Geometry and Topology Seminar

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The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Alexandra Kjuchukova or Lu Wang .


Fall 2016

date speaker title host(s)
September 9 Bing Wang (UW Madison) "The extension problem of the mean curvature flow" (Local)
September 16 Ben Weinkove (Northwestern University) "Gauduchon metrics with prescribed volume form" Lu Wang
September 23 Jiyuan Han (UW Madison) "Deformation theory of scalar-flat ALE Kahler surfaces" (Local)
September 30
October 7 Yu Li (UW Madison) "Ricci flow on asymptotically Euclidean manifolds" (Local)
October 14 Sean Howe (University of Chicago) "Representation stability and hypersurface sections" Melanie Matchett Wood
October 21 Nan Li (CUNY) "TBA" Lu Wang
October 28 Ronan Conlon "TBA" Bing Wang
November 4 Jonathan Zhu (Harvard University) "TBA" Lu Wang
November 7 Gaven Martin (University of New Zealand) "TBA" Simon Marshall
November 11
November 18 Caglar Uyanik (Illinois) "TBA" Kent
Thanksgiving Recess
December 2 Peyman Morteza (UW Madison) "TBA" (Local)
December 9
December 16

Fall Abstracts

Ronan Conlon


Jiyuan Han

Deformation theory of scalar-flat ALE Kahler surfaces

We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.

Sean Howe

Representation stability and hypersurface sections

We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}!

Nan Li


Yu Li

In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature.

Gaven Marin


Peyman Morteza


Caglar Uyanik


Bing Wang

The extension problem of the mean curvature flow

We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3. A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded. This is a joint work with Haozhao Li.

Ben Weinkove

Gauduchon metrics with prescribed volume form

Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.

Jonathan Zhu


Archive of past Geometry seminars

2015-2016: Geometry_and_Topology_Seminar_2015-2016

2014-2015: Geometry_and_Topology_Seminar_2014-2015

2013-2014: Geometry_and_Topology_Seminar_2013-2014

2012-2013: Geometry_and_Topology_Seminar_2012-2013

2011-2012: Geometry_and_Topology_Seminar_2011-2012

2010: Fall-2010-Geometry-Topology