Max Riestenberg
email: max.riestenberg (at) mis (dot) mpg (dot) de
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Hello, I am Max! I am currently a postdoc in Anna Wienhard's group at the Max Planck Institute for Mathematics in the Sciences (MiS) in Leipzig. I completed my PhD in 2021 under the supervision of Jeff Danciger.
I work in geometry and topology with a focus on discrete subgroups of semisimple Lie groups.
My research interests include:
Anosov representations and (higher) Teichmüller theory
Coarse and differential geometry of symmetric spaces
Geometric structures on manifolds
Geometric machine learning
Papers
Papers
Certifying Anosov Representations. [arxiv:2409.08015]
Concave Foliated Flag Structures and the SL_3(R) Hitchin Component (with Alex Nolte). [arxiv:2407.06361]
Finite-sided Dirichlet domains and Anosov subgroups (with Colin Davalo). [arxiv:2402.06408].
Normed Spaces for Graph Embedding (with Diaaeldin Taha, Wei Zhao, and Michael Strube). Transactions on Machine Learning Research, (2024)
Modeling Graphs Beyond Hyperbolic: Graph Neural Networks in Symmetric Positive Definite Matrices (with Wei Zhao, Federico Lopez, Michael Strube, Diaaeldin Taha, and Steve Trettel). European Congress of Machine Learning, (2023).
Restrictions on Anosov subgroups of Sp(2n, R) (with Subhadip Dey and Zack Greenberg). Transactions of the American Mathematical Society, (2024). [arXiv:2304.13564]
Verifying the straight and spaced condition. Contemporary Mathematics, Vol. 783, “Computational aspects of discrete subgroups of Lie groups,” (2023).
A quantified local-to-global principle for Morse quasigeodesics. Groups, Geometry and Dynamics (2024). [arxiv:2101.07162]
Organization
Organization
I organized the 2024 log-cabin workshop in Higher Teichmüller theory with Alex Nolte and Suzanne Schlich, supported by François Labourie, which took place August 24-29 in Aussois, France.
I organized Diverse Aspects of Groups, Geometry and Dynamics with Julia Heller, and Levin Maier, supported by Peter Albers, Beatrice Pozzetti and Roman Sauer September 18-20, 2023 in Heidelberg, Germany.
Notes, etc.
Notes, etc.
I was invited to speak about Anosov representations at a log cabin workshop in 2019. I made some notes that might be useful to someone learning about Anosov representations for the first time, available here. More information, including a complete set of notes from the workshop, is available here.
I gave a mini-course at UT Austin in the summer of 2020 on Lie groups and symmetric spaces. If you want to practice your symmetric space skills you can try the exercises: 1 2 3 4 5.
I made 2 videos as part of the Nearly Carbon Neutral Geometry and Topology Conference in June 2021. The first video is about undistorted subgroups of isometries of hyperbolic space and their local-to-global principle. In the second video I describe a characterization of Anosov representations due to Kapovich-Leeb-Porti that directly generalizes the undistortion condition. They defined Morse quasigeodesics in higher rank symmetric spaces and proved a suitable local-to-global principle. The talk concludes with applications of a quantified version of the local-to-global principle.
I spoke at the Young Researcher's Workshop on Positivity in Lie Groups in January 2022, organized by Xenia Flamm, Arnaud Maret, and Mareike Pfeil. There are some notes for this floating around.
These are my notes for a lecture series titled "Discrete and faithful representations of surface groups" given in Summer 2022 to the RTG “Asymptotic Invariants and Limits of Groups and Space,” a joint research training group of Heidelberg University and the Karlsruhe Institute of Technology. Topics include the Milnor-Wood inequality and Goldman's Theorem for representations to PSL(2,R), (G,X)-structures on manifolds, Hitchin representations and convex real projective structures, Higher Teichmüller spaces and positivity, and infinitesimal deformations and proper affine actions
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