Advised by Professor Sormani:
Doctorate, CUNY Graduate Center, 2008
Thesis: "Volume growth and the topology of manifolds of nonnegative Ricci curvature"
Mike asked to study with me before coming to the CUNY Graduate Center. He began to work with me even before taking all his written qualifying exams. His oral qualifying exam was on Nonnegative Ricci Curvature focusing on the Abresch-Gromoll Excess Theorem and the Bishop-Gromov Volume Comparison Theorem. His thesis was based strongly on these theorems and Perelman's work. As a student, Mike also had an interest in Gromov-Hausdorff convergence, metric measure convergence and the mass transport approach to nonnegative Ricci curvature. In addition to the courses he took at CUNY, he attended classes taught by Professors Cheeger and Masmoudi at NYU. His papers are available on the ArXiV. When Mike graduated from CUNY he was offered an NSF International Postdoctoral Fellowship working with Peter Topping at Warwick University. He was tenure track at U Missouri but chose to return to NYC to work as a clinical instructor at NYU. He now works at Google NY and has recently published a book, Machine Learning Design Patterns, with two fellow google engineers.
Pedro Solórzano (Pedro Antonio Ricardo Martín Solórzano Mancera)
Doctorate, SUNY Stony Brook, May 2011
Thesis: ``Group Norms and their Degeneration in the Study of Parallelism"
Pedro began working with me and Blaine Lawson when his original doctoral advisor, Detlef Gromoll, passed away suddenly in 2008. Pedro's second examination was on Riemannian Submersions, the Cheeger-Gromoll Soul Theorem and Group Actions which he passed "with distinction" a few weeks after starting to work with us. Pedro's doctoral thesis concerns tangent bundles, holonomy groups and Gromov-Hausdorff convergence. He completed his first paper in August 2010 and his second paper in Spring 2011. His papers are available on the ArXiV. Pedro's first position was a visiting assistant professorship at UC Riverside working with Fred Wilhelm. His second postdoc was at Universidade Federal de Santa Catarina in Brazil. He is currently a CONACYT Fellow at UNAM in Oaxaca.
Doctorate, CUNY Graduate Center, May 2013
Thesis: "Smooth Convergence away from Singular Sets and Continuity of Ricci Flow"
Sajjad completed a masters at Tehran Polytechnic University before contacting me and coming to CUNY. In addition to his classes at CUNY, he has taken courses at Columbia with Hamilton and at Courant with Cheeger, Lin and Kleiner. Sajjad first completed a joint paper with me on smooth convergence away from singular sets was accepted for publication in Communications in Analysis and Geometry in 2012. He has built upon this work in a first solo preprint and has applied it to Ricci flow through singularities in another preprint. These two preprints were completed before he applied for jobs and were combined together to form his doctoral thesis. All his preprints are available on the ArXiV. Sajjad's first postdoc was at MSRI in the Optimal Transport Program. His second postdoc was with Sturm at the Hausdorff Center in Bonn. He was then a postdoc at Fordham University working with Breiner and is now a tenure track doctoral faculty member at Isfahan University of Technology. He has won the Kazemi Ashtiani Prize (an early career grant awarded in Iran to selected academics) and the Abu Reyhan Biruni’s Award in Mathematics (for distinguished young researchers by The Academy of Sciences of Iran).
Raquel Perales (Raquel del Carmen Perales Aguilar)
Doctorate, SUNY Stony Brook, May 2015
Thesis: "Convergence of Manifolds and Metric Spaces with Boundary"
Raquel was a doctoral student at SUNY Stony Brook who completed her oral qualifying exam on Riemannian Geometry and Geometric Measure Theory in the Spring of 2012. She has studied Partial Differential Equations with Marcus Khuri, Geometric Measure Theory with Ranaan Schul. and Advanced Riemannian Geometry with Blaine Lawson. We completed a joint preprint in early 2013 on the convergence of Riemannian manifolds with boundary. She has also written a solicited survey article on the convergence of Riemannian manifolds with boundary in Spring 2013. In the summer of 2013 she worked as my visiting research student at CUNY and at MSRI completing her first solo preprint which will form part of her doctoral dissertation along with a second solo preprint appearing soon. She has also completed a joint paper with Nan Li. All her preprints are available on the ArXiV. She has a video on Geometric Analysis in Spanish with over 5000 viewers. Raquel's first postdocs were at UNAM in Mexico City and MSRI in the Differential Geometry Program. She served as a CONACYT Fellow at UNAM in Oaxaca while working with collaborators like Guofang Wei, Xianzhe Dai, and Andrea Mondino. She has won an IMSA Young Mathematician Award for a Latin American woman mathematician. She is now a tenure track doctoral faculty member at CIMAT.
