Fall 2016

** Organizers: Gennadi Kasparov, Ioana
Suvaina, ****Rares Rasdeaconu**

** Fridays,
3:10-4:00pm in SC 1310 (unless otherwise noted) **

Calabi-Yau manifolds. The focus will be on four dimensional symplectic CYs, which resemble the Kahler

CY surfaces topologically. In particular, their Betti numbers are bounded. In contrast, in higher dimension,

they are known to be much more flexible via both topological and differential geometric constructions. For instance,

any finitely presented group can be realized as the fundamental group of a six dimensional symplectic CY.

Tea at 3:30 pm in SC 1425. (Contact Person: Ioana Suvaina)

**Friday, September 23rd**

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

__Title:__ **Waldhausen's Algebraic
K-Theory**

__Abstract__**: **In preparation for my
talk next week, I'll introduce algebraic K-theory. In
particular, I'll introduce

a formulation due to Waldhausen, which is the most general
version of the algebraic K-theory machine.

I'll discuss some examples, and discuss some places of
interest where this machine fails to work (which I

will discuss in the next talk). The talk will require no
previous knowledge of algebraic K-theory.

**Friday, September 30th**

__Speaker:__** Ioana
Suvaina, Vanderbilt University**

__Title:__ **Seiberg-Witten Theory and
Geometry of 4-Manifolds**

__Abstract__**: **The Seiberg-Witten
theory provides a smooth invariant, which can be used to
distinguish homeomorphic,

non-diffeomorphic, smooth structures. It also has a deep
impact on the Riemannian properties of 4-manifolds.

We will discuss how obstructions to the existence of Einstein
metrics arise, and how one can compute the Yamabe

invariant for Kahler surfaces and some symplectic 4-manifolds.

**Friday, October 7th**

__Speaker:__** Ioana
Suvaina, Vanderbilt University**

__Title:__ **ALE Kahler manifolds**

__Abstract__**: **The study of
asymptotically locally Euclidean Kahler manifolds had a
tremendous development in the last

few years. This talk presents a survey of the main results and
the open problems in this area. When the manifolds

support an ALE Ricci flat Kahler metric the complex surfaces
and their metric structures are classified. The remaining

case to be studied is that of ALE scalar flat Kahler
manifolds. In this direction, we have a description of the
underlying

complex manifold. It is exhibited as a resolution of a
deformation of an isolated quotient singularity. As a
consequence,

there exists only finitely many diffeomorphism types of
minimal ALE Kahler surfaces.

**Friday, October 21st**

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

__Title:__ **The K-Theory of Varieties**

__Abstract__**: **The Grothendieck ring
of varieties is a fundamental object of study for algebraic
geometers. As with all

Grothendieck rings, one may hope that it arises as π_0 of a
K-theory spectrum, K(Var_k). Using her formalism

of assemblers, Zahkarevich showed that this is in fact that
case. I'll present an alternate construction of the spectrum

that allows us to quickly see various structures on K(Var_k)
and produce character maps out of K(Var_k). I'll end

with a conjecture about K(Var_k) and iterated K-theory.

**Friday, October 28th**

__Speaker:__** Grace Work,
Vanderbilt University**

__Title:__ **Translation Surfaces**

__Abstract__**: **Translation surfaces
arise naturally out of the study of the classical dynamical
system of idealized

billiards in a rational polygon. We will provide several
definitions and examples and explore dynamical properties

of flows on the moduli spaces of these surfaces.

Old Seminar Web-Pages: Fall 2009, Fall
2010