ***Please note special date and location |
| Topic: |
A Quillen Stratification for Hochschild Cohomology of Blocks |
| Presenter: |
Jonathan Pakianathan, University of Rochester |
| Date: |
Tuesday, April 25, 2006, Time: 3:00 p.m., Location: Fine Hall 401 |
| Abstract: |
(This talk is based on joint work with Sarah Witherspoon.)
Let G be a finite group and k an algebraically closed field of characteristic p, then kG can be decomposed into indecomposable ideal
direct summands called blocks which are very important in understanding the modular representations of the group G. The Hochschild cohomology of
kG and of these blocks is one of the tools that is commonly used
to study their structure. The Hochschild cohomology HH^*(kG) also comes up
in topology as additively (but not as a ring!) it is isomorphic to H^*(LBG), where LBG is the free loop space of BG.
In this talk I will discuss how one can
stratify the spectrum of the Hochchild cohomology rings HH^*(kG) and HH^*(B) using a method analogous to that used by Quillen to stratify the
spectru of the
normal cohomology ring H^*(G,k). We will see that the spectrum is determined by the poset of elementary abelian p-subgroups of G together
with the Alperin-Broue correspondence of blocks. In particular we will prove that the spectrum of the Hochschild cohomology of the principal block of a finite group is always homeomorphic to the spectrum of the k-algebra H^*(G;k), even though the rings in general are not isomorphic. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Martin Olsson, U. Texas |
| Date: |
Tuesday, April 25, 2006, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Mathematical Physics Seminar |
| Topic: |
TBA |
| Presenter: |
Peter Hislop, University of Kentucky |
| Date: |
Tuesday, April 25, 2006, Time: 4:30 p.m., Location: Jadwin 343 |
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| Number Theory Seminar |
| Topic: |
Identities in theta correspondence |
| Presenter: |
Zhengyu Mao, Rutgers at Newark |
| Date: |
Wednesday, April 26, 2006, Time: 2:00 p.m., Location: Fine Hall 314 |
| Abstract: |
I will describe some identities of linear forms and
distributions attached to representations in theta correspondence. These
identities can be used to prove formula of special values of L-functions. |
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| Algebraic Topology Seminar ***Please note special date and location |
| Topic: |
Stable Homology of Aut(F_n) |
| Presenter: |
Soren Galatius, Stanford University |
| Date: |
Wednesday, April 26, 2006, Time: 3:00 p.m., Location: Fine Hall 801 |
| Abstract: |
Let Aut(F_n) denote the automorphism group of a free group
on n generators. It is known that H_k(Aut(F_n)) is independent of n
as long as n >> k. There is a natural homomorphism from the symmetric
group S_n to Aut(F_n), I will sketch a proof that it induces an
isomorphism from H_k(S_n) to H_k(Aut(F_n)) for n >> k. An important
point of view here is that BAut(F_n) can be thought of as a moduli
space of metric graphs, i.e. graphs equipped with metrics, considered
up to isometry. |
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| Department Colloquium |
| Topic: |
Coarse geometry of mapping class groups |
| Presenter: |
Yair Minsky, Yale University |
| Date: |
Wednesday, April 26, 2006, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
The mapping class group of a compact surface can be studied from the
point of view of geometric group theory, in which coarse or
large-scale properties of its Cayley graph can be related to algebraic
properties of the group. I will give a partial picture of this coarse
geometry, including a distance formula, a description of some
quasi-isometrically embedded subgroups, and a solution of the
Brock-Farb rank conjecture. This represents joint work with Masur and
with Behrstock. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Geometric Coincidence Conjecture for Pisot Substitutions |
| Presenter: |
Jaroslaw Kwapisz, Montana State University |
| Date: |
Thursday, April 27, 2006, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: |
The talk will focus on the central conjecture in the theory of Pisot substitutions (i.e. substitutions over a finite alphabet with the spectral
radius of the abelianization that is a P.V. number) asserting that the translation
action on the tiling spaces (or substitutive systems) of unimodular Pisot
substitutions has pure discrete spectrum. I will identify the discrete spectrum,
recast the conjecture as a problem about injectivity of a natural geometric
realization map, and further boil it down to an algorithmically verifiable
Geometric Coincidence Condition (GCC). I will indicate how the GCC can be
verified for some families of substitutions (including a broad class of beta shifts). |
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| Algebraic Topology Seminar |
| Topic: |
Moduli Space of Nodal curves and Homotopy Theory |
| Presenter: |
Soren Galatius, Stanford University |
| Date: |
Thursday, April 27, 2006, Time: 3:00 p.m., Location: Fine Hall 401 |
| Abstract: |
Riemann's moduli space M_g classifies isomorphism classes of
genus g Riemann surfaces (or algebraic curves). M_g is a non-compact
algebraic variety and has a natural compactification due to Deligne,
Mumford and Knudsen. A point in the compactification is an isomorphism
class of a nodal curve, ie. a Riemann surface with a certain mild kind of
singularities. Madsen and Weiss' proof of Mumford's conjecture tells much
about M_g. I will describe an attempt to understand the compactification
from a similar point of view. This is joint work with Y. Eliashberg. |
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| Analysis Seminar |
| Topic: |
Optimal transportation and Ricci curvature for metric measure spaces |
| Presenter: |
Karl-Theodor Sturm, University of Bonn |
| Date: |
Thursday, April 27, 2006, Time: 4:00 p.m., Location: Fine Hall 322 |
| Abstract: |
We introduce and analyze generalized Ricci curvature bounds for
metric measure spaces (M,d,m), based on convexity properties of
the relative entropy Ent(. | m). For Riemannian manifolds,
Curv(M,d,m) \ge K if and only if Ric_M\ge K on M. For the
Wiener space, Curv(M,d,m)=1. One of the main results is that these lower
curvature bounds are stable under (e.g. measured Gromov-Hausdorff)
convergence. Moreover, we introduce a curvature-dimension condition
CD(K,N) being more restrictive than the curvature bound
Curv(M,d,m)\ge K. For Riemannian manifolds, CD(K,N) is equivalent to
Ric_M(\xi,\xi)\ge K\cdot |\xi|^2 and dim}(M)\le N.
