Informal Geometric Analysis Archives for Academic Year 2018

Permanental point processes on tori and real Monge-Ampere equations

When: Tue, September 5, 2017 - 4:00pm
Where: MATH2300
Speaker: Jakob Hultgren (Chalmers University) -

The Gartner-Ellis theorem

When: Tue, September 12, 2017 - 4:00pm
Where: 2300.0
Speaker: Y.A. Rubinstein (UMD) -
Abstract: I will continue the proof of the G\"artner-Ellis theorem from my course (Math 742: Geometric Analysis)

Stability of ALE Ricci-flat manifolds under Ricci-flow

When: Tue, September 26, 2017 - 4:00pm
Where: MATH 2300
Speaker: Klaus Kroencke (Hambrug) -
Abstract: We prove that if an ALE Ricci-flat manifold (M,g) is linearly stable and integrable, it is dynamically stable under Ricci flow, i.e. any Ricci flow starting close to g exists for all time and converges modulo diffeomorphism to an ALE Ricci-flat metric close to g. By adapting Tian's approach in the closed case, we show that integrability holds for ALE Calabi-Yau manifolds which implies that they are dynamically stable. This is joint work with Alix Deruelle.

Complete translating solitons to the mean curvature flow in R^3  with nonnegative mean curvature

When: Tue, October 3, 2017 - 4:00pm
Where: MATH2300
Speaker: Joel Spruck (JHU) -
Abstract: We prove that any complete immersed two sided mean convex translating 3D soliton Sigma for the mean curvature flow is convex. As a corollary it follows that any entire mean convex graphical translating soliton in R^3 is the axisymmetric ''bowl soliton''. We also show that if the mean curvature of Sigma tends to zero at infinity, then Sigma can be represented as an entire graph and so is the bowl soliton. Finally we classify all locally strictly convex graphical translating solitons defined over strip regions (the only other possibility).This is joint work with Ling Xiao.

Scattering theory and variants of the Yamabe problem

When: Tue, October 10, 2017 - 4:00pm
Where: MATH2300
Speaker: Yannick Sire (JHU) -
Abstract: In a seminal paper, Graham and Zworksi developed a new theory for GJMS operators, which are conformally covariant operators of higher order. I will explain this theory, based on scattering theory on Poincare-Einstein manifolds and move on to extend some results on the Yamabe problem to several recent cases in the regular and singular case.


When: Tue, October 17, 2017 - 4:00pm
Where: MATH2300
Speaker: Yanir Rubinstein (UMD) -

Existence and Boundedness of Isoperimetric Regions in Surfaces of Revolution with Density

When: Tue, November 14, 2017 - 4:00pm
Where: MATH2300
Speaker: Alejandro Diaz (UMD) -
Abstract: The isoperimetric problem with a density or weight-
ing seeks to enclose prescribed weighted volume with minimum
weighted perimeter. According to Chambers’ recent proof of the
log-convex density conjecture, for many densities on R^n the answer
is a sphere about the origin. We seek to generalize his results to
some other spaces of revolution or to two different densities for
volume and perimeter. We provide general results on existence
and boundedness and their proofs.

Lagrangian mean curvature flow of Milnor fibres (after Thomas-Yau)

When: Tue, February 6, 2018 - 4:00pm
Where: MATH 2300
Speaker: Matthew Dellatorre (UMD) -

Mean curvature flow and Milnor fibers continued

When: Thu, March 8, 2018 - 4:00pm
Where: math 2300
Speaker: Matt Dellatorre (umd) -

Log-concavity of the volume of positive currents

When: Tue, March 13, 2018 - 4:00pm
Where: Kirwan Hall 2300
Speaker: Eleonora Di Nezza (IHES) -
Abstract: In this talk we present a proof of the log-concavity property of total masses of positive currents on a given compact Kähler manifold, that was conjectured by Boucksom, Eyssidieux, Guedj and Zeriahi. The proof relies on the resolution of complex Monge-Ampère equations with prescribed singularities. This is based on a joint work with Tamas Darvas and Chinh Lu.

Structure of four dimensional shrinking Ricci solitons

When: Tue, March 27, 2018 - 4:00pm
Where: Math 2300
Speaker: Ovidiu Munteanu (University of Connecticut) -
Abstract: I will describe recent results about the asymptotic geometry of complete four dimensional shrinking Ricci solitons. These are self similar solutions to the Ricci flow and appear in blowups of singularities of the flow

Relative Chow stability of extremal Kahler metrics

When: Tue, April 3, 2018 - 4:00pm
Where: Math 2300
Speaker: Reza Seyyedali (Howard University) -
Abstract: In 2001, Donaldson proved that any constant scalar curvature polarized manifold is asymptotically Chow stable provided that the group of hamiltonian athromorphisms is discrete. In this talk, we discuss some generalization of Donaldson's result to extremal metrics.

Apriori estimates for scalar curvature type equations on compact Kahler manifolds

When: Tue, May 1, 2018 - 4:00pm
Where: Math 2300
Speaker: Jingrui Cheng (Wisconsin) -
Abstract: We develop apriori estimates for scalar curvature type equations on compact Kahler manifolds. As an application, we show that K-energy being proper with respect to L^1 geodesic distance implies the existence of constant scalar curvature Kahler metrics. This is joint work with Xiuxiong Chen.