GH and SWIF Convergence of Smocked Metric Spaces 2019

Gromov-Haursdorff and Sormani Wenger Intrinsic Flat Convergence of Smocked Metric Spaces

Independent Research with Professor Sormani and Dr. Demetre Kazaras in Spring 2019

References:

[BBI] Burago-Burago-Ivanov's A Course in Metric Geometry

[S-CoM] Spivak Calculus on Manifolds

[M-GMT] Morgan Geometric Measure Theory

[AK] Ambrosio-Kirchheim Currents on Metric Spaces

[SW] Sormani-Wenger Intrinsic Flat Convergence

Continuing from the January 2019 Course/Research Project on GH Convergence of Smocked Metric Spaces we now study some Geometric Measure Theory and the GH and SWIF Convergence of Smocked Metric Spaces writing a second paper with a smaller team of students.

Required Initial Meetings:

Th Jan 24 10:00-6:00 pm at CUNY GC:

Splitting of the = and H teams to this new project

Th Jan 31 2:30-4:00 pm at Stony Brook:

Basic idea of Intrinsic Flat Convergence

Fri Feb 8 10:00-5:00 pm at CUNY GC: Introduction to Geometric Measure Theory

Integer rectifiable currents, integral currents, integral current spaces, intrinsic flat convergence

assignment of different projects to work on towards a joint paper

Prof Sormani is available for questions:

Th Feb 14 time 6pm at Lehman

Fri Feb 15 time 4pm at Stony Brook

Th Feb 21 time 6pm at Lehman

Fri Feb 22 time 4pm at Stony Brook

Mon Mar 25 at Stony Brook 4-5 pm

Tu Mar 26 at CUNYGC 3:30-5pm

Wed Mar 27 at Stony Brook 9-12 am

Fri Mar 29 at CUNYGC (cancelled)

Mon April 1 at Stony Brook 2:30-4:30 pm

Th April 4 at CUNYGC 4:30-5:30 pm

Mon April 8 at Stony Brook 1-3 pm

Wed April 17 at GC 5:30-6:30 pm

Th April 18 at Stony Brook 1-3 pm

Mon April 22 at Stony Brook 3-5 pm

Fri April 26 at Stony Brook 1-2 pm

Mon Apr 29-May 3 no meetings

Mon May 6 1-3 pm at Stony Brook

Wed May 8 1-3 pm at Stony Brook

May 9 at Lehman 5-7 pm

May 13-15 at Stony Brook all day

May 17 at Lehman 3-5 pm

May 20 at Stony Brook 3-5 pm

May 24 at Lehman 3-5 pm (cancelled)

Work will continue in January 2020.

Research Team:

Victoria Antonetti (Lehman)

Moshe Dinowitz (Stony Brook)

Hindy Drillick (Stony Brook)

Maziar Farahzad (Stony Brook)

Leslie Trang Huynh (Lehman)

Julinda Pillati Mujo (Lehman)

Ajmain Yamin (Stony Brook)

Address by Prof. Sormani at the MAA Metropolitan New York Annual Meeting 2019.

Talk by the students at the Lehigh Geometry and Topology Conference in 2019

Talk by the students at the NYC Math Alliance in 2019

Papers:

Ajmain, Antonetti, Farahzad “The checkered smocked space and its tangent cone” version one is on the arxiv

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