“What is Life?” annual lecture

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 …

Two PhD students graduate

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!

Paper on big algebras appeared

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

Jakub Löwit awarded ÖAW DOC-fellowship

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 …

Videos and slides from minicourse at Simons Institute in Geometry and Physics

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 …

Proceedings of ICM 2022 appeared

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 …

Paper by summer intern Vladyslav Zveryk

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 …

Bourbaki seminar on P=W

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.