Spring 2020

** Organizers: ****Anna Marie Bohmann, Rares
Rasdeaconu and Ioana Suvaina**

** Tuesdays, 10:00-10:50am in SC 1320
(unless otherwise noted) **

__Speaker:__** Jocelyne
Ishak, Vanderbilt University**

__Title____:__** Introduction to
Chromatic Localization** **
**

__Abstract__**: **This talk is meant to
provide an introduction to key tools and ideas in used in
homotopy theory today that are

essential in calculations of homotopy groups of spheres.

**Tuesday, February 18th**

__Speaker:__** Anna Marie
Bohmann, Vanderbilt University**

__Title____:__** (Rational)
equivariant K-theory and its multiplicative structure** ** **

__Abstract__**: **Topological K-theory
is a classical invariant of spaces that connects topology,
geometry, physics and other fields.

At heart, it is built out of vector bundles, and in the
presence of a group action, there is a natural equivariant
version due to

Segal that is built out of vector bundles with group actions.
Both equivariant and non-equivariant K-theory are "rings," in

the sense that they have nice commutative cup products.
In this talk, we discuss the rationalized versions of these
rings and

using recent work of Barnes, Greenlees and Kedziorek, we show
that this multiplication is suitably unique. This is
joint work

with Hazel, Ishak, Kedziorek and May.

**Tuesday, Feb 25th** -- TALK CANCELLED

__Speaker:__** Viatcheslav
Kharlamov, University of Strasbourg, France
**

__Title____:__** On maximality
and chirality for real non-singular projective cubic
hypersurfaces** ** **

__Abstract__**: **A natural measure of
topological complexity for a topological space is the total
Betti number. According to Smith theory of

periodic transformations, such a complexity of a real locus of
a real algebraic variety is bounded from above by the
complexity

of the locus of complex points. When the complexity of the
real locus attains the complexity of the complex one, a number
of

remarkable topological properties show up. However, it is
still an open question when such a maximality can be achieved.

Another important topological characteristic of a real
projective variety is its chirality: IS or IS NOT it, say,
deformation equivalent to its

own image in a hyperplane mirror.

In this talk we will survey the latest known results on
chirality problem for cubic hypersurfaces and will explain how
a strong achirality

helps to construct maximal cubic hypersurfaces in all
dimensions. (Contact person: Rares Rasdeaconu)

**Tuesday, Mar 10th**

__Speaker:__** Rares
Rasdeaconu, Vanderbilt University
**

__Title____:__** Moduli
spaces of stable rank one torsion free sheaves on real
curves** **
**

__Abstract__**: **The
counting of rational curves representing primitive
homology classes on complex or real K3 surfaces is
governed by the

Yau- Zaslow formula and its real analog, respectively. An
approach to extend such formulae to the non-primitive case
has been

suggested by Jun Li and requires the computation of the
Euler characteristic of moduli spaces of stable, rank one
sheaves on curves

which are possibly reducible and non-reduced. Recent
developments in this direction will be presented. The talk
is based on a joint

work in progress with V. Kharlamov.

**Tuesday, Mar 17th**

__Speaker:__** Peter
Bonventre, University of Kentucky
**

__Title____:__** TBA**

** **__Abstract__**:
**TBA (Contact person: Anna Marie Bohmann)

**Tuesday, April 21st**

__Speaker:__** Jonathan
Campbell, Duke University**

__Title____:__** TBA** ** **

__Abstract__**: **TBA (Contact person:
Anna Marie Bohmann)