Geometry/Topology Seminar
Fall 2017
Thursdays (and sometimes Tuesdays) 34pm, in
Eckhart 308

 Thursday September 28 at 34pm in Eck 308
 Andy Putman, Notre Dame
 The Johnson filtration is finitely generated

Abstract: A recent breakthrough of ErshovHe shows
that the Johnson kernel subgroup of the mapping class group
is finitely generated for g at least 12. In joint work with
Ershov and Church, I have extended this to show that every
term of the lower central series of the Torelli group is
finitely generated once the genus is sufficiently large. A
byproduct of our work is a proof that the Johnson kernel is
finitely generated for g at least 4 which is remarkably
simple (so simple, in fact, that I will be able to give in
nearly complete detail in this talk).

 Friday October 27
 Multiple speakers,
 (Conference) No Boundaries: Groups in Algebra, Geometry, and Topology
A Celebration of the Mathematical Contributions of Benson Farb

Abstract: Conference in honor of Benson Farb, 10/27
through 10/29. See
http://people.math.gatech.edu/~dmargalit7/noboundaries/schedule.shtml
for speakers.

 Thursday November 2 at 34pm in Eck 308
 Nate Harman, University of Chicago

The Deligne category approach to representation stability

Abstract: Deligne defined a family of categories
Rep(S_{t}) which "interpolate" the categories of
representations of symmetric groups over a field of
characteristic zero. I will discuss these categories and
their generalizations with emphasis on their connection to
the theory of representation stability. In particular I will
explain a uniform proof of stability in characteristic zero,
periodicity in characteristic p, and mixed
rank/characteristic stability for FImodules (and if there
is time, for VImodules).

 Wednesday November 8 at 23pm in Eck 358
 Hannah Alpert, The Ohio State University
 Morse broken trajectories and hyperbolic volume (Geometric Analysis seminar)

Abstract: (This is a Geometric Analysis Seminar talk
which may be of interest to G/T seminar regulars) A large
family of theorems all state that if a space is
topologically complex, then the functions on that space must
express that complexity, for instance by having many
singularities. For the theorem in this talk, our preferred
measure of topological complexity is the hyperbolic volume
of a closed manifold admitting a hyperbolic metric (or more
generally, the Gromov simplicial volume of any space). A
Morse function on a manifold with large hyperbolic volume
may still not have many critical points, but we show that
there must be many flow lines connecting those few critical
points. Specifically, given a closed ndimensional manifold
and a MorseSmale function, the number of npart broken
trajectories is at least the Gromov simplicial volume. To
prove this we adapt lemmas of Gromov that bound the
simplicial volume of a stratified space in terms of the
complexity of the stratification.

 Thursday November 9 at 34pm in Eck 308
 Daniel Studenmund, Notre Dame
 Semiduality in group cohomology

Abstract: A duality group has a pairing exhibiting
isomorphisms between its homology and cohomology groups.
Examples include solvable BaumslagSolitar groups and
arithmetic groups over number fields, by work of Borel and
Serre. Many naturally occurring groups fail to be duality
groups, but are morally very close. In this talk we make
this precise with the notion of a semiduality group, and
prove that the lamplighter group is a semiduality group.
This illustrates methods used to prove the rank 1 case of a
general conjecture that certain arithmetic groups in
positive characteristic are semiduality groups, building on
the result of BorelSerre. This talk covers work joint with
Kevin Wortman.

 Thursday November 16 at 34pm in Eck 308
 Daniel Allcock, UT Austin
 Steinberg Groups as Amalgams

Abstract: We discuss a new presentation of the
Steinberg groups, including Tits' generalization to the
infinitedimensional KacMoody case. Even for the classical
cases ABCDEFG treated by Steinberg, this has several
advantages over other presentations, such as being defined
in terms of the Dynkin diagram rather than the whole root
system, and avoiding the fussy sign problem completely. Our
motivating application is that infinitedimensional
arithmetic groups like E10(Z) have explicit finite
presentations. In fact "most" KacMoody groups over finitely
generated rings are finitely presented. (The Weyl group of
E10 is a lattice in O(9,1), corresponding to the Cartan
subalgebra having an invariant Lorentzian metric.)

 Monday December 4 at 34pm in Eck 308
 Wouter Van Limbeek, Michigan
 Symmetry and selfsimilarity in Riemannian geometry

Abstract: In 1893, Hurwitz showed that a Riemann
surface of genus g ≥ 2 admits at most
84(g1) automorphisms; equivalently, any
2dimensional hyperbolic orbifold X has
Area(X)≥ \pi / 42. In contrast, such a lower
bound on volume fails for the ndimensional torus
T^{n}, which is closely related to the
fact that T^{m} covers itself
nontrivially. Which geometries admit bounds as above? Which
manifolds cover themselves? In the last decade, more than
100 years after Hurwitz, powerful tools have been developed
from the simultaneous study of symmetries of all covers of a
given manifold, tying together Lie groups, their lattices,
and their appearances in differential geometry. In this talk
I will explain some of these recent ideas and how they lead
to progress on the above (and other) questions. (This talk
is on a Monday instead of the usual Thursday.)

 Thursday December 7 at 3:304:30pm in Eck 203
 Zinovy Reichstein, UBC
 The HermiteJoubert Problem

Abstract: (Note the unusual time and room due to
finals) An 1861 theorem of Ch. Hermite asserts that for
every field extension E/F of degree 5 there exists an
element a in E such that F(a) = E and the minimal polynomial
of a over F is of the form f(x) = x^{5} +
b_{2} x^{3} + b_{4} x +
b_{5}, for some b_{2}, b_{4}.
b_{5} in F. In classical language, this can be
rephrased as follows: every polynomial of degree 5 can be
transformed to the above form (with missing x^{4}
and x^{2} terms) by a Tschirnhaus transformation
without auxiliary radicals. Equivalently (via Newton's
formulas), Tr_{E/F}(a) =
Tr_{E/F}(a^{3}) = 0. A similar result for
field extensions of degree 6 was proved by P. Joubert in
1867. In this talk I will address the following (still
largely open) question: Do these classical theorems remain
true for field extensions E/F (or equivalently, polynomials)
of degree >= 7?

 Tuesday December 12 at 34pm in Eck 308
 Tathagata Basak, Iowa State
 A complex ball quotient and the monster

Abstract: Let B be the unit ball in the standard
13dimensional complex vector space. We shall talk about a
ball quotient obtained by removing a locally finite
collection of complex hyperplanes from B and then
quotienting the rest by the action of a discrete subgroup of
U(13,1). We shall state a conjecture that relates the
fundamental group of this ball quotient and the monster
simple group and describe our results towards this
conjecture. The Leech lattice plays a central role. This is
joint work with Daniel Allcock.

 Wednesday February 22 at 34pm in Eck 308
 Eric Ramos, University of Michigan
 TBA

Abstract: TBA
Due to the high number of requests, we are no longer accepting speakers via selfinvitations.
For questions, contact