2017, Volume 682

Conference Proceeding

2015, University lecture series, ISBN 9781470423971, Volume 63., x, 114

Book

Advances in Mathematics, ISSN 0001-8708, 11/2017, Volume 320, pp. 115 - 156

We prove a determinantal formula that describes the K-theoretic degeneracy loci classes for Grassmann bundles. We further prove Pfaffian formulas for...

K-theory | Schubert calculus | Determinant | Pfaffian | MATHEMATICS | SCHUBERT POLYNOMIALS

K-theory | Schubert calculus | Determinant | Pfaffian | MATHEMATICS | SCHUBERT POLYNOMIALS

Journal Article

1981, Lecture notes in mathematics, ISBN 0387106987, Volume 854., 517

Book

Advances in Mathematics, ISSN 0001-8708, 12/2017, Volume 322, pp. 378 - 472

We establish an equivalence of homotopy theories between symmetric monoidal bicategories and connective spectra. For this, we develop the theory of Γ-objects...

2-categories | K-theory | Symmetric monoidal bicategory | Connective spectra

2-categories | K-theory | Symmetric monoidal bicategory | Connective spectra

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2012, Volume 14, Issue 4, pp. 1041 - 1079

For a prime p >= 5, we compute the algebraic K -theory modulo p and v(1) of the mod p Adams summand, using topological cyclic homology. On the way, we evaluate...

Morava K-theory | Topological cyclic homology | Topological Hochschild homology | Algebraic K-theory | topological cyclic homology | MATHEMATICS, APPLIED | Algebraic K -theory | STABLE-HOMOTOPY | SPHERES | RING SPECTRA | Morava K -theory | MATHEMATICS | COHOMOLOGY | MODULES | CYCLIC HOMOLOGY | INTEGERS | topological Hochschild homology | SEQUENCE | CYCLOTOMIC TRACE

Morava K-theory | Topological cyclic homology | Topological Hochschild homology | Algebraic K-theory | topological cyclic homology | MATHEMATICS, APPLIED | Algebraic K -theory | STABLE-HOMOTOPY | SPHERES | RING SPECTRA | Morava K -theory | MATHEMATICS | COHOMOLOGY | MODULES | CYCLIC HOMOLOGY | INTEGERS | topological Hochschild homology | SEQUENCE | CYCLOTOMIC TRACE

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2017, Volume 304, pp. 646 - 727

Spectral Mackey functors are homotopy-coherent versions of ordinary Mackey functors as defined by Dress. We show that they can be described as excisive...

Equivariant stable homotopy theory | Spectral Mackey functors | Unfurling | Equivariant algebraic K-theory | MATHEMATICS

Equivariant stable homotopy theory | Spectral Mackey functors | Unfurling | Equivariant algebraic K-theory | MATHEMATICS

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 04/2019, Volume 99, Issue 2, pp. 516 - 534

We study a categorical construction called the cobordism category, which associates to each Waldhausen category a simplicial category of cospans. We prove that...

57R90 (secondary) | 19D10 (primary) | MATHEMATICS | CATEGORIES

57R90 (secondary) | 19D10 (primary) | MATHEMATICS | CATEGORIES

Journal Article

Physical Review Letters, ISSN 0031-9007, 07/2005, Volume 95, Issue 1, p. 016405

Nonrelativistic Fermi liquids in d+1 dimensions exhibit generalized Fermi surfaces: (d-p)-dimensional submanifolds in the (k,omega)-space supporting gapless...

PHYSICS, MULTIDISCIPLINARY | MATERIALS SCIENCE | BAND THEORY | STABILITY | FERMI LEVEL

PHYSICS, MULTIDISCIPLINARY | MATERIALS SCIENCE | BAND THEORY | STABILITY | FERMI LEVEL

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2020, Volume 360, p. 106919

We define and study the quantum equivariant K-theory of cotangent bundles over Grassmannians. For every tautological bundle in the K-theory we define its...

Quantum K-theory | Representation theory | Algebraic geometry | MATHEMATICS | REPRESENTATIONS | R-MATRIX

Quantum K-theory | Representation theory | Algebraic geometry | MATHEMATICS | REPRESENTATIONS | R-MATRIX

Journal Article

Advances in Mathematics, ISSN 0001-8708, 07/2019, Volume 351, pp. 761 - 803

We construct a relative version of topological K-theory, in the sense of [11], over an arbitrary quasi-compact, quasi-separated C-scheme X. This has as input a...

K-theory | Derived algebraic geometry | Algebraic topology | MATHEMATICS | MOTIVES | Algebra

K-theory | Derived algebraic geometry | Algebraic topology | MATHEMATICS | MOTIVES | Algebra

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 02/2018, Volume 97, Issue 1, pp. 1 - 23

This paper explores further the connection between Langlands duality and T‐duality for compact simple Lie groups, which appeared in work of Daenzer–van Erp and...

81T30 | 57T10 (secondary) | 19L50 (primary) | ORIENTIFOLDS | TOPOLOGY | STRANGE DUALITY | WZW MODELS | H-FLUXES | SPACE | MATHEMATICS | LEVEL-RANK DUALITY | TORUS BUNDLES | HOMOLOGY | D-BRANES

81T30 | 57T10 (secondary) | 19L50 (primary) | ORIENTIFOLDS | TOPOLOGY | STRANGE DUALITY | WZW MODELS | H-FLUXES | SPACE | MATHEMATICS | LEVEL-RANK DUALITY | TORUS BUNDLES | HOMOLOGY | D-BRANES

Journal Article

2010, Mathematical surveys and monographs, ISBN 9780821851890, Volume 169, v, 318

Book

Journal of Functional Analysis, ISSN 0022-1236, 01/2018, Volume 274, Issue 1, pp. 278 - 340

Quantitative (or controlled) K-theory for C⁎-algebras was used by Guoliang Yu in his work on the Novikov conjecture, and later developed more formally by Yu...

[formula omitted] operator algebra | Quantitative operator K-theory | Subquotient of [formula omitted] space | Filtered Banach algebra | operator algebra | space | Subquotient of L | MATHEMATICS | L-p operator algebra | ASYMPTOTIC DIMENSION | SPACES | OPERATOR-ALGEBRAS | Subquotient of L-p space | CONJECTURE

[formula omitted] operator algebra | Quantitative operator K-theory | Subquotient of [formula omitted] space | Filtered Banach algebra | operator algebra | space | Subquotient of L | MATHEMATICS | L-p operator algebra | ASYMPTOTIC DIMENSION | SPACES | OPERATOR-ALGEBRAS | Subquotient of L-p space | CONJECTURE

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 07/2018, Volume 14

This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely...

Quantum integrability | K-theory | Loop models | VARIETY | KNIZHNIK-ZAMOLODCHIKOV EQUATION | quantum integrability | PHYSICS, MATHEMATICAL | SCHUBERT | loop models | POLYNOMIALS | SCHEME | ALGEBRAS | COHOMOLOGY | COTANGENT BUNDLE | GEOMETRY | Two dimensional models | Sheaves | Partitions (mathematics) | Mathematical models | Statistical mechanics

Quantum integrability | K-theory | Loop models | VARIETY | KNIZHNIK-ZAMOLODCHIKOV EQUATION | quantum integrability | PHYSICS, MATHEMATICAL | SCHUBERT | loop models | POLYNOMIALS | SCHEME | ALGEBRAS | COHOMOLOGY | COTANGENT BUNDLE | GEOMETRY | Two dimensional models | Sheaves | Partitions (mathematics) | Mathematical models | Statistical mechanics

Journal Article

Geometry and Topology, ISSN 1465-3060, 09/2012, Volume 16, Issue 4, pp. 2037 - 2065

We interpret this as a correspondence between the virtual 2 - vector bundles over a space X and their associated anomaly bundles over the free loop space LX....

MATHEMATICS | COHOMOLOGY | SPACES | CYCLOTOMIC TRACE | MODEL | HOCHSCHILD HOMOLOGY | SPECTRA | CATEGORIES

MATHEMATICS | COHOMOLOGY | SPACES | CYCLOTOMIC TRACE | MODEL | HOCHSCHILD HOMOLOGY | SPECTRA | CATEGORIES

Journal Article

GEOMETRY & TOPOLOGY, ISSN 1465-3060, 2019, Volume 23, Issue 1, pp. 101 - 134

We calculate pi K-*(S) circle times Z[1/2], the homotopy groups of K(S) away from 2, in terms of the homotopy groups of K(Z), the homotopy groups of CP-1...

MATHEMATICS | LOCALIZATION | FIELDS | EXTENSIONS

MATHEMATICS | LOCALIZATION | FIELDS | EXTENSIONS

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 04/2018, Volume 97, Issue 2, pp. 145 - 148

We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K‐theory ring of a cominuscule flag variety to the...

19E08 | 14M15 (secondary) | 14N15 | 14N35 (primary) | MATHEMATICS | VARIETIES | POSITIVITY

19E08 | 14M15 (secondary) | 14N15 | 14N35 (primary) | MATHEMATICS | VARIETIES | POSITIVITY

Journal Article

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