---
res:
  bibo_abstract:
  - "We develop and employ techniques from equivariant algebraic K-theory and related
    invariants\r\nin the context of geometric representation theory, in both arithmetic
    and topological situations.\r\nWe showcase the use of such techniques on the affine
    Grassmannian Gr, a space of fundamental\r\ninterest in the geometric Langlands
    program.\r\n\r\nIt is a deep development of mathematics of the last century that
    many concrete, yet combina-\r\ntorially complex algebraic problems may be effectively
    studied through the lens of algebraic\r\ngeometry. The objects of interest can
    be often realized as cohomological invariants of algebraic\r\nvarieties, and good
    understanding of their geometry sheds light into the original questions.\r\nSuch
    techniques have seen immense applications in the Langlands program, where they
    go\r\nunder the label of geometric representation theory.\r\n\r\nOne source of
    powerful invariants in algebraic geometry comes from algebraic K-theory,\r\nHochschild
    homology, and their relatives. These localizing invariants contain large amount\r\nof
    information, but are quite hard to compute. For this reason, their usage in geometric\r\nrepresentation
    theory has been limited.\r\n\r\nThe aim of this thesis is to showcase how to control
    such invariants in the situations of\r\ninterest and use them to obtain new insights.
    We start by reinterpreting equivariant Hochschild\r\nhomology in terms of functions
    on certain fixed-point schemes, which are of independent\r\ninterest. We compare
    it to equivariant K-theory via the trace map. We give new computations\r\nand
    comparisons of such invariants of affine Schubert varieties in Gr, including arithmetic\r\nsituations.
    We show that they behave much better than expected.\r\n\r\nWe finally utilize
    this circle of ideas in a purely topological setting. We describe the varying\r\nfixed
    points of the extended torus action on the affine Grassmannian, and use it to
    compute\r\nits equivariant topological K-theory ring. The answer is nontrivial
    and verifies an outstanding\r\nconjecture in the subject.\r\n\r\nWe compare, partly
    conjecturally, the resulting K-theory ring to the completed center of an\r\nintegral
    even hybrid quantum group and its deformed quantum category O. This gives a\r\ngenuine
    application of our computations in pure representation theory.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Jakub
      foaf_name: Löwit, Jakub
      foaf_surname: Löwit
      foaf_workInfoHomepage: http://www.librecat.org/personId=e3b80ae2-eb8e-11eb-b029-9aef4a9108a0
  bibo_doi: 10.15479/AT-ISTA-22694
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2663-337X
  dct_language: eng
  dct_publisher: Institute of Science and Technology Austria@
  dct_title: Equivariant K-theory of affine Grassmannians in representation theory
    and arithmetic@
...