 Past seminars:
Fall 2006,
Spring 2007,
Fall 2007
Spring 2008,
Fall 2008,
Spring 2009,
and
Fall 2009
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Spring 2010:
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Jan. 29: Ara Basmajian (Hunter College and Graduate Center of CUNY)
Universal Length Bounds for Non-Simple Closed Geodesics
We consider the relationship between the length of a closed geodesic on a hyperbolic
surface and its self-intersection number. In the 1993 paper The stable neighborhood theorem and lengths of closed geodesics
it was shown that a closed geodesic with intersection number k has length bounded from below by a constant Mk
that goes to infinity with k. The Mk are universal constants in that they only depend on k and not
on any particular hyperbolic structure. In this talk we show that the Mk grow like Log k. Our techniques
are elementary and involve using a quantitative version of the Margulis lemma.
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Feb. 5: Sarah Koch (Harvard University)
Böttcher Coordinates in Cm
A well-known theorem of Böttcher asserts that an analytic germ
f:(C,0) → (C,0) which has a superattracting fixed
point at 0, more precisely of the form f(z) = a zk + o(zk) for some non-zero
a, is analytically conjugate to the power map z ↦ a zk by an
analytic germ (C,0) → (C,0) which is tangent
to the identity at 0. In this talk, we generalize this result and
give a Böttcher criterion for analytic maps in several complex
variables.
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Feb. 12: No meeting
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Feb. 19: Trevor Clark (Toronto/Stony Brook University)
Regular or Stochastic Dynamics in Higher Degree Families of Unimodal Maps
About twenty years ago, Palis conjectured that typical dynamical systems should possess good statistical properties.
Through the work of Avila, Lyubich, de Melo and Moreira, this has been proven for unimodal maps with a non-degenerate
critical point. I will show how to remove the condition on the critical point in analytic families of unimodal maps;
along the way proving that the hybrid classes in the space of unimodal maps yield a lamination near all but
countably many maps in the family. The essential difference in the higher
degree case is the presence of non-renormalizable maps without "decay of geometry." The key to their study is
the use of a generalized renormalization operator, which has much in common with the usual renormalization operator.
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Feb 26: Jason Behrstock (Lehman College of CUNY)
Curve Complex Projections and the Mapping Class Group
We will explain a certain natural way to project elements of
the mapping class to simple closed curves on subsurfaces. Generalizing
a coordinate system on hyperbolic space, we will use these projections
to describe a way to parametrize the mapping class group in terms of
these projections; we will also explain a similar parametrization for
Teichmuller space. This point of view is useful in several
applications; time permitting we shall discuss how we have used this
to prove the Rapid Decay property for the mapping class group. This
talk will include joint work with Kleiner, Minsky, and Mosher.
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Mar. 5: Moira Chas (Stony Brook University)
TBA
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Mar. 12: Robert Devaney (Boston University)
TBA
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March 19: Gabino Gonzalez-Diez (UAM, Spain)
TBA
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Mar. 26: Xiao Jun Huang (Rutgers University)
TBA
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Apr. 2: No Meeting
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Apr. 9: Jian Song (Rutgers University)
TBA
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Apr. 16: Reza Chamanara (Brooklyn College of CUNY)
TBA
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Apr. 23: Melkana Brakalova (Fordham University)
TBA
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Apr. 30: Shou-Wu Zhang (Columbia University)
TBA
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May 7: Clifford Earle (Cornell University)
TBA
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May 14: Sudeb Mitra (Queens College of CUNY)
TBA
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