Organizers: Anna Marie Bohmann, Rares Rasdeaconu, Ioana Suvaina
Speaker:
Rares Rasdeaconu (Vanderbilt University)
Title: The loss of maximality in Hilbert squares
Abstract: In an ongoing joint
work with V. Kharlamov, we investigate the maximality of
the Hilbert square of maximal
real varieties. We found that starting from dimension two
many of deformation classes of algebraic varieties do not
contain
any real variety whose Hilbert square is maximal. For
example, the K3-surfaces have never a maximal Hilbert
square.
The talk will be an introduction to the maximality of real
algebraic manifolds and Hilbert squares, outlining the
current
state of affairs and open problems.
Speaker:
Qi Yao (Stony Brook University)
Title: Asymptotic behaviors of solutions to homogeneous complex Monge-Ampere equations on ALE K\"ahler manifolds
Abstract: Initiated by Mabuchi,
Semmes, Donaldson, homogeneous complex Monge-Ampere (HCMA)
equations become
a central topic in understanding the uniqueness and
existence of canonical metrics in K\"ahler classes. Under
the setting of
asymptotically locally Euclidean (ALE) K\"ahler manifolds,
one of the main difficulties is the asymptotic behaviors
of solutions
to HCMA equations. In this talk, I will give an
introduction to canonical metric problems under the
setting of ALE K\"ahler
manifolds and discuss the recent progress in studying
asymptotic behaviors of solutions to HCMA equations. It is
still an
ongoing project.
(Contact person: Ioana Suvaina).
Speaker:
Chloe Lewis (University of Wisconsin-Eau Claire)
Title: Tools for computing Real topological Hochschild homology
Abstract: In the trace methods approach to
studying algebraic K-theory, we work with more
computationally accessible invariants
of rings and their topological analogues. One such
invariant is topological Hochschild homology (THH),
which has proven quite
computationally tractable, in part due to the existence
of the Bokstedt spectral sequence and the Hopf algebra
structure of THH.
In this talk, we'll investigate an equivariant
generalization of THH called Real topological Hochschild
homology (THR) which encodes
the C_2-action of involution. We'll develop equivariant
analogues of these computational tools by constructing a
Real Bokstedt spectral
sequence and will give a description of the algebraic
structures that are present in THR.
(Contact person: Anna Marie Bohmann and
Hannah Housden).
Speaker:
Bar Roytman (University of Michigan)
Title:
Geometry of Operads in Equivariant Homotopical Algebra