Geometry/Topology Seminar
Spring 2015
Thursdays (and sometimes Tuesdays) 34pm, in
Eckhart 308

 Thursday April 16 at 34pm in Eck 308
 Steven Boyer, UQAM
 Foliations, leftorders, and Lspaces

Abstract: Much work has been devoted in recent years
to examining relationships between the existence of a
cooriented taut foliation on a closed, connected, prime
3manifold W, the leftorderability of the fundamental group
of W, and the property that W not be a HeegaardFloer
Lspace. Classic work shows that each of these conditions
holds when W has a positive first Betti number and it has
been conjectured that they coincide when the first Betti
number of W âis zero. In this talk I will discuss the known
connections between these conditions and survey the current
status of the conjectures.

 Thursday April 30 at 34pm in Eck 308
 Stefan Witzel, Bielefeld
 Higher finiteness properties of arithmetic groups in positive characteristic

Abstract: Topological finiteness properties of
groups generalize the properties of being finitely generated
and of being finitely presented. Groups having some but not
all of these properties naturally arise in the realm of
arithmetic groups. For example,
SL_{3}(F_{q}[t]) is finitely
generated but not finitely presented. I will speak about how
this €example generalizes. The talk is based on joint work
with KaiUwe Bux and Ralf Kohl.

 Monday May 4 at 1:302:30pm in Eck 202
 Alex Kontorovich, Rutgers
 The Unreasonable Effectiveness of Thin Groups

Abstract: Thin groups are certain arithmetic
subgroups of Lie groups whose quotient manifolds have
infinite volume. We will describe a number of problems in
pseudorandom numbers, numerical integration, and homogeneous
dynamics which, it turns out, are all the same problem when
viewed through the lens of thin groups.

 Tuesday May 5 at 34pm in Eck 308
 Dave Witte Morris, Lethbridge
 Arithmetic subgroups whose representations all map into GL(n,Z)

Abstract: Suppose Gamma is an arithmetic subgroup of
a semisimple Lie group G. For any homomorphism rho from
Gamma to GL(n,R), a classical paper of J.Tits
determines whether rho(Gamma) is conjugate to a subgroup of
GL(n,Z). Combining this with an easy surjectivity
result in Galois cohomology provides a short proof of the
known fact that every G has an arithmetic subgroup Gamma,
such that the containment is true for every homomorphism
rho. We will not assume the audience is acquainted with
arithmetic groups, Galois cohomology, or the theorem of
Tits.

 Thursday May 7 at 34pm in Eck 308
 Jeff Danciger, Austin
 Convex projective structures on nonhyperbolic threemanifolds

Abstract: Y. Benoist proved that if a closed
threemanifold M admits a convex real projective structure,
then M is topologically the union along tori of finitely
many submanifolds each of which admits a complete finite
volume hyperbolic structure on its interior. We describe
some initial results in the direction of a potential
converse to Benoist's theorem. Specifically, we show that a
cusped hyperbolic threemanifold may (under assumptions) be
deformed to convex projective structures with totally
geodesic torus boundary. Such structures may be (convexly)
glued together whenever the geometry at the boundary matches
up. In particular, we prove that many doubles of cusped
hyperbolic threemanifolds admit convex projective
structures. Joint work with Sam Ballas and Gye Seon Lee.

 Friday May 8 at 1:302:30pm in Eck 202
 Alex Suciu, Northeastern University
 Resonance, representations, and the Johnson filtration

Abstract: I will describe a relationship between the
classical representation theory of a complex, semisimple Lie
algebra \mathfrak{g} and the resonance varieties
R(V,K)\subset V^{*} attached to
irreducible \mathfrak{g}modules V and
submodules K\subset V\wedge V. In the process, I
will give a precise rootsandweights criterion insuring the
vanishing of these varieties. In the case when
\mathfrak{g}= \mathfrak{sl}_{n}(C)
or \mathfrak{sp}_{2g}(C), our
approach yields a unified proof of two vanishing results for
the resonance varieties of the (outer) Torelli groups of
finitely generated free groups and surface groups. In turn,
these vanishing results reveal certain homological
finiteness properties of the Johnson filtration. This is
joint work with Stefan Papadima.

 Tuesday May 19 at 45pm in Eck 308
 Christoforos Neofytidis, Binghamton
 Groups presentable by products and an ordering of Thurston geometries by
maps of nonzero degree

Abstract: The existence of a map of nonzero degree
defines a transitive relation on the homotopy types of
closed oriented manifolds of the same dimension, called
domination relation. Gromov suggested investigating the
domination relation as defining an ordering of manifolds and
formulated numerous conjectures regarding classes that might
(not) be comparable under this relation. A particular case
of the domination question, which specifies Steenrod's
classical problem on the realization of homology classes by
manifolds, and is motivated by MilnorThurston and Gromov's
theory of functorial seminorms on homology (such as the
simplicial volume), is when the domain is a nontrivial
direct product. In this talk, I will discuss the
(non)existence of maps of nonzero degree from direct
products to aspherical manifolds with fundamental groups
with nontrivial center. As an application, I will describe
an ordering of all nonhyperbolic aspherical 4manifolds
possessing a Thurston geometry.

 Tuesday May 26 at 34pm in Eck 308
 Ailsa Keating, Columbia University
 Higherdimensional Dehn twists and symplectic mapping class
groups

Abstract: Given a Lagrangian sphere S in a
symplectic manifold M of any dimension, one can associate to
it a symplectomorphism of M, the Dehn twist about S. This
generalises the classical twodimensional notion. These
higherdimensional Dehn twists naturally give elements of
the symplectic mapping class group of M, i.e.
\pi_{0} (Symp (M)). The goal of the talk
is to present parallels between properties of Dehn twists in
dimension 2 and in higher dimensions, with an emphasis on
relations in the mapping class group.

 Tuesday June 2 at 34pm in Eck 308
 Michael Hull, UIC
 Acylindrically hyperbolic groups

Abstract: Hyperbolic and relatively hyperbolic
groups have played an important role in the development of
geometric group theory. However, there are many other groups
which admit interesting and useful actions on hyperbolic
metric spaces, including mapping class groups,
Out(F_{n}), rightangled Artin groups,
and many 3manifold groups. The class of acylindrically
hyperbolic groups provides a framework for studying all of
these groups (and many more) using many of the same
techniques developed for hyperbolic and relatively
hyperbolic groups. We will give a brief survey of examples
and properties of acylindrically hyperbolic groups and show
how the study of this class has yielded new results in a
number of particular cases.
For questions, contact