Geometry Seminar

                                                                                                                      Vanderbilt University
                                                                                                                                Spring 2020

   Organizers: Anna Marie Bohmann, Rares Rasdeaconu and Ioana Suvaina

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

                  Tuesday, January 28th

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)

                  March 3rd -- no meeting (Spring Break)

                  Shanks Workshop: "Real Enumerative Geometry and Beyond", March 6-7, 2020, Vanderbilt University

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)



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