Informal Geometric Analysis Seminar

University of Maryland

PREVIOUS YEARS: 2012-2013, 2013-2014, 2014-2015, 2015-2016, 2016-2017.

- September 5

Jakob Hultgren (Chalmers)

*Title: Permanental point processes on tori and real Monge-Ampere equations* - September 26

Klaus Kroencke (Hamburg)

*Title: Stability of ALE Ricci-flat manifolds under Ricci-flow*

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. - October 3

Joel Spruck (JHU)

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

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. - October 10

Yannick Sire (JHU)

*Title: Scattering theory and variants of the Yamabe problem*

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. - October 17

Yanir Rubinstein (UMD)

*Title: TBA* - October 24

Yanir Rubinstein (UMD)

*Title: TBA* - November 14

Alejandro Diaz (UMD)

*Title: Existence and Boundedness of Isoperimetric Regions in Surfaces of Revolution with Density*

Abstract: The isoperimetric problem with a density or weighting 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. - February 6

Matthew Dellatorre (UMD)

*Title: Lagrangian mean curvature flow of Milnor fibres (after Thomas-Yau)* - February 12

Hopkins-Maryland Complex Geometry Seminar talk - February 20

Matthew Dellatorre (UMD)

*Title: Lagrangian mean curvature flow of Milnor fibres (after Thomas-Yau) continued* - February 27

(Tamas is away) - March 6

Matthew Dellatorre (UMD)

*Title: Lagrangian mean curvature flow of Milnor fibres (after Thomas-Yau) continued* - March 13

Eleonora Di Nezza (IHES)

*Title: Log-concavity of the volume of positive currents*

Abstract: In this talk we present a proof of the log-concavity property of total masses of positive currents on a given compact Kahler manifold, that was conjectured by Boucksom, Eyssidieux, Guedj and Zeriahi. The proof relies on the resolution of complex Monge-Ampere equations with prescribed singularities. This is based on a joint work with Tamas Darvas and Chinh Lu. - March 20

Spring Break - March 27

Ovidiu Munteanu (Uconn)

*Title: Structure of four dimensional shrinking Ricci solitons.*

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. - April 3

Reza Seyyedali (Howard)

*Title: Relative Chow stability of extremal Kahler metrics*

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. - April 10

Hopkins-Maryland Complex Geometry Seminar talk - April 24

Hopkins-Maryland Complex Geometry Seminar talk - May 1

Jingrui Cheng (Wisconsin)

*Title: Apriori estimates for scalar curvature type equations on compact Kahler manifolds*

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. - May 8

Hopkins-Maryland Complex Geometry Seminar talk

Driving and parking directions to UMD: Park in Paint Branch Drive Visitor Lot (highlighted in yellow in the lower right corner of the second map in the previous link), or in Regents Drive Garage (highlighted in the upper right corner). If you arrive after 4pm you do not need to pay: see the instructions in the previous link.