GH-Convergence-of-Metric-Spaces-2019

Winter Semester 2019

The CUNY Graduate Center is on 34th Street and Fifth Avenue (365 Fifth Avenue), and is an easy walk from the LIRR Penn Station and numerous subway stops. Bring id to show and sign in with the guards on arrival each day.

References:

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

[M] Marsden's Elementary Classical Analysis

Undergraduate students and masters students (who already have completed a course with metric spaces) will learn about pulled string spaces and conduct original research on the geometry of periodic pulled string spaces and their Gromov-Hausdorff limits at infinity. The completed research will be original and publishable.

Contact Professor Sormani if you would like to participate. (sormanic at gmail)

Week 1: Pulled string metric spaces, smocking spaces,

Tuesday Jan 8: all meet at 10am-4pm at CUNYGC in 3207

Morning: Teams 1 (exploring balls in the spaces)

Afternoon: Teams 2 (distances in the spaces)

Wedensday Jan 9: Prof Sormani emailed everyone notes

Thursday Jan 10: Prof Sormani will be at CUNYGC 2-7pm to answer questions (4th floor math lounge)

Friday Jan 11: Teams emailed their work to Professor Sormani

Monday Jan 14: 3D Teams will meet 10am - 5pm (4th floor math lounge or 8th floor cafeteria)

Week 2: Gromov-Hausdorff convergence of metric spaces, tangent cones at infinity

Tuesday Jan 15: 10am-4pm at CUNYGC on 34th and Fifth Ave in 3207

Morning: Rescaling Metric Spaces, Teams 1, 2 and 3D report on their progress.

Afternoon: Teams R (compute rescaled limits, Gromov-Hausdorff Convergence)

Wednesday: (in 8th floor cafeteria) Demetre will be available for questions

Thursday: 10-12: (in 8th floor cafeteria) Teams 1; 1-3pm: Teams 2 ; 3-5 pm: Teams R

Friday: flexible hours

Week3: More about GH convergence, Writing up our Results (in a publishable format using latex)

Monday Jan 21: Martin Luther King Day GC is closed

Tuesday Jan 22: 10am-4pm at CUNYGC on 34th and Fifth Ave in 3207

Wednesday: Teams 3DR

Thursday: Intrinsic Flat Convergence

Friday: Final Day to finish

Research Team:

David Afrifa (Lehman)

Victoria Antonetti (Lehman)

Moshe Dinowitz (Stony Brook)

Hindy Drillick (Stony Brook)

Maziar Farahzad (Stony Brook)

Shanell George (Lehman)

Aleah Lydeatte Hepburn (Lehman)

Leslie Trang Huynh (Lehman)

Emilio Minichiello (Queens)

Julinda Pillati Mujo (Lehman)

Srivishnupreeth Rendla (Stony Brook)

Ajmain Yamin (Stony Brook)

Outcomes:

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

Short Talk for students to present alone as needed.

Our published paper:

C Sormani, D Kazaras, and students: David Afrifa, Victoria Antonetti, Moshe Dinowitz, Hindy Drillick, Maziar Farahzad, Shanell George, Aleah Lydeatte Hepburn, Leslie Trang Huynh, Emilio Minichiello, Julinda Mujo Pillati, Srivishnupreeth Rendla, Ajmain Yamin “Smocked Metric Spaces and their Tangent Cones'' Missouri Journal of Mathematics, Vol. 33, No. 1 (2021) 27-98. (reprint) (arxiv) (NSF DMS 1612049) (SCGP) (CUNYGC)

add photos from googledoc

Two additional papers were completed in subsequent years by members of the team that continued to work in 2020-2021.