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 intersection of analysis, geometry and topology. I am particularly interested in problems involving the scalar curvature of Riemannian manifolds and related questions in mathematical general relativity.

My research is supported by Simons Foundation Travel Support for Mathematicians.

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 Algebraic Topology I and Linear Algebra. I am also 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!

Preprints

• (with G. Frenck and R. Zeidler) Positive scalar curvature and point singularities. arXiv

• (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

Papers

• (with B. Hanke and T. Schick) Lipschitz rigidity for scalar curvature.
  Journal of the European Mathematical Society (JEMS), to appear. 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), 2024. arXiv journal

• (with R. Zeidler) The positive mass theorem and distance estimates in the spin setting.
  Transactions of the American Mathematical Society, 2024. arXiv journal

• (with R. Zeidler) Scalar and mean curvature comparison via the Dirac operator.
  Geometry & Topology, 2024. arXiv journal

• (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, 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, 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

• Fall 2024, MATH 643: Algebraic Topology I.

• Fall 2024, MATH 304: Linear Algebra.

• 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

• December 2024, Joint meeting of the NZMS, AustMS and AMS. University of Auckland, New Zealand.

• December 2024, Geometry/Topology Seminar. Stony Brook University, New York.

• November 2024, Conference Curvature and Geometric Analysis in Rome. Sapienza University of Rome, Italy.

• November 2024, Geometry Seminar. Michigan State University, Michigan.

• October 2024, Geometry Seminar. Rice University, Texas.

• September 2024, AMS Sectional Meeting. UT San Antonio, Texas.

• July 2024, Oberseminar Differentialgeometrie. Augsburg University, Germany.

• July 2024, Analysis and Geometry Seminar. University of Münster, Germany.

• April 2024, Geometry seminar (online). Beijing Institute of Technology.

• March 2024, Workshop MAGEC 2024. Caltech, California.

• February 2024, Workshop on Analysis, Geometry and Topology of Positive Scalar Curvature Metrics. Oberwolfach, Germany.

• December 2023, Workshop on Operator Algebras and Applications: Non-Commutative Geometry. Fields Institute, Toronto, Canada.

• November 2023, Geometry and Topology Seminar. Washington University in St. Louis, Missouri.

• October 2023, Geometry Topology Dynamical Systems Seminar. UT Dallas, Texas.

• April 2023, Texas Geometry and Topology Conference. Texas Christian University, Texas.

• January 2023, Topology/Geometry Zoom Seminar. Organized by the University of Oregon.

• November 2022, Analysis and Geometry Seminar. Columbia University, New York, USA.

• November 2022, Geometry & Topology Seminar. Duke University, North Carolina, USA.

• August 2022, YMNCGA. Texas A&M University, USA.

• August 2022, NSF-CBMS Conference: K-theory of operator algebras and its applications to geometry and topology. University of Puerto Rico.

• July 2022, SUMIFRAS. Texas A&M University, USA.

• June 2022, Dirac Operators in Topology, Geometry, and Representation Theory. Cortona, Italy.

• May 2022, Oberseminar Topologie. University of Münster, Germany.

• April 2022, GNOSC Seminar (online).

• April 2022, Seminar at the Research Center for Operator Algebras (online). ECNU, China.

• February 2022, Geometry/Topology Seminar (online). Stony Brook University, USA.

• October 2021, Topology/Geometry  Zoom  Seminar. University of Oregon, USA.

• October 2021, Noncommutative Geometry Seminar. Texas A&M University, USA.

• October 2021, Darboux geometry seminar. Montpellier, France.

• October 2021, UC-Berkeley Differential Geometry Seminar (online).

• September 2021, The 4th Geometric Analysis Festival.

• June 2021, Oberwolfach workshop Analysis, Geometry and Topology of Positive Scalar Curvature Metrics.

• May 2021, Oberseminar Globale Analysis (online). University of Regensburg, Germany.

• 9 December 2020, Topology/Geometry  Zoom  Seminar. University of Oregon, USA.

• 30 September 2020, Online Noncommutative Geometry Seminar.

• August 2020, 2020 Virtual Workshop on Ricci and Scalar Curvature in honor of Misha Gromov. Video.

• 20 July 2020, Oberseminar Differentialgeometrie. Universität Augsburg, Germany.

• 9 July 2020, Geometry and Physics Seminar. Institut für Mathematik der Universität Potsdam, Germany.

• 1-4 July 2020, Workshop “Non-Commutative Geometry and Cyclic Homology’’ (attended). Oberwolfach, Germany.