Geometry Seminar

                                                                                                                      Vanderbilt University
                                                                                                                                   Fall 2013

   Organizers:  Gennadi Kasparov, Rares Rasdeaconu, Ioana Suvaina

   Mondays, 4:10-5:00pm in SC 1312 (unless otherwise noted)

   Related seminars also announced.

  Thursday, September 26th

Speaker: Hang Wang, University of Adelaide, Australia

Title: Localized index and L^2-Lefschetz fixed point formula

Abstract In this talk , we introduce a class of localized indices for the Dirac type operators on a complete Riemannian manifold, where a discrete group acts properly,
co-compactly and isometrically. These localized indices, generalizing the $L^2$-index of Atiyah, are obtained by taking certain traces of the higher index for the Dirac type
operators along conjugacy classes of the discrete group. Applying the local index technique, we also obtain an $L^2$-version of the Lefschetz fixed point formula for
orbifolds. These cohomological formulae for the localized indices give rise to a class of refined topological invariants for the quotient orbifold. The talk is related to the joint
work with Bai-Ling Wang (ArXiv 1307.2088).

              Monday, October 7th, (will start at 4:05pm)

                Speaker:  Caner Koca, Vanderbilt University

                Title:  Bach-Maxwell Equations and Extremal Kahler Metrics

    Abstract:  The Bach-Maxwell Equations on a 4-dimensional compact oriented manifold can be thought of as a conformally invariant version of the classical
    Einstein-Maxwell Equations in general relativity. Riemannian metrics which solve the BM equations have interesting geometric properties. In this talk,
     I will introduce these equations and give several variational characterizations. I will also show that extremal Kahler metrics are among the solutions and
    discuss their role in this variational setting.

              Monday, October 28th

                 Speaker:  Laurentiu Maxim, University of Wisconsin-Madison

                 Title:  Characteristic classes of Hilbert schemes of points via symmetric products

Abstract: I will explain a formula for the generating series of (the push-forward under the Hilbert-Chow morphism of) homology characteristic
                 classes of the Hilbert schemes of points for a smooth quasi-projective variety of arbitrary pure dimension. The result is based on a geometric construction
                 of a motivic exponentiation generalizing the notion of motivic power structure, as well as a formula for the generating series of homology characteristic
                 classes of symmetric products. This is joint work with Cappell, Schuermann, Ohmoto and Yokura.


Monday, November 18th

Speaker:  Kamran Reihani, Vanderbilt University

Title:  In search for invariant structures in analysis, topology and geometry

Abstract: The talk reports on a frequent appearance of a strategy that seems to be useful when some sort of "type-III" phenomena prevent the
existence of certain invariant structures for dynamical systems in analysis, topology and geometry. The approach is called "reduction to type
II", and usually involves some extension of the dynamical system in such a natural way that the resulting system is large enough to carry the desired
invariant structure. Our examples will demonstrate that - in search for such extensions - one naturally needs to involve (or to develop) some very
important techniques relevant to the context.


Old Seminar Web-Pages: Fall 2009, Fall 2010, Spring 2011, Fall 2011, Spring 2012, Fall 2012, Spring 2013