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Schedule
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| Preconference Talks |
| Thursday, April 16
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3:10 - 4:00 PM
4088 East Hall |
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Thomas Koberda |
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Homological Representation Theory of The Mapping Class
Group
I seek to understand the algebraic structure of the mapping class
group and the dynamical behavior of
individual classes by studying the representation theory of the
mapping class group on the homology of
certain finite covers. I will explain how we can construct a faithful
infinite-dimensional representation of
the mapping class group and recover the Nielsen-Thurston
classification of each class. I will also indicate
connections with the representation theory of nilpotent Lie groups.
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4:10 - 5:00 PM
1360 East Hall |
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Benson Farb |
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Surface bundles over surfaces
The goal of this talk will be to survey the theory of
surface bundles over surfaces. This topic connects to areas
from algebraic geometry to combinatorial group theory to
Teichmuller theory. This largely unexplored subject has many
open questions, some of which will be presented in this talk.
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| RTG WORKSHOP ON GEOMETRIC GROUP THEORY |
| Friday, April 17 -
B844 East Hall |
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1:30 - 2:30 PM |
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Mladen Bestvina |
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Prehistory
Nielsen, Magnus, Whitehead. Stallings'
folds. Finite generation of Out(F_n) and related algorithms
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2:45 - 3:45 PM |
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Kai-Uwe Bux |
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Symmetric spaces, Siegel domains and consequences.
Definition of arithmetic groups, elementary properties;
the geometries associated to arithmetic groups and
Siegel domains. SL_n(Z) will be the running example.
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4:15 - 5:15 PM |
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Benson Farb |
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Algebraic Structure
Dehn twists, finite generation, the lantern and H_1, presentations,the symplectic representation, virtual torsion-freeness |
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| Saturday,
April 18 - B844 East Hall |
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9:00 - 10:00 AM |
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Benson Farb
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The Nielsen-Thurston Classification and pseudo-Anosov theory
Construction of pseudo-Anosovs, the main theorem, analogy with SL(2,Z), Thurston proof, Bers proof
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10:30 - 11:00 AM |
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Chia-Yen Tsai |
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Asymptotics of least pseudo-Anosov
dilatations
The mapping class group of S is the
set of all surface homeomorphisms of S up to isotopy. The
Nielsen-Thurston classification says that a mapping class is
either periodic, reducible, or pseudo-Anosov. Each pseudo-Anosov
mapping class is equipped with a real number >1 called the
dilatation. We will consider the least dilatation for each
surface. In this talk, we will discuss the asymptotic behavior
of least pseudo-Anosov dilatations when we vary genus and the
number of marked points of a surface. |
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11:15 - 11:45 AM |
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Johanna Mangahas |
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Uniform uniform exponential growth of subgroups of the
mapping class group
Like linear groups and hyperbolic
groups, subgroups of the mapping class group with exponential
growth have uniform exponential growth; furthermore, their
minimal growth rates have a lower bound which depends on the
surface, and not the particular subgroup. I'll describe the
proof, and also show why any lower bound necessarily depends on
the topological type of the surface. |
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1:15 - 2:15 PM |
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Kai-Uwe Bux |
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Homological properties and duality
Further
exploiting the action on symmetric spaces; homological
properties in particular Bieri-Eckmann duality
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2:30 - 3:00 PM |
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Tom Church |
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Orbits of curves under the
Torelli group and the Johnson kernel
It is not difficult to determine when two collections of
curves are in the same orbit under the mapping class group; the
solution relies just on the classification of surfaces. A major
advance came in work of Dennis Johnson, who gave a simple but powerful
argument to describe the orbit of a bounding pair or separating curve
under the action of the Torelli group. We will describe the proof of
Johnson's theorem and explain how to extend the result to arbitrary
collections of curves. Finally, we will outline a new perspective on
the Johnson homomorphism that allows us to characterize orbits of
curves under the Johnson kernel. |
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3:15 - 3:45 PM |
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Jing Tao |
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Linearly Bounded Conjugator Property for the Mapping Class Group
Given two conjugate mapping classes f and g, we produce a
conjugating element w such that |w| ≤ K (|f| + |g|), where | · |
denotes the word metric with respect to a fixed generating set, and K
is a constant depending only on the generating set. As a consequence,
the conjugacy problem for mapping class groups is exponentially
bounded. |
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4:15 - 5:15 PM |
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Mladen Bestvina |
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Topology of Out(F_n)
Definition
of outer space, spine, finiteness properties. Proof of homology
stability. Train-tracks. |
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6:00 PM |
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Banquet |
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Middle Kingdom
332 S Main St
(734) 668-6638
Ann Arbor, MI 48104 |
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| Sunday, April 19 -
B844 East Hall |
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9:15 - 10:15 AM |
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Mladen Bestvina
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Geometry of Outer space.
Proof of existence of train-tracks for irreducible autos a la Bers. Where do we stand? |
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10:45 - 11:45 AM |
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Kai-Uwe Bux |
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Generalizations of arithmetic groups
S-arithmetic groups and arithmetic groups in positive
characteristic and the associated geometries
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12:00 - 1:00 PM |
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Benson Farb |
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Comparisons between mapping class groups and arithmetic groups
Analogies, similarities, differences ((co)homological, algebraic, geometric).
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