Geometry/Topology Seminar
Winter 2024
Thursdays 3:304:30pm, in
Eckhart 308

 Thursday January 18 at 3:304:30pm in E308
 Ismael Sierra, Toronto
 Homological stability of even and odd symplectic groups

Abstract: I will define the "odd" symplectic groups
Sp_{2g+1}(Z), which fit in between the usual "even"
symplectic groups, and state new homological stability
results for them. I will explain the sense in which the
above can be seen as an algebraic analogue of the proof of
homological stability of mapping class groups of surfaces by
HarrVistrupWahl. Finally, I will mention how these ideas
can then be applied to the study of diffeomorphism groups of
highdimensional manifolds, and I will state some open
problems of potential applications of these ideas.

 Thursday February 1 at 3:304:30pm in E308
 Tobias Shin, UChicago
 Almost complex manifolds are (almost?) complex

Abstract: What is the difference topologically
between an almost complex manifold and a complex manifold?
Are there examples of almost complex manifolds in higher
dimensions (complex dimension 3 and greater) which admit no
integrable complex structure? We will discuss these two
questions with the aid of a deep theorem of Demailly and
Gaussier, where they construct a universal space that
induces almost complex structures for a given dimension. A
careful analysis of this space shows the question of
integrability of complex structures can be phrased in the
framework of Gromov's hprinciple. If time permits, we will
conclude with some examples of almost complex manifolds that
admit a family of Nijenhuis tensors whose sup norms tend to
0, despite having no integrable complex structure (joint
with L. Fernandez and S. Wilson).

 Thursday February 8 at 3:304:30pm in E308
 Franco VargasPallete, Yale
 Minimal surface entropy for asymptotically cusped metrics in 3manifolds

Abstract: We say that a metric g in a torus cusp is
asymptotically cusped if there exists a hyperbolic cusped
metric so that its difference with g converges to 0 in
C^{1} as we go along the cusp. In this talk we will
describe minimal surface entropy for asymptotically cusped
metrics, which is a geometric invariant established by
CalegariMarquesNeves and defined as the asymptotic
counting of compact minimal surfaces as area grows. We will
show an entropy rigidity for finite volume hyperbolic
3manifolds. Namely, if M is a 3manifold that admits a
cusped hyperbolic metric of finite volume, then the
hyperbolic metric can be characterized as the metric
minimizing minimal surface entropy among negatively curved,
asymptotically cusped metrics. This is based on upcoming
joint work with Ruojing Jiang.

 Thursday February 15 at 3:304:30pm in E308
 Jing Tao, Oklahoma
 Taming tame maps of surfaces of infinite type

Abstract: A cornerstone in lowdimensional topology
is the NielsenThurston Classification Theorem, which
provides a blueprint for understanding homeomorphisms of
compact surfaces. However, extending this theory to
noncompact surfaces of infinite type remains an elusive
goal. The complexity arises from the behavior of curves on
surfaces with infinite type, which can become increasingly
intricate with each iteration of a homeomorphism. To address
some of the challenges, we introduce the notion of tame
maps, a class of homeomorphisms that exhibit nonmixing
dynamics. In this talk, I will present some recent progress
on extending the classification theory to such maps. This is
joint work with Mladen Bestvina and Federica Fanoni.

 Thursday February 22 at 3:304:30pm in E308
 Danylo Radchenko, Lille
 Steinberg module and multiple polylogarithms

Abstract: It was recently proved that the Steinberg
module is Koszul in a certain category of VBmodules.
Furthermore, its Koszul dual was identified with the tensor
square of the Steinberg module. We show that for the field
of rational numbers, one can identify the Koszul dual of the
Steinberg module with a certain space of multiple
polylogarithms on the torus. We will discuss a proof of this
result and its applications to the Goncharov program. If
time permits, we will also discuss the relation between
multiple polylogarithms and the ChurchFarbPutman
conjecture. The talk is based on joint work in progress with
Steven Charlton and Daniil Rudenko.

 Thursday March 7 at 3:304:30pm in E308
 Grigori Avramidi, MPI Bonn
 Group rings and hyperbolic geometry

Abstract: In the 60's Cohn showed that all ideals in
the group algebra of a free group are free. Bass and Wall
used this result to show that all twodimensional complexes
with free fundamental groups are standard: they are all
homotopy equivalent to wedges of circles and 2spheres. The
goal of this talk is to describe recent results of this type
for groups acting on hyperbolic spaces. I will explain an
algorithm showing that in the group algebra of a group
acting on a hyperbolic space, ideals generated by
“few” elements are free (where “few”
is a function of the minimal displacement of the action) and
mention applications to cohomological dimension of
“few relator” groups, topology of 2complexes
with hyperbolic fundamental groups, and complexity of cell
decompositions of hyperbolic manifolds. Joint work with
Thomas Delzant.
Due to the high number of requests, we are no longer accepting speakers via selfinvitations.
For questions, contact