CUNY Graduate Center

Geometric Measure Theory Reading Seminar

Ambrosio-Kirchheim "Currents in Metric Spaces"

This seminar is for doctoral students who have participated in the

Spring 2011 GMT Reading Seminar covering "Geometric Measure Theory" by Lin and Yang and the

Fall 2011 GMT Reading Seminar covering [AK] Sections 1-5.

Sajjad Lakzian (CUNY) presents to Dan Lee (CUNY), Jorge Basilio (CUNY), Mike Munn (U Missouri), Jim Portegies (NYU), Maria Hempel (ETH Zurich), Christine Breiner (Columbia), Raquel Perales (Stony Brook) and Christopher Loncke (Carnegie Mellon).

In Spring 2012, we will met on Tuesdays 11am-1pm in Room 4214-03. The organizer of this seminar is Professor Sormani. The CUNY Graduate Center is located at 365 Fifth Avenue at 34th Street, diagonally across the street from the Empire State Building, just two blocks from Penn Station (NYC).

This is a continuation of a seminar that has been meeting since Spring 2011. Anyone who has completed a semester course in Geometric Measure Theory may attend. At the moment we are halfway through Ambrosio-Kirchheim. When we start Sormani-Wenger, we welcome new participants.

Spring 2012: (11am -1pm Room 4214-03)

• Tuesday, 1/31: AK 6: w* convergence (Jorge)

• Tuesday, 2/7: AK 6: w* compactness (Jorge)

• Tuesday, 2/14: Finish AK 6: w* Compactness (Jorge) and start AK 7 (Jim)

• Tuesday, 2/21: no seminar, classes follow Monday schedule

• Tuesday, 2/28: AK 7: Metric Space Valued BV Functions (Jim)

• Tuesday, 3/6: AK 8: Closure (Jorge)

• Tuesday, 3/13: AK 8: Boundary Rectifiability (Jorge)

• Tuesday, 3/20: AK 8: Boundary Rectifiability (Jorge)

• Tuesday, 3/27: no seminar, Zhen Lei speaks at NYU at 11:30 am

• Thursday 2/29: AK 9: Intrinsic Representation of Integral Currents (Jim) ?

• Tuesday, 4/3: Jim and Sajjad give Jorge a practice qual on AK 1-5.

• Tuesday, 4/10: Spring Break

• Tuesday, 4/17: AK 9: Representation of Mass (Jim)

• Tuesday, 4/24: AK 9: Representation of Mass (Jim)

• Tuesday, 5/1: Overview of Sormani-Wenger

Summer 2012: (Gromov-Hausdorff and Intrinsic Flat Convergence):

We will merge with the Metric Geometry Reading Seminar: 2-4 pm 4214-03

We will follow Sormani-Wenger's paper [SW] and Sormani's survey article for the first few weeks and volunteers may present papers they are studying.

• Tuesday, 5/15: Survey on Convergence 2.1-2.2, 3.1-3.2 (Sormani)

• & Differential Geometry Seminar at 3pm

• Tuesday, 5/22: Gromov's Embedding Theorem [Gromov] (Susse)

• & Intrinsic Flat Convergence [SW] Section 1(Perales)

• Tuesday, 5/29: Wilmore Conjecture (surprise visit from Neves)

• & Integral Current Spaces [SW] Section 2 (Basilio)

• Tuesday, 6/5: Ambrosio-Kirchheim Compactness Theorem to Intrinsic Flat Convergence [SW] Section 3 (Perales)

• Tuesday, 6/12: Lipschitz and Intrinsic Flat Convergence [SW] Sect 5

• & Smooth Convergence away from Singular Sets [SL] (Lakzian)

• Thursday, 6/14 (special time 4-6pm): Properties [SW] Section 4 (Basilio)

• Tuesday, 6/19: no meeting

• Thursday, 6/21 (special time 3-5pm): Cancellation and Filling Volume (Sormani)

• Tuesday, 6/26: Detailed Examples [SW] Section 6 (Sormani)

• Tuesday, 7/3: Fukaya's Metric Measure Convergence [F](Portegies)

• Thursday, 7/10: (special time 3-5pm) Ricci Flow up to Singularities by Angenent and Knopf [AK] (Lakzian)

• Tuesday, 7/17: (special time 1-3pm) Ricci Flow through Singularities by Angenent, Caputo and Knopf [AK2][ACK] (Lakzian)

• Thursday, 7/19 (special time 1-3pm): Weak Mean Curvature Flow (Breiner)

• Tuesday, 7/24: Ricci Flow through Singularities by Angenent, Caputo and Knopf [ACK] (Lakzian)

• No meetings in August, we will resume in the Fall.