Geometry Seminar
Vanderbilt University
Fall 2018
Organizers: Rares Rasdeaconu, Larry
Rolen
Fridays, 3:10-4:00pm in SC 1310 (unless
otherwise noted)
Tuesday,
October 9th, 3:10-4:00pm, Room SC1310
Speaker: Ian Wagner, Emory
University
Title:
Harmonic Hecke eigenlines and
Mazur's problem
Abstract: We construct two families of
harmonic Maass Hecke eigenforms. Using these families we
construct p-adic
harmonic Maass forms in the sense of
Serre. The p-adic properties of these forms answer a
question of Mazur about the
existence of an "eigencurve-type" object in
the world of harmonic Maass forms. (Contact Person:
Larry Rolen)
Friday, Oct 19th - No meeting
(Fall Break)
Friday, October 26th
Speaker:
Rudy Rodsphon,
Northeastern University
Title:
On a conjecture of Connes and
Moscovici
Abstract:
In the early
eighties, Connes developed his Noncommutative Geometry
program, mostly to extend index theory
to situations where usual tools of
differential topology are not applicable. A typical
situation is foliations whose holonomy
does not necessarily preserve any
transverse measure, or equivalently the orbit space of the
action of the full group of
diffeomorphisms of a manifold. In the end
of the nineties, Connes and Moscovici worked out an
equivariant index problem
in these contexts, and left a conjecture
about the calculation of this index in terms of
characteristic classes. A large portion of
the talk will be expository, and will
survey the history of this problem. Time permitting, we will
explain our recent solution to
this conjecture. No prior knowledge of
the subject will be assumed. This is a joint work with Denis
Perrot. (Contact Person:
Gennadi Kasparov)
Friday, November 9th
Speaker:
Scott Wilson, CUNY
Queens College
Title:
Extensions of some results in complex
and Kahler geometry to the
non-integrable setting
Abstract:
In this talk I
will survey recent joint work with Joana Cirici which
extends Dolbeault cohomology to all
almost complex manifolds, and generalizes
many of the foundational results for compact Kahler
manifolds to the
non-integrable setting. Among these are
the so-called Hodge, Serre and Lefschetz dualities, as well
as certain topological
bounds on solutions to geometric
equations. All of this work stems from a careful study of
the exterior derivative on the
differential forms of an almost complex
manifold, and this talk will begin with an elementary
discussion of that situation.
Preprints are available at:
arXiv:1809.1416 and arXiv:1809.1414. (Contact Person: Rares
Rasdeaconu)
Friday, Nov 16 & Nov 23 - No
meeting (Thanksgiving Break)
Friday, November
30th
Speaker:
Frank Thorne, University
of South Carolina
Title:
TBA
Abstract:
TBA. (Contact Person: Larry Rolen)
Friday, December
7th
Speaker:
Gueo Grancharov, Florida
International University
Title:
Non-Kaehler structures on foliations
Abstract:
After briefly explaining the difference
between Kaehler and non-Kaehler structures, I'll focus on
one of
the main sources of compact non-Kaheler
manifolds - various types of foliations. These include
twistor spaces, principal
bundles and complex suspensions. I'll
explain what type of special Hermitian metrics they carry
and report on some
topologically new examples of manifolds
admitting solutions of Strominger-Hull system. (Contact Person: Rares Rasdeaconu)
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