Graduate Student Geometric Analysis Seminar

Spring 2016


We meet in Math 520 every Monday at 4:30.



Feb. 15

Karsten Gimre

Morse theory for the distance function
Ref: K. Grove & K. Shiohama and M. Gromov

Feb. 22

Karsten Gimre

Pinching constants for hyperbolic manifolds
Ref: M. Gromov & W. Thurston

Feb. 29

Karsten Gimre

Harmonic maps and the topology of manifolds with nonnegative Ricci curvature
Ref: S.-T. Yau and R. Schoen & S.-T. Yau

Mar. 7

Pei-Ken Hung

Almost-splitting theorem
Ref: J. Cheeger & T. Colding

Mar. 14

Pei-Ken Hung

Almost-splitting theorem II
Ref: J. Cheeger & T. Colding

Mar. 21

Spring Break

No Talk

Mar. 28

Pei-Ken Hung

Ricci curvature and volume convergence
Ref: T. Colding

Nov. 9

TBD

TBD

Nov. 16

TBD

TBD

Nov. 23

TBD

TBD

Nov. 30

TBD

TBD

Dec. 7

TBD




Graduate Student Geometric Analysis Seminar

Fall 2015


We meet in Math 520 every Monday at 4:30.



Sep. 21

Karsten Gimre

The Plateau problem

Sep. 28

Pei-Ken Hung

Compensated compactness

Oct. 5

Cancelled

Cancelled

Oct. 12

Pei-Ken Hung

Compensated compactness

Oct. 19

King Lee

Scalar curvature and stability of toric varieties
Ref: S. Donaldson

Oct. 26

Cancelled

Cancelled

Nov. 2

No Seminar

University holiday?

Nov. 9

Zhijie Huang

Fully nonlinear convex elliptic equations
Ref: L. Evans

Nov. 16

Xuan Wu

Fully nonlinear elliptic equations with convex level sets
Ref: L. Caffarelli and Y. Yuan

Nov. 23

Sebastien Picard

ABP estimate
Ref: Q. Han and F. Lin

Nov. 30

Kyeongsu Choi

Pogorelov computation on submanifold

Dec. 7

Kyeongsu Choi




Graduate Student Geometric Analysis Seminar

Spring 2015


We meet in Math 520 every Monday at 4:30.



Feb. 2

Karsten Gimre

Uniform decay estimates and the Lorentz invariance of the classical wave equation
Ref: S. Klainerman

Feb. 9

Cancelled

Cancelled

Feb. 16

Karsten Gimre

The null condition and global existence to nonlinear wave equations
Ref: S. Klainerman

Feb. 23

Cancelled

Cancelled

Mar. 2

Karsten Gimre

Mean curvature flow of surfaces in Einstein four-manifolds
Ref: M.-T. Wang

Mar. 9

Karsten Gimre

Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension
Ref: M.-T. Wang and M.-T. Wang

Mar. 16

Spring Break

No Seminar

Mar. 23

Pei-Ken Hung

Mean curvature flows of Lagrangian submanifolds with convex potentials
Ref: K. Smoczyk & M.-T. Wang and M.-T. Wang

Mar. 30

Cancelled

Cancelled

Apr. 6

Karsten Gimre

Bounding scalar curvature and diameter along the Kahler Ricci flow
Ref: N. Sesum & G. Tian

Apr. 13

Zhijie Huang

On stability and the convergence of the Kahler Ricci flow
Ref: D.H. Phong & J. Sturm

Apr. 20

Dan Rubin

The Kahler Ricci flow with positive bisectional curvature
Ref: D.H. Phong, J. Song, J. Sturm & B. Weinkove

Apr. 27

Connor Mooney

The minimal surface system

I will review existence and gradient estimates for codimension one minimal graphs, explain why they fail in the higher codimension case, and discuss a sufficient condition to extend these results.
Ref: B. Lawson & R. Osserman, M.-T. Wang, and M.-T. Wang

May 4

Donovan McFeron

The Kahler Ricci flow and the dbar operator on vector fields
Ref: D.H. Phong, J. Song, J. Sturm & B. Weinkove

May 11

Kyeongsu Choi

The uniqueness of complete convex solutions to the mean curvature flow
Ref: K. Ecker & G. Huisken

May 18

No Seminar

No Seminar

May 25

Karsten Gimre

Spacetime estimates for null forms and the local existence theorem
Ref: S. Klainerman & M. Machedon



Graduate Student Geometric Analysis Seminar

Fall 2014


We meet in Math 622 every Monday at 4:30.



Sep. 29

Karsten Gimre

Monotonicity formula and reverse Poincare inequality

Oct. 6

Karsten Gimre

?-regularity and compactness

Oct. 13

No Seminar

No Seminar

Oct. 20

Karsten Gimre

Nonuniqueness of tangent maps

Oct. 27

Pei-Ken Hung

On the structure of manifolds with positive scalar curvature

Nov. 3

No Seminar

No Seminar

Nov. 10

Karsten Gimre

Lyapunov-Schmidt reduction

Nov. 17

No Seminar

No Seminar

Nov. 24

Karsten Gimre

Lojasiewicz-Simon inequality

Dec. 1

Pei-Ken Hung

On the singular set of stationary harmonic maps



Graduate Student Geometric Analysis Seminar

Spring 2014


We meet in Math 528 every Tuesday at 4:30.



Jan. 21

Karsten Gimre

Curvature evolution equations and Shi's estimates

Jan. 28

Karsten Gimre

Hamilton's maximum principle and pinching set criterion for convergence of Ricci flow

Feb. 4

Alex Waldron

4-manifolds with positive curvature operator

Feb. 11

Zhijie Huang

Ricci flow on the 2-sphere

Feb. 18

Karsten Gimre

Perelman's F- and W- functionals, and first no local collapsing result

Feb. 25

Karsten Gimre

Comparison geometry for Perelman's reduced length and monotonicity of the reduced volume

Mar. 4

Karsten Gimre

Second no local collapsing result, Hamilton's Harnack inequality, and Hamilton's compactness theorem

Mar. 11

No Seminar

No Seminar

Mar. 18

No Seminar

No Seminar

Mar. 25

No Seminar

No Seminar

Apr. 1

Kyeongsu Choi

Asymptotic behavior of ?-solutions

Apr. 8

Kyeongsu Choi

Two-dimensional ?-solutions, Perelman's curvature estimates and classification of three-dimensional shrinking solitons

Apr. 15

Kyeongsu Choi

Universal noncollapsing of ?-solutions, and elliptic estimates for their scalar curvature

Apr. 22

Kyeongsu Choi

Compactness of the space of ?-solutions and the structure of ?-necks

May 14

Karsten Gimre

Finite extinction time for Ricci flow of prime nonaspherical 3-manifolds

May 16

Alex Waldron

Canonical neighborhoods theorem