Hausel Group

Commutative avatars of representations of semisimple Lie groups​by Tamás Hausel and Daniel BedatsWolfram Community, STAFF PICKS, October 2, 2024​https://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 …

The proceedings of the virtual 2022 International Congress of Mathematicians has appeared. It can be freely downloaded. Our contribution with title “Enhanced mirror symmetry for Langlands dual Hitchin systems” can be found here. Its abstract is: “The first part of this paper is a survey of mathematical results on mirror symmetry phenomena between Hitchin systems Read More …

In a new paper on arxiv: “Dynkin automorphisms actions on Gaudin algebras” 2022 ISTern and 2023 ISTA summer intern Vladyslav Zveryk gives a proof of the twining conjecture on big algebras. “In this paper, we study the action of a Dynkin automorphism σ of a simple Lie algebra 𝔤 on the generalized Gaudin algebras. In particular, we show isomorphisms Read More …

The next Bourbaki seminar on 18 November at 14:30 will feature the talk Victoria Hoskins: “Two proofs of the P = W conjecture, after Maulik–Shen, Hausel–Mellit–Minets–Schiffmann“ The talk could be followed live at this link.

The paper “Big algebras” is in the arxiv. Here is the abstract: “Here we announce the construction and properties of a big commutative subalgebra of the Kirillov algebra attached to a finite dimensional irreducible representation of a complex semisimple Lie group. They are commutative finite flat algebras over the cohomology of the classifying space of Read More …

Michael Gröchenig, DPhil (=PhD) student in Oxford 2009-2013, received a 2024 New Horizons prize in Mathematics – the Breakthrough prize for early career researchers – “For contributions to the theory of rigid local systems and applications of p-adic integration to mirror symmetry and the fundamental lemma.” Congratulations to Michael!