Condition CD(K,N) implies sharp version of the
Brunn-Minkowski inequality, of the Bishop-Gromov volume comparison
theorem and of the Bonnet-Myers theorem. Moreover, it allows to
construct canonical Dirichlet forms with {Gaussian upper and lower
bounds} for the corresponding heat kernels. |
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| Topology Seminar |
| Topic: |
Contact structures, Giroux torsion and contact invariants |
| Presenter: |
Andras Stipsicz, Renyi Institute of Mathematics |
| Date: |
Thursday, April 27, 2006, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
Contact structures with positive Giroux torsion are expected to behave quite differently than the ones with vanishing torsion. For example
it is conjectured that the positivity of the Giroux torsion
of a contact structure is an obstruction for fillability. We give
some evidence for this conjecture through verifying a vanishing result for
the contact Ozsvath-Szabo invariants of contact structures with large enough torsion on certain 3-manifolds. |
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| Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Christina W. Tonnessen-Friedman, Union College |
| Date: |
Friday, April 28, 2006, Time: 3:00 p.m., Location: Fine Hall 314 |
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MAY 1 - 5, 2006 |
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| PACM Seminar |
| Topic: |
TBA |
| Presenter: |
Eric Vanden-Eijnden, Courant Institute of Mathematical Sciences, New York University |
| Date: |
Monday, May 1, 2006, Time: 4:00 p.m., Location: Fine Hall 214 |
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| Algebraic Geometry Seminar |
| Topic: |
Filtrations on cohomology arising from geometry |
| Presenter: |
Mark Andrea de Cataldo, Stony Brook, State University of New York |
| Date: |
Tuesday, May 2, 2006, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
I will report on work in progress with Luca Migliorini at Bologna. Given a map of complex algebraic varieties, the Leray spectral sequence and the perverse Leray spectral sequence induce filtrations on the (intersection) cohomology (with compact supports) of the domain. We describe these filtrations geometrically in terms of hyperplane sections and deduce various new Hodge-theoretic consequences for the homology of complex varieties. A very interesting precursor of this new point of view, concerning the Leray spectral sequence for cohomology, is due to Donu Arapura. |
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| Operation Research and Financial Engineering Seminar |
| Topic: |
Climate Risk, Securitization, and Equilibrium Bond Pricing |
| Presenter: |
Ulrich Horst, University of BC Vancouver |
| Date: |
Tuesday, May 2, 2006, Time: 4:30 p.m., Location: Friend Center Bowl 008 |
| Abstract: |
We propose a method of pricing financial securities written on non-tradable underlyings such as temperature or precipitation
levels. To this end, we analyze a financial market where agents
are exposed to financial and non-financial risk factors. The
agents hedge their financial risk in the stock market and trade a
risk bond issued by an insurance company. From the issuer's point
of view the bond's primary purpose is to shift insurance risks
related to non-catastrophic weather events to financial markets.
As such its terminal payoff and yield curve depend on an
underlying climate or temperature process whose dynamics is
independent of the randomness driving stock prices. We prove that
if the bond's payoff function is monotone in the external risk
process, it can be priced by an equilibrium approach. The
equilibrium market price of climate risk and the equilibrium price process
are characterized as solution of non-linear backward stochastic differential
equations. Transferring the BSDEs into PDEs, we represent the bond prices as
smooth functions of the underlying risk factors.
The talk is based on joint work with Matthias Muller. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
Alexander Braverman, Brown University |
| Date: |
Wednesday, May 3, 2006, Time: 3:00 p.m., Location: Fine Hall 214 |
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| Department Colloquium |
| Topic: |
Asymptotics for prime specialization over finite fields |
| Presenter: |
Brian Conrad, University of Michigan |
| Date: |
Wednesday, May 3, 2006, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
It is a classical and extremely difficult problem to prove theorems about prime values of irreducible polynomials over the integers. For example, it is still not known if there are infinitely many primes of the form n2 + 1. There is a long history of analogies between the integers and polynomials (in one variable) over a finite field, and so one can formulate an analogous problem in this other setting. It was discovered several years ago (joint work with K. Conrad and R. Gross) that there are some surprises. We illustrate the unexpected behavior by means of some explicit examples, and discuss theorems that predict these phenomena. The main goal of the talk is to motivate (by examples) and (briefly!) discuss the proofs of recent asymptotic results as the finite field and polynomial being specialized are allowed to vary; these asymptotics accord well with a general philosophy of Katz concerning limiting behavior over large finite fields and behavior over number fields. The case of characteristic 2 is not suitable for a general audience, but anyone interested can ask me about it at the colloquium dinner. |
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| Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Steve Zelditch, Johns Hopkins University |
| Date: |
Friday, May 5, 2006, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Geometric Analysis Seminar ***Please note special time |
| Topic: |
TBA |
| Presenter: |
Fernando Marques, Stanford University |
| Date: |
Friday, May 5, 2006, Time: 4:00 p.m., Location: Fine Hall 314 |
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MAY 15- 19, 2006 |
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| Operation Research and Financial Engineering Seminar |
| Topic: |
TBA |
| Presenter: |
Pauline Barrieu |
| Date: |
Tuesday, May 16, 2006, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
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