Nikita Markarian

I am interested in the following subjects:

• derived and higher categories;
• Hochschild homology and cohomology, cyclic homology;
• factorization homology;
• little discs operad and other operads;
• multiple zeta values and the Grothendieck-Teichmuller 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

Recent talks

• Multiple zeta values and their generalizations, mini-course at the Université de Strasbourg, 17-22 May, 2023,
    notes
• Perturbative Chern-Simons invariants and factorization homology, talk at the ETH seminar, 2 October, 2023,
    video
• Multiplicative convolution and double shuffle relations, ART seminar, Université de Strasbourg, 11 February, 2025,
    slides

Theses

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