Research interests:
I am interested in various aspects of the theory of integrable systems. I am also interested in the intersection theory of the moduli space of curves, and I've recently been interested in tropical algebraic geometry.
Andreas Gross, Arne Kuhrs, Martin Ulirsch, Dmitry Zakharov, Tropical reductive groups and principal bundles on metric graphs, arXiv:2511.05422 [PDF]
Dmitry Zakharov, The trigonal construction and the second moment of the tropical Prym variety, arXiv:2507.06401 [PDF]
Mariia Vetluzhskikh, Dmitry Zakharov, Critical groups in abelian harmonic quotients, arXiv:2409.04629 [PDF]
Martin Ulirsch, Dmitry Zakharov, Tropical double ramification loci, arXiv:1910.01499 [PDF]
Papers:
Felix Röhrle, Dmitry Zakharov, A matroidal perspective on the tropical Prym variety, The Versatility of Integrability: In Memory of Igor Krichever, Contemp. Math. 923, 47-81, 2025 [PDF]
Margaret Meyer, Dmitry Zakharov, Chip-firing on graphs of groups, Discr. Math. 348 (12), 114631, 2025 [PDF]
Felix Röhrle, Dmitry Zakharov, The tropical n-gonal construction, Algebr. Comb. 8 (2), 319-378, 2025 [PDF]
Arkabrata Ghosh, Dmitry Zakharov, The Prym variety of a dilated double cover of metric graphs, Ann. Comb. 29 (2), 439-460, 2025 [PDF]
Yoav Len, Martin Ulirsch, Dmitry Zakharov, Abelian tropical covers, Math. Proc. Cambridge Philos. Soc. 176 (2), 395-416, 2024 [PDF]
Emily Clader, Felix Janda, Xin Wang, Dmitry Zakharov, Topological recursion relations from Pixton's formula, Mich. Math. J. 73, 227-241, 2023 [PDF]
Andreas Gross, Martin Ulirsch, Dmitry Zakharov, Principal bundles on metric graphs: the GL_n case, Adv. Math. 411, 108775, 2022, [PDF]
Yury Stepanyants, Dmitry Zakharov, Vladimir Zakharov, Lump interactions with plane solitons, Radiophysics and Quantum Electronics 64, No. 10, 665-680, 2022, [PDF]
Yoav Len and Dmitry Zakharov, Kirchhoff's theorem for Prym varieties, Forum Math. Sigma 10:e11, 1-54, 2022, [PDF]
Dmitry Zakharov, Zeta functions of edge-free quotients of graphs, Lin. Alg. Appl. 629, 40-71, 2021 [PDF]
Charles Lester, Andrey Gelash, Dmitry Zakharov, Vladimir Zakharov, Lump chains in the KP-I equation, Stud. Appl. Math. 147.4, 1425-1442, 2021 [PDF]
Sergey Dyachenko, Patrik Nabelek, Dmitry Zakharov, Vladimir Zakharov, Primitive solutions of the Korteweg-de Vries equation, Theor. Math. Phys. 202 (3), 334-343, 2020
Patrik Nabelek, Dmitry Zakharov, Vladimir Zakharov, On symmetric primitive potentials, J. Integrable Syst. 4 (2019), no. 1, xyz006, 20 pp. [PDF]
Dmitry Zakharov, Vladimir Zakharov, Non-periodic one-gap potentials in quantum mechanics, Geometric methods in physics XXXV, 213-225, Trends Math., Birkhäuser/Springer, Cham, 2018. [PDF]
Emily Clader, Samuel Grushevsky, Felix Janda, Dmitry Zakharov, Powers of the theta divisor and relations in the tautological ring, Int. Math. Res. Not. IMRN 2018. no. 24, 7725-7754. [PDF]
Sergey Dyachenko, Dmitry Zakharov, Vladimir Zakharov, Non-periodic one-dimensional ideal conductors and integrable turbulence, Phys. Lett. A 380 (2016), no. 46, 3881-3885
Sergey Dyachenko, Dmitry Zakharov, Vladimir Zakharov, Primitive potentials and bounded solutions of the KdV equation, Phys. D 333 (2016), 148-156
Federico Buonerba, Dmitry Zakharov, Closed symmetric 3-differentials on complex surfaces, European Journal of Mathematics, 2 (2016), no.4, 984-992 [PDF]
Sergey Dyachenko, Dmitry Zakharov, Vladimir Zakharov, Bounded solutions of KdV and non-periodic one-gap potentials in quantum mechanics, Lett. Math. Phys. 106 (2016), no. 6, 731-740
Izzet Coskun, Majid Hadian, Dmitry Zakharov, Dense PGL-orbits in products of Grassmannians, J. Algebra 429 (2015), 75-102 [PDF]
Samuel Grushevsky, Dmitry Zakharov, The double ramification cycle and the theta divisor, Proc. Amer. Math. Soc. 142 (2014), no. 12, 4053-4064 [PDF]
Samuel Grushevsky, Dmitry Zakharov, The zero section of the universal semiabelian variety, and the double ramification cycle, Duke Math. J. 163 (2014), no. 5, 953-982 [PDF]
Dmitry Zakharov, The Weierstrass representation of discrete isotropic surfaces in R^{2,1}, R^{3,1} and R^{2,2}, Funct. Anal. Appl. 45 (2011), no. 1, 25-32 [PDF]
Igor Krichever, Dmitry Zakharov, A note on critical points of soliton equations, Anal. Math. Phys. 1 (2011), no. 1, 15-35 [PDF]
Dmitry Zakharov, A discrete analogue of the modified Novikov-Veselov hierarchy, Int. Math. Res. Not. IMRN 2010, 18, 3463-3488 [PDF]
Dmitry Zakharov, Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation, Theoret. and Math. Phys. 153 (2007), no. 1, 1388-1397 [PDF]
