Nikita Markarian

My research lies at the interface of algebraic geometry, homotopical algebra, and mathematical physics. I study the geometric origins of algebraic structures, with applications to operads, factorization homology, Poisson geometry, and multiple zeta values.

My research interests include:

• derived and higher categories;
• Hochschild homology and cohomology, cyclic homology;
• factorization homology;
• little discs operad and other operads;
• multiple zeta values and the Grothendieck–Teichmüller group;
• Feigin–Odesski Poisson structures and other Poisson structures.

My publications on arXiv.

My publications on HAL.

Research articles

Riemann–Roch theorem

• Poincaré–Birkoff–Witt isomorphism, Hochshild homology and Riemann–Roch theorem, MPIM Preprint Series, 2001 (52)
    preprint
• The Atiyah class, Hochschild cohomology and the Riemann–Roch theorem, Journal of the London Mathematical Society, Volume 79, Issue 1, February 2009, 129–143
    journal     arXiv

Factorization homology and operads

• Hypercommutative operad as a homotopy quotient of BV (with Anton Khoroshkin and Sergey Shadrin), Communications in Mathematical Physics, Volume 322, Issue 3, September 2013, 697–729
    journal     arXiv
• Weyl n-algebras, Communications in Mathematical Physics, Volume 350, Issue 2, March 2017, 421–442
    journal     arXiv
• Weyl n-algebras and the Kontsevich integral of the unknot, Journal of Knot Theory and Its Ramifications, Volume 25, Issue 12, October 2016, 1642008
    journal     arXiv
• Weyl n-algebras and the Swiss cheese operad, Forum Mathematicum, Volume 33, Issue 2, 2021, 531–545, March 2021
    journal     arXiv

Feigin–Odesski Poisson structures

• A note on the symplectic structure on the space of G-monopoles (with Michael Finkelberg, Alexander Kuznetsov and Ivan Mirković), Communications in Mathematical Physics, Volume 201, Issue 2, March 1999, 411–421
    journal     arXiv
• Compatible Feigin–Odesskii Poisson brackets (with Alexander Polishchuk), manuscripta mathematica, Volume 173, Issue 3, March 2024, 907–923
    journal     arXiv
• Compatible Poisson Brackets Associated with Elliptic Curves in G(2,5) (with Alexander Polishchuk), SIGMA, Volume 20, Issue 037, May 2024, 19 pages
    journal     arXiv
• On Conormal Lie Algebras of Feigin–Odesskii Poisson Structures (with Leonid Gorodetsky)
    journal     arXiv

Multiple zeta values

• On generalized stuffle relations between cell-zeta values, Communications in Number Theory and Physics, Volume 17, Issue 1, February 2023, 63–76
    journal     arXiv
• On algebra of big zeta values
    arXiv
• Multiplicative convolution and double shuffle relations: convolution
    arXiv

Selected recent talks

• Multiple zeta values and their generalizations, mini-course at the Université de Strasbourg, 17–22 May, 2023,
    notes
• Multiplicative convolution and double shuffle relations, ART seminar, Université de Strasbourg, 11 February, 2025,
    slides
• Aspects géométriques et homotopiques des relations entre les valeurs zêta multiples, Séminaire Homotopie et géométrie algébrique, Université de Toulouse, 14 October, 2025
• Les invariants de Rozansky–Witten supérieurs, Séminaire de l’équipe TA, LAGA, Paris-Nord , 18 December, 2025

Theses

• Homologie de factorisation, opérades et structures de Poisson, my habilitation (HDR) thesis defended at the University of Strasbourg 18.11.2024
    pdf   slides.