Mihajlo Cekić I am an SNSF Ambizione Fellow at University of Zurich. Previously, I was a postdoc at the Max-Planck Institute for Mathematics, Bonn, and at University of Paris-Saclay. I graduated in 2017 from University of Cambridge under supervision of Gabriel Paternain.

My research interests lie in Geometric Inverse Problems and Chaotic Dynamics, and I often use tools from microlocal analysis. In the former subject, I study the Calderón problem and the related X-ray transforms, as well as length and holonomy inverse problems, while in the latter one, I research hyperbolic and partially hyperbolic dynamics, Pollicott-Ruelle resonances, Ruelle zeta functions, Teichmüller dynamics, as well as eigenfunction concentration.

