GEOMETRY AND ITS INTERFACES
The project ViaFiPos has been funded by a €2.5M ERC advanced grant. It will run 2026-2031. The title and abstract of the project: Representation theory, equivariant topology and Langlands duality via fixed point schemes (ViaFiPoS) We propose a three-way dictionary between representation theory of complex semisimple Lie groups, equivariant topology of affine Schubert varieties and Read More …
New arxiv paper by PhD student Miguel González: “Very stable regular G-Higgs bundles“. This follows three other arxiv papers by PhD students.
Three papers by Hausel group PhD students appeared in the arxiv. They relate to various aspects of big algebras:
The public talk “Anatomy of big algebras” was delivered as the 2024 “What is Life?” annual lecture — formerly Schrödinger lecture — in the historic physics lecture theater at Trinity College Dublin organized jointly by the School of Mathematics and the Austrian embassy in Dublin. Abstract: Starting with Schrödinger’s critique of the difficulty of visualising Read More …
Anna Sisák defended her thesis: “T-dual branes on hyperkähler manifolds“, while Kamil Rychlewicz defended his: “Equivariant cohomology and ring of functions“. Congratulations to both!
Commutative avatars of representations of semisimple Lie groupsby Tamás Hausel and Daniel BedatsWolfram Community, STAFF PICKS, October 2, 2024https://community.wolfram.com/groups/-/m/t/3290514
Hausel T. 2024. Commutative avatars of representations of semisimple Lie groups. Proceedings of the National Academy of Sciences of the USA (PNAS). DOI: 10.1073/pnas.2319341121, arXiv:2311.02711 Press release PNAS showcase Staff pick at Wolfram community big and medium skeletons over baryon octet — connecting particles under up-down quark symmetry, like the neutron and proton
With a project titled “Arithmetic, Geometry, Topology and Representation Theory Arising from the Affine Grassmannian” Jakub received a 2 year PhD DOC-fellowship starting September 2024. This follows Kamil Rychlewicz’s successful 2022 application with title “Topology of open smooth varieties with a torus action” and Anna Sisák’s successful 2021 application with title “Branes on hyperkähler manifolds“. Congrats Read More …
Conference: 2nd Summer Math Summer Workshop: Moduli, Simons Institute, Stony Brook, July 2024 Minicourse: Mirror symmetry and big algebras After surveying some mirror symmetry phenomena in the geometry of Langlands dualHitchin systems, we will model the Hitchin system on cominuscule upward flows by the equivariantcohomology of cominuscule flag varieties like the Grassmannian. Then we will Read More …
Check out the Zoo: Daniel Bedats, a rotation student, has designed several Mathematica images and 3d prints of skeletons, crystals and nerves of the triplet (standard representation of SL(3)) the decuplet (third symmetric power of the standard representation of SL(3)) and the octet (the adjoint representation of SL(3)). Skeletons are the spectra of the base Read More …