Algebraic Torus Action: Geometry and Combinatorics

• Polish National Science Center grant 2016/23/G/ST1/04282
• Deutsche Forschungsgemeinschaft grant HA 4383/8-1

Institutions Freie Univeristaet Berlin The University of Warsaw Researchers Klaus Altmann, PI (Berlin) Christian Haase, PI (Berlin) Jakub Koncki (Warsaw) Eleonora Romano, (Warsaw) Karin Schaller, (Berlin) Andrzej Weber, PI (Warsaw) Jaroslaw Wisniewski, PI (Warsaw) Project summary Activities related to the project Algebraic Geometry seminar at UW September Algebraic Geometry Schools

Workshops, meetings

• Condensed mathematics and liquid tensor experiment
• Sopot Workshop, October 2021
  • Klaus Altmann, Inhomogeneous toric deformations
  • Karin Schaller, NObodies are perfect, semigroups are not.
  • Christian Haase, More on NObodies and semigroups
  • Jaroslaw Wisniewski, Birational geometry via C* actions, an introduction
  • Alberto Franceschini, Birational trasnformations from bandwidth two C* actions
  • Eleonora Romano, C*-actions and Mori Dream Spaces
  • Luis Sola Conde, Geometric realizations of birational maps via C* actions
  • Andrzej Weber, Torus equivariant characteristic classes for nilpotent cones
  • Jakub Koncki, Equivariant motivic Chern class of Bialynicki-Birula cells
• School Homogeneous Spaces, Characteristic Classes, September 2019.
  • Luis Sola Conde, Geometry of rational homogeneous spaces
  • Andrzej Weber, Characteristic classes of singular varieties in equivariant theories
• Warsaw Workshop, November 2018
  • Klaus Altmann, T-varieties via polyhedral divisors
  • Jaroslaw Buczynski, T-varieties via fixed points and moment polytopes
  • Maksymilian Grab, Grids in resolving quotient singularities
  • Joachim Jelisiejew, ABB decomposition for monoids
  • Eleonora Romano, Adjunction for varieties with torus action
  • Michal Lech, Degenerations of some homogeneous varieties
  • Andrzej Weber, Localization theorems and cohomology

Publications

• Buczynski, Weber, Wisniewski Algebraic torus actions on contact manifolds, J. Diff. Geom. 121 (2022).
• Feher, Rimanyi, Weber Motivic Chern classes and K-theoretic stable envelopes, Proc. London Math. Soc. on-line
• Feher, Rimanyi, Weber Characteristic classes of orbit stratifications, the axiomatic approach, in: Schubert Calculus and Its Applications in Combinatorics and Representation Theory, ed. J. Hu, C. Li, L. Mihalcea. Springer 2020
• Koncki Motivic Chern classes of configuration spaces, Fundamenta Mathematicae 254 (2021).
• Koncki Comparison of motivic Chern classes and stable envelopes for cotangent bundles, Journal of Topology 15 (2022).
• Koncki, Weber Twisted motivic Chern class and stable envelopes, Adv. Math. 404 (2022).
• Kumar, Rimanyi, Weber Elliptic classes of Schubert varieties, Math. Ann. 378 (2020), no. 1-2, 703-728
• Michalek, Monin, Wisniewski Maximum likelihood, complete quadrics and C* actions SIAM J. Alg. Geom. (2021)
• Mikosz, Weber Elliptic classes, McKay correspondence and theta identities, J. Algebraic Comb., on-line
• Montero, Romano, A characterization of some Fano 4-folds through conic fibrations, Int. Math. Res. Notices (2019).
• Occhetta, Sola Conde, Romano Manifolds with two projective bundle structures, Proc. AMS 150 (2022).
• Occhetta, Sola Conde, Romano, Wisniewski, Small bandwidth C* actions and birational geometry J. Alg. Geom. 32 (2023)
• Occhetta, Sola Conde, Romano, Wisniewski, Higher rank torus action on contact manifolds Selecta Mathematica (2021)
• Occhetta, Sola Conde, Romano, Wisniewski Small modifications of Mori dream spaces arising from C*-actions, European Journal of Mathematics 8 (2022).
• Rimanyi, Weber Elliptic classes of Schubert cells via Bott-Samelson resolution, J. Topol. 13 (2020), no. 3, 1139-1182
• Rimanyi, Weber Elliptic Classes On Langlands Dual Flag Varieties, Commun. Contemp. Math. 24 (2022).
• Romano, A note on flatness of some fiber type contractions, Proc. Japan Acad. (2019).
• Romano, Wisniewski Adjunction for varieties with C* action, Transformation Groups (2020)
• Rudnicki, Weber Characteristic classes of Borel orbits of square-zero upper-triangular matrices, Journal of Algebra 598 (2022).