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Simone Cecchini

Assistant Professor

Department of Mathematics
Texas A&M University
College Station, TX 77843-3368, USA

Email: cecchini <at> tamu.edu

Office: Blocker 525G

I am an Assistant Professor in the Department of Mathematics at Texas A&M University.

My research lies at the interface of global analysis and topology. I am particularly interested in topological invariants of elliptic operators and their relationship with the metric properties of manifolds.

Before joining Texas A&M, I was a Postdoctoral Researcher at the University of Göttingen, under the mentorship of Thomas Schick. I earned my PhD from Northeastern University in 2017, under the guidance of Maxim Braverman, following the completion of my Masters at the University of Rome “La Sapienza’’ in 2012, where I was advised by Paolo Piazza. Here you can find my CV.

I co-organized the Workshop MAGEC 2024, which took place at Caltech and was generously funded by the NSF. Additionally, I dedicate my time to instructing at TAMU Math Circle and PReMa(Program for Research in Mathematics), initiatives at Texas A&M designed to foster a love for mathematics among high school students.

Currently, I am teaching Topology II and co-organizing the Noncommutative Geometry Seminar at Texas A&M. If you are interested in contributing a talk to our seminar, please do not hesitate to reach out to me!

Papers

  • (with S. Hirsch and R. Zeidler) Rigidity of spin fill-ins with non-negative scalar curvature. arXiv

  • (with J. Wang, Z. Xie and B. Zhu) Scalar curvature rigidity of the four-dimensional sphere. arXiv

  • (with M. Lesourd and R. Zeidler) Positive mass theorems for spin initial data sets with arbitrary ends and dominant energy shields. International Mathematics Research Notices (IMRN). arXiv journal

  • (with B. Hanke and T. Schick) Lipschitz rigidity for scalar curvature. Journal of the European Mathematical Society (JEMS), to appear. arXiv

  • (with R. Zeidler) Scalar and mean curvature comparison via the Dirac operator. Geometry & Topology, to appear. arXiv journal

  • (with R. Zeidler) The positive mass theorem and distance estimates in the spin setting. Transactions of the American Mathematical Society, to appear. arXiv

  • (with D. Räde and R. Zeidler) Nonnegative scalar curvature on manifolds with at least two ends. Journal of Topology, 2023. arXiv journal

  • (with M. Seyedhosseini and V. Zenobi) Relative torsion and bordism classes of positive scalar curvature metrics on manifolds with boundary. Mathematische Zeitschrift, 2023. arXiv journal

  • (with T. Schick) Enlargeable metrics on nonspin manifolds. Proceedings of the American Mathematical Society, vol. 149, 2021. arXiv journal

  • A long neck principle for Riemannian spin manifolds with positive scalar curvature. Geometric and Functional Analysis (GAFA), 2020. arXiv journal

  • Callias-type operators in C*-algebras and positive scalar curvature on noncompact manifolds. Journal of Topology and Analysis, 2020. arXiv journal

  • (with M. Braverman) Callias-type operators in von Neumann algebras. Journal of Geometric Analysis, vol. 28, no. 1, 2018. arXiv journal

  • (with M. Braverman) Spectral theory of von Neumann algebra valued differential operators over non-compact manifolds. Journal of Noncommutative Geometry, 2016. arXiv journal

Surveys

  • (with R. Zeidler) Scalar curvature and generalized Callias operators. Perspectives in Scalar Curvature, volume edited by M. Gromov and B. Lawson, World Scientific, 2022. PDF (via sciebo)

Recent Teaching

  • Spring 2024, MATH 637: Topology II.

  • Fall 2023, MATH 636: Topology I.

  • Spring 2023, MATH 407: Complex Variables.

  • Fall 2022, MATH 304: Linear Algebra.

Recent and upcoming events