Surveys and Chapters

Published Surveys and Chapters 

by Professor Sormani 

See also google scholar, my research papers page, and my preprints page. Only survey articles, chapters, conference proceedings, and undergraduate research are below.

Survey Articles and Chapters:

Chen-Yun Lin and Christina Sormani, ``From Varadhan's limit to eigenmaps: a guide to the geometric analysis behind manifold learning.'' Mat. Contemp. 57 (2023), 32–115. (arxiv) 

C Sormani "Conjectures on Convergence and Scalar Curvature" Chapter for Perspectives in Scalar Curvature edited by Gromov and Lawson, World Scientific (2023) (arxiv) (order here) (NSF DMS 1612049) 

C Sormani ``Compactness Theorems for Sequences of Riemannian Manifolds'' AMS Sampler, AMS Notices, April 2019. (reprint)

C Sormani, ``Scalar Curvature and Intrinsic Flat Convergence"  (arxiv preprint) (reprint) Chapter 9 in Measure Theory in Non-Smooth Spaces, edited by Nicola Gigli, De Gruyter Press, (2017) pp 288-338. (DMS 1309360)

Z. Shen and C. Sormani, "The Topology of Open Manifolds of Nonnegative Ricci Curvature"   Communications in Mathematical Analysis, Conf. 01 (2008), pp 11-19.  (arxiv preprint June 2006) (reprint)

C. Sormani, "How Riemannian Manifolds Converge: a Survey"   Metric and Differential Geometry: The Jeff Cheeger Anniversary Volume edited by X. Rong and X. Dai, Progress in Mathematics Vol 297, (2012) 27pp. (arxiv preprint June 2010)

Published Undergraduate Research

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)

Conference Reports and Proceedings:

C Sormani "Oberwolfach Workshop Report: Analysis, Geometry and Topology of Positive Scalar Curvature Metrcs: Limits of sequences of manifolds with nonnegative scalar curvature and other hypotheses" (with Wenchaun Tian and Changliang Wang) Oberwolfach 9/24 (2024) (arxiv)

M Gromov and C Sormani “IAS Emerging Topics Report on Scalar Curvature and Convergence” IAS, Fall 2018 (reprint)

C Sormani “Oberwolfach Report: 2018 Spacetime Intrinsic Flat Convergence” (arxiv) (DMS 1309360)

C Sormani "Oberwolfach Report: 37/2012" by C. Sormani,  Mathematical Aspects of General Relativity Workshop, Organized by Dafermos, Isenberg and Ringstrom copy in pdf and link to full workshop.

C Sormani "Oberwolfach Report: 38/2011" by C.  Sormani,  Partial Differential Equations Workshop  Organized by Ambrosio, Chang, Schatzle and Weiss copy in pdf and link to full workshop.

C Sormani "The Stability of the Spacelike Friedmann Model" by C. Sormani  Proceedings of the XXVI International Collquium on Group Theoretical Methods in Physics, Edited by J.L. Birman, S. Catto, and B. Nicolescu, (2009), pp 495-500. ISBN 978-0-9549846-8-7, (preprint.pdf) (reprint)