George Basilio (Jorge Eduardo Basilio)
Doctorate, CUNY Graduate Center, May 2017
Thesis "Manifold Convergence: Sewing Sequences of Riemannian Manifolds with Positive or Nonnegative Scalar Curvature"
Jorge completed his dissertation with Professor Jozef Dodziuk and I at the CUNY Graduate Center. He had completed his oral qualifying exam in Geometric Measure Theory and was an active participant in my reading seminar the summer before I hired him as my research assistant to work on a project related to intrinsic flat convergence. In Spring 2014, he began his doctoral work with me and then also with Professor Dodziuk, before taking time off to work full time at Sarah Lawrence College. In 2017 he completed a joint paper with us constructing sequences of manifolds with positive scalar curvature. After completing his doctorate he has written additional work related to his dissertation work with me, as well as a paper with Demetre Kazaras and I that is in a new direction. All his preprints are available on the ArXiV. Jorge has worked at Sarah Lawrence College, at Pitzer College, and at Pasadena City College.
Other Doctoral Students who have conducted some research with Professor Sormani:
Doctorate, Courant Institute with Prof Fanghua Lin, May 2014
Jim was an active member of the CUNY Metric Geometry Reading Seminar and is an expert on Ambrosio-Kirchheim's notion of currents on metric spaces as well as intrinsic flat convergence. He has completed two papers on the semicontinuity of eigenvalues of the Laplacan of submanifolds converging in the flat sense and of Riemannian manifolds converging in the intrinsic flat sense respectively. He conducted dissertation research with Fanghua Lin on embeddings via eigenfunctions. His papers are available on the ArXiV. Jim's first postdoc was with Jost at Max Plank in Leipzig and now he is a professor at the Eindhoven University of Technology.
Doctorate, Dartmouth University with Prof Carolyn Gordon, May 2015
Ian has done work on the length spectrum of a Riemannian manifold and Gromov-Hausdorff convergence building on a paper of mine which has a number of open problems. We only met a few times but each conversation was quite interesting and we have communicated extensively by email. His papers are available on the arxiv. Ian is currently working as a Lecturer at Yale.
Doctorate, Stony Brook with Prof Marcus Khuri (Dec 2018)
Edward has proven the W1p stability of the positive mass theorem for axisymmetric manifolds and is investigating the locations of minimal surfaces as a next step towards proving intrinsic flat convergence. We met often at my workshops and with Marcus Khuri. His first paper is on the arxiv. After a semester visiting me at CUNY, Edward took a postdoc position at Tuebingen working with Cederbaum, and is now at the University of Antwerp.
Doctorate, Stony Brook with Prof Mike Anderson (May 2021)
Lisandra was a member of the Fields Institute team that published a paper on Warped Tori Almost Rigidity. Subsequently she worked with me intensively one summer reading the work of Schoen and Yau on the Positive Mass Theorem in high dimensions and applying the ideas there to a related question in almost rigidity theory. When she chose to work on prescribing Gauss curvature with conical singularities with Mike Anderson as her doctoral advisor, it was decided she should focus on just the one project with him. She took a position at Combinatronix Laboratory and is now working at Marathon Petroleum Corporation.
Doctorate, Stony Brook with Khuri and Schul (May 2024)
Paul completed his dissertation with Professors Marcus Khuri and Raanan Schul, presenting examples of sequences of manifolds with uniformly positive scalar curvature involving tunnel constructions with bubbles, wells, and sewing. He worked very independently but did ask me for some conjectures and I suggested further applications of his work. Postdoc information is not yet official but will appear here soon!
Teams of postdocs and doctoral students that have worked with me:
Teams at the Fields Institute (starting in Summer 2017)
Team at the Fourier Institute (starting in Summer 2021)
Current doctoral students:
At the moment I have no doctoral students at the CUNY GC. I am working with various international doctoral students and postdocs on various projects online. Students who would like to attend our team meetings are welcome so please email me if you are interested. I am happy to include more people at the meetings and also workshops.
Future doctoral students:
Doctoral students who wish to work with me on a project should have a different primary doctoral advisor who supports the project plan. I am no longer working with students alone (due to health reasons that may force me to retire within the next five years).
Doctoral students who wish to work with me in Geometry need to have completed a year of Real Analysis and a year of Differential Geometry. We will then complete independant study courses together to learn Riemannian Geometry (following do Carmo), Metric Geometry (following Burago-Burago-Ivanov) and Geometric Measure Theory (following Morgan). Any student who wishes to work with me should also complete the Fourier Institute Couse I taught at the Fourier Institute in Summer 2021. You might wish to work with Renato Bettiol (CUNY), Dan Lee (CUNY), Raquel Perales (CIMAT), or Marcus Khuri (SUNYSB) as a primary advisor.
Doctoral Students who wish to work with me in Mathematical General Relativity need to have background in this area prior to working with me including background in Partial Differential Equations and General Relativity. We will then complete independant studies on Metric Geometry (following Burago-Burago-Ivanov) and Geometric Measure Theory (following Morgan). I also recommend completing the Fields Institute Course I taught in Summer 2017. You might wish to work with Dan Lee (CUNY) or Marcus Khuri (SUNYSB) as a primary advisor.
Advice for Doctoral Students is here.
Postdocs who have worked with me are listed here. Back to Professor Sormani's homepage.