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.
Felix Roehrle, Dmitry Zakharov, A matroidal perspective on the tropical Prym variety, arXiv:2311.09872, [PDF]
Margaret Meyer, Dmitry Zakharov, Chip-firing on graphs of groups, arXiv:2307.03348, [PDF]
Arkabrata Ghosh, Dmitry Zakharov, The Prym variety of a dilated double cover of metric graphs, arXiv:2303.03904, [PDF]
Felix Roehrle, Dmitry Zakharov, The tropical n-gonal construction, arXiv:2210.02267, [PDF]
Martin Ulirsch, Dmitry Zakharov, Tropical double ramification loci, arXiv:1910.01499 [PDF]
Papers:
Yoav Len, Martin Ulirsch, Dmitry Zakharov, Abelian tropical covers, to appear in Mathematical Proceedings of the Cambridge Philosophical Society, 2023 [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]
