The program of the school includes series of main lectures, workshop and poster session. The following programme is tentative and is updated regularly.

The timetable of the Scientific Program: PDF

Courses

A) Foundations of Finsler Geometry and its Generalizations

A1) Finsler and pseudo-Finsler geometry - a fresh look at a century-old problem (Nicoleta Voicu):

The lectures present a completely coordinate-free treatment of variational problems in Finsler and pseudo-Finsler spaces, based on differential forms and Lie derivatives. 

Contents: 

- A brief history of Finsler geometry. Tangent bundle, pulled-back bundle, projectivised sphere bundle approaches. Basic Finslerian geometric objects.

- Coordinate-free variational calculus on Finsler spaces. Lepage forms, first and second variation formulas, Noether currents.

- Mathematical aspects of Finslerian relativity. Pseudo-Finsler spaces and their specific problems: singularities of metric tensor, non-compactness of indicatrix. Field-theoretical functionals on pseudo-Finsler spaces and their extremals.

A2) Variational foundations of Finsler geometry: Projective spaces, Grassmann bundles and the Hilbert form (Demeter Krupka)

Contents: PDF


B) Geometric control theory, sub-Riemannian geometry, and their applications in robotics and vision (Yuri Sachkov)

Lecture 1: Introduction to geometric control (Smooth manifolds, vector fields and flows, Lie brackets. Dynamical and control systems. Statement of controllability and optimal control problems. Examples of control problems: stopping a train, linear oscillator, car with trailers, Dubins car, rotations of rigid body, rolling sphere, curve reconstruction, quantum systems.)

Lecture 2: Controllability and attainability (Controllability of linear systems. Local controllability of nonlinear systems. Orbit theorem. Frobenius theorem. Attainable sets of full-rank systems.)

Lecture 3: Optimal control problems (Existence of optimal controls (Filippov's theorem). Elements of symplectic geometry. Necessary optimality conditions (Pontryagin maximum principle). Solution to optimal control problems.)

Lecture 4: Controllability and optimal control on Lie groups (Lie groups, Lie algebras, homogeneous spaces. Left-invariant control systems on Lie groups. Controllability of left-invariant and bilinear systems. Elements of sub-Riemannian geometry. Sub-Riemannian geometry on Lie groups (Heisenberg group, SO(3), SL(2), Engel group, Cartan group).)

Lecture 5: Applications. (The plate-ball problem. Mobile robots with trailers. Euler elasticae. Image inpainting. Vessel tracking and diabetic retinopathy diagnostics.)

Literature

- A.A. Agrachev, Yu.L. Sachkov, Control Theory from the Geometric Viewpoint, Springer-Verlag, 2004.

- A.A. Agrachev, D. Barilari, and U. Boscain, Introduction to Riemannian and sub-Riemannian geometry, https://webusers.imj-prg.fr/ davide.barilari/Notes.php.

- Yu.L. Sachkov, Controllability and symmetries of invariant systems on Lie groups and homogeneous spaces (in Russian), Moscow, Fizmatlit, 2007.

- Yu.L. Sachkov, Control Theory on Lie Groups, Journal of Mathematical Sciences, Vol. 156, No. 3, 2009, 381-439.

Workshop

The Workshop will have two sections:
      A. 100 years after Finsler - Foundations and advances in Finsler geometry (organizer: N. Voicu)
      B. Geometric control theory (organizer: Yu. Sachkov).

The goal is to present recent results in differential geometry, geometric control theory, and applications. Presentations of posters are also possible. The concrete workshop program of oral contributions will be scheduled with respect to the number of registered talks.

Note that the lecture series and the workshop program will be conducted independetly, so that all participants may attend both.

Workshop talks

Tadashi  Aikou Negativity of holomorphic vector bundles and complex Finsler structures
Chang-Wan  Kim Rigidity theorems in Finsler geometry (poster)
Demeter  Krupka Variational forces
Chayan Kumar  Mishra Curvature Inheritance symmetry on Finsler space
Bankteshwar  Tiwari  TBA
Praveen  Agarwal Note on Multple Gamma functions and Multiple Hurwitz zeta functions
Xinyue  Cheng TBA
Dipankar  Debnath On N(k) mixed quasi Einstein manifold and some global properties
CTJ  Dodson Information geometry as a possible control tool
Manuel Hohmann Cosmological observations in Finsler spacetimes
Miguel Angel  Javaloyes On the definition and examples of cones and Finsler spacetimes
Young Ho  Kim Application of Laplace operator on manifolds
Ville Kivioja Classification of Lie groups by metric geometry
Enrico Le Donne Tangents of sub-Riemannian geodesics
Huageng Liu  Discrete optimal control of a car on the sphere
Colin MacLaurin Time slicings of black holes
Kishore  Marathe What is Physical Mathematics?
Mohamed  Menad Subdivision schemes in modelling geometry (poster)
Terhi Moisala Infinite-dimensional Carnot groups and Rademacher's theorem
Gilbert  Nibaruta Conformal change of Chern connection
Alvaro Pampano Criticality of Sub-Riemannian Geodesics Projections and Applications
Dhriti Sundar Patra The Fisher-Marsden conjecture on contact manifold
Ioan Radu Peter Hardy type inequaliities in Finsler geometry
Christian  Pfeifer Finsler spacetimes
Liviu  Popescu Lie algebroids framework for drift-less control affine systems
Paul  Popescu Constructions and examples related to skew-symmetric algebroids
Ghanashyam Kumar Prajapati On Semi C-Reducibility of general (α, β)-Finsler metrics
Matthew Romney Quasiconformal mappings on sub-Riemannian manifolds
Narasimhamurthy  Senajji Kampalappa Einstein theory of Finsler-Randers Cosmological Model
Hemangi  Shah Geometry  of  Asymptotically  Harmonic  Manifolds with Minimal  Horospheres
Gao  Shan Hamel's field variational integrators for geometrically exact beam and Chaplygin-Timoshenko sleigh
Gauree  Shanker TBA
Sarita  Singh Parametric Experimental & Numerical Study of Human Bifurcated Artey with their topological behaviour
Francesca Tripaldi $\\ell^{q,1}$-cohomology of Heisenberg groups
Zbynek Urban Global variational principle
Paweł  Walczak Integral formulae for codimension-one foliated Randers spaces (O)

Social program

Excursions will be organized on Wednesday, August 22. We offer three options: either a trip to castles and Saxon fortresses around Brasov, or a hiking trip in Piatra Craiului National Park (hiking boots are necessary for the hiking trip), or a tour of the city of Brasov.

On Thursday, August 23 in the evening, a conference dinner will take place in Brasov.