Possible research titles

Singularities of ordinary differential equations in various fields, including differential geometry, calculus of variations, optimal control theory, dynamical systems, physics (singular Lagrangians), etc. Related interests: geometry of vision, image reconstruction (inpainting), history of differential equations and differential geometry.

Supervisor’s research interests

Main interests:

Singularities of ordinary differential equations in various fields, including differential geometry, calculus of variations, optimal control theory, dynamical systems, physics (singular Lagrangians), etc.

Related interests:

Geometry of vision, image reconstruction (inpainting), history of differential equations and differential geometry.

Research highlights

Collaboration with foreign scientists and research centers. For singularities of ordinary differential equations and differential geometry: University of Liverpool (UK), University of Sao Paolo (Brazil), several research centers in Japan (Kyoto, Sapporo). For image reconstruction: France (Ecole Polytechnique, Sorbonne University, University of Toulon). We permanently apply for grants.

Main publications

• N. G. Pavlova, A. O. Remizov, Completion of the classification of generic singularities of geodesic flows in two classes of metrics, Izv. Math., 83:1 (2019), 104–123.
• O. Remizov, F. Tari, Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics, Geometriae Dedicata, 185:1 (2016), 131–153
• O. Remizov, On the local and global properties of geodesics in pseudo-Riemannian metrics, Differ. Geom. Appl., 39 (2015), 36–58
• U. Boscain, R.A. Chertovskih, J P. Gauthier, D. Prandi, A O. Remizov, Highly Corrupted Image Inpainting Through Hypoelliptic Diffusion, J. Math. Imaging Vis., 60:8 (2018), 1231–1245
• U. Boscain, R.A. Chertovskih, J. P. Gauthier, A.O. Remizov, Hypoelliptic diffusion and human vision: a semidiscrete new twist, SIAM J. Imaging Sci., 7:2 (2014), 669–698.
• I. R. Shafarevich, A. O. Remizov, Linear Algebra and Geometry, Springer, Heidelberg, 2013 , xxii+526 pp.