- \n
- the method of the differential separability conditions\; \n
- the method of th e vector fields $Z$. \n

- \n
- \; geodesics\, \n
- \; their local and global optimality\, \n
- \; cut ti me\, cut locus\, and spheres\, \n
- \; infinite geodesics\,\n
- \; bicycle transform and relation of geodesics with Euler e lasticae\, \n
- \; group of isometries and homogeneous geodesi cs\, \n
- \; applications to imaging and robotics. \n

\n https://dx.doi. org/10.1080/14029251.2017.1418057

\narXiv:1608.03994

\narXiv:2101.04523\, Mi tmf10046

\narXiv:2 203.07062

\narXiv:2212. 07583\n LOCATION:https://master.researchseminars.org/talk/GDEq/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Georgy Sharygin DTSTART;VALUE=DATE-TIME:20221221T162000Z DTEND;VALUE=DATE-TIME:20221221T180000Z DTSTAMP;VALUE=DATE-TIME:20241013T134851Z UID:GDEq/76 DESCRIPTION:Title: Chopping integrals of the full symmetric Toda system\, a new approach \nby Georgy Sharygin as part of Geometry of differential equations sem inar\n\nLecture held in room 303 of the Independent University of Moscow.\ n\nAbstract\nIn my talk I will try to answer the questions that has been c ausing my anxiety for a rather long time: where do the additional integral s of the full symmetric Toda system come from\, why they are rational and what does all this have to do with "chopping". Even if we can use the AKS method there remains the question\, why do the initial functions actually commute (and whether it is possible to find other with the same property). The known answers were concerned either with rather hard straightforward computations\, or with the properties of a Gaudin system\; they look prett y complicated. In my talk I will show how one can obtain these integrals w ith the help of some simple differential operators (in the manner of the a rgument shift method). Besides this\, we will discuss some other possible integrals as well as the method to solve the corresponding flows by QR dec omposition.\n\nThe talk is based on a common work with Yu. Chernyakov and D. Talalaev.\n LOCATION:https://master.researchseminars.org/talk/GDEq/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin DTSTART;VALUE=DATE-TIME:20221207T162000Z DTEND;VALUE=DATE-TIME:20221207T180000Z DTSTAMP;VALUE=DATE-TIME:20241013T134851Z UID:GDEq/77 DESCRIPTION:Title: On normal forms of differential operators\nby Valentin Lychagin a s part of Geometry of differential equations seminar\n\nLecture held in ro om 303 of the Independent University of Moscow.\n\nAbstract\nIn this talk\ , we classify linear (as well as some special nonlinear) scalar diff\neren tial operators of order $k$ on $n$-dimensional manifolds with respect to t he diffeomorphism pseudogroup.\n Cases\, when $k = 2$\, $\\forall n$\ , and $k = 3$\, $n = 2$\, were discussed before\, and now we consider case s $k\\ge5$\, $n = 2$ and $k\\ge4$\, $n = 3$ and $k\\ge3$\, $n\\ge4$. In al l these cases\, the fields of rational differential invariants are generat ed by the 0-order invariants of symbols.\n\nThus\, at first\, we consider the classical problem of Gl-invariants of $n$-ary forms. We'll illustrate here the power of the differential algebra approach to this problem and sh ow how to find the rational Gl-invariants of $n$-are forms in a constructi ve way.\n\nAfter all\, we apply the $n$ invariants principle in order to g et (local as well as global) normal forms of linear operators with respect to the diffeomorphism pseudogroup.\n\nDepending on available time\, we sh ow how to extend all these results to some classes of nonlinear operators. \n LOCATION:https://master.researchseminars.org/talk/GDEq/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Tsarev\, Folkert Müller-Hoissen\, Dmitry Millionschikov\, Boris Konopelchenko DTSTART;VALUE=DATE-TIME:20221214T140000Z DTEND;VALUE=DATE-TIME:20221214T180000Z DTSTAMP;VALUE=DATE-TIME:20241013T134851Z UID:GDEq/78 DESCRIPTION:Title: One day workshop in honor of Maxim Pavlov's 60th birthday\nby Ser gey Tsarev\, Folkert Müller-Hoissen\, Dmitry Millionschikov\, Boris Konop elchenko as part of Geometry of differential equations seminar\n\nLecture held in room 303 of the Independent University of Moscow.\n\nAbstract\n\n

\n

- \n
- Integrable systems of Jordan bl ock type and modified KP hierarchy\; \n
- Hamiltonian aspects of quas ilinear systems of Jordan block type\; \n
- Example: delta-functional reductions of the soliton gas equation. \n