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.

Emily Clader, Felix Janda, Xin Wang, Dmitry Zakharov, Topological recursion relations from Pixton's formula, arXiv:1704.02011 [PDF]

Papers:

Sergey Dyachenko, Patrik Nabelek, Dmitry Zakharov, Vladimir Zakharov, Primitive solutions of the Korteweg-de Vries equation, to appear in Theor. Math. Phys.

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.

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]