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I am a research group leader at the Max Planck Institute for Mathematics in the Sciences.
Email: dani (dot) kaufman (at) mis.mpg.de
My primary research interests are centered around cluster algebras and their applications to Geometry, Physics, and Number Theory.
See the Gallery tab for a collection of pictures of exchange complexes of various cluster algebras.
Papers:
Non-commutative Cluster Algebras
SL2 -like Properties of Matrices Over Noncommutative Rings and Generalizations of Markov Numbers:
https://arxiv.org/abs/2402.19300
Non-commutative Polygonal Cluster Algebras: https://arxiv.org/abs/2410.08813
Cluster Symmetries
Special folding of quivers and cluster algebras: https://arxiv.org/abs/2304.07510 ( in Mathematica Scandinavica)
Cluster Modular Groups of Affine and Doubly Extended Cluster Algebras : Available at https://arxiv.org/abs/2107.10334
Mutation Invariant Functions on Cluster Algebras Associated With Surfaces: My thesis, available at https://drum.lib.umd.edu/handle/1903/27440
Invariant Functions on Cluster Ensembles: Available at https://arxiv.org/abs/2010.15179 (in Journal of Pure and Applied Algebra)
3d Chern-Simons Theory:
A Wilson Line Realisation of Quantum Groups: https://arxiv.org/abs/2307.10830 (in Letters in Mathematical Physics)
Polylogarithms
Hopf algebras of multiple polylogarithms, and holomorphic 1-forms: https://arxiv.org/abs/2211.08337
The Lie coalgebra of multiple polylogarithms: https://arxiv.org/abs/2203.11588 (in Journal of Algebra)
CV, Updated Fall 2024: CV.pdf
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