Friday, August 25th (joint with Subfactor Seminar,
3:10-4:00pm)
Speaker: Christian Fleischhack,
University of Paderborn
Title: Loop Quantization
of Geometry
Abstract: Loop quantum gravity
aims at a mathematically rigorous quantization of general
relativity. It relies on
a reformulation of gravity as a gauge field
theory with constraints, which is canonically quantized. The
classical
configuration space
A is
formed by connections in some principal fibre bundle and gets
compactified
during quantization. The resulting space can
be seen as the spectrum of an appropriate C*-algebra of bounded
functions on
A or as a
projective limit of powers of the structure group. Moreover, it
exhibits a canonical
measure induced by the Haar measure. In my
talk, I am going to present the background and the basic
structures of the
theory. If time permits, I will also discuss
applications to the quantization of geometric entities like area
or how
diffeomorphism invariance restricts the
freedom in quantizing the full theory.
(Contact Person:
Ioana Suvaina and
Dietmar Bisch)
Friday,
September 22nd
Speaker: Bert Guillou,
University of Kentucky
Title: The slice filtration
for certain RO(K_4)-graded suspensions of HF_2
Abstract: A
space X can be described by its Postnikov tower, whose stages
have only the homotopy groups of X in a range.
Equivariantly, there is an analogue of the
Postnikov filtration called the slice filtration. After
reviewing some previously known
examples, I will describe the slice
filtration for twisted Eilenberg-Mac Lane spectra when the group
of equivariance is K_4, the
Klein four group. This is joint work with C.
Yarnall.
(Contact Person: Anna Marie Bohmann
)
Friday,
September 29th
Speaker:
Jesse Leo Kass, University of South Carolina
Title:
How to count lines on a cubic surface arithmetically
Abstract:
A celebrated 19th century
result is that a smooth cubic surface over the complex numbers
contains
exactly 27 lines. Over the real
numbers, the count of lines depends on the surface, but Segre
showed that a certain
signed count is independent of the
surface. In my talk, I will explain how to extend Segre's
to an arbitrary field.
This result is an application of recent ideas
about Euler classes in A1-homotopy theory. All work is
joint with Kirsten
Wickelgren.
(Contact
Person: Rares Rasdeaconu
)
Friday, October 6th
Speaker: Peter Bonventre,
University of Kentucky
Title: Genuine
Equivariant Operads
Abstract: A
classic result by Elmendorf states that G-spaces and
G-coefficient systems are Quillen equivalent. Moreover,
this result remains true if one replaces
spaces with other well-behaved categories (including simplicial
sets and categories).
However, when considering G-operads, this
equivalence fails to capture certain desired subtleties. In this
talk, I will introduce
(G-)operads and review this failure. I will
then define a new algebraic gadget called genuine G-operads
(playing the role of
coefficient systems), and state an
Elmendorf-type result in this context. This is joint work with
L. Pereira. (Contact Person:
Anna Marie Bohmann)
Friday, Oct 13th -
no meeting, Fall Break
Friday, October 20th
Speaker: Ryan Grady, Montana
State University
Title: Manifold
Invariants via Perturbative QFT
Abstract: Assuming
only elementary differential topology, I will introduce the
Batalin-Vilkovisky formalism for quantum
field theory (QFT). I will then give some
elementary/foundational examples. Finally, I will introduce a
family of QFTs
(sigma models) and illustrate how they can be
used to study the topology and geometry of smooth manifolds.
(Contact Person:
Anna Marie Bohmann)
Friday, November
3rd
Speaker: Matthew
Gentry Durham, Yale University
Title: Geometrical
finiteness and Veech subgroups of mapping class groups
Abstract: I
will discuss work in progress with Dowdall, Leininger, and
Sisto, in which we aim to develop a notion of
geometrical finiteness for subgroups of
mapping class groups. Motivated by the theory of convex
cocompact subgroups,
which are precisely those which determine
hyperbolic surface group extensions, I will describe some
hyperbolic properties
of the surface group extensions coming from
lattice Veech subgroups. (Contact Person: Spencer Dowdall)
Friday,
November 10th
Speaker:
Joseph Migler, Ohio
State University
Title:
Torsion invariants in operator algebras and
K-theory
Abstract:
Determinant-type
invariants known as joint torsion may be associated to
collections of operators that commute
modulo trace ideals. These have been
applied to problems in operator theory, asymptotics of
determinants, and the classification
of almost normal operators up to almost
unitary equivalence. We will review the construction of
these invariants and discuss
recent work on their applications. (Contact
Person: Rudy Rodsphon
)
Wednesday, November
15th (3:10-4pm, in SC 1420)
Speaker:
Samuel Guerin,
Universite Lyon 1, France
Title:
Real K-theory
Abstract:
It
was realized by Atiyah and Singer in the sixties that the index
theory of complex elliptic operators can be well
understand using K-theory. This led them to a
new proof of their famous theorem. They also show how these idea
can be adapted
for real elliptic operators. This led to the
KO/KR theory. This new theory exhibits new features as an 8 fold
periodicity and to new
topological invariants, namely mod 2
invariants. Following Atiyah and Singer, we will speak about the
Atiyah-Singer index theorem
for families of real elliptic operators and
how this gives the mod 2 index theorem for skew-adjoint elliptic
operators.
Friday, Nov 24th
- no meeting, Thanksgiving Break