nLab Alexander Givental

• webpage

Selected writings

On quantum cohomology rings:

• Alexander Givental, A tutorial on Quantum Cohomology [pdf, pdf]

Introducing a quantum K-theory-analog of quantum cohomology rings:

• Alexander B. Givental, On the WDVV-equation in quantum K-theory, Michigan Math. J. 48 1 (2000) 295-304 [arXiv:math/0003158, doi:10.1307/mmj/1030132720]

On quantum K-theory rings for some form of equivariant K-theory:

• Alexander B. Givental, Permutation-equivariant quantum K-theory [webpage]

  I. Definitions. Elementary K-theory of $\overline{\mathcal{M}}_{0,n}/S_n$ [arXiv:1508.02690]

  II. Fixed point localization [arXiv:1508.04374]

  III. Lefschetz’ formula on $\overline{\mathcal{M}}_{0,n}/S_n$ and adelic characterization [arXiv:1508.06697]

  IV. $D_q$-modules [arXiv:1508.06697]

  V. Toric $q$-hypergeometric functions [arXiv:1509.03903]

  VI. Mirrors [arXiv:1509.07852]

  VII. General theory [arXiv:1510.03076]

  VIII. Explicit reconstruction [arXiv:1510.06116]

  IX. Quantum Hirzebruch-Riemann-Roch in all genera [arXiv:1709.03180]

  X. Quantum Hirzebruch-Riemann-Roch in genus 0, SIGMA 16 031 (2020) [arXiv:1710.02376, doi:10.3842/SIGMA.2020.031]

  XI. Quantum Adams-Riemann-Roch [arXiv:1711.04201]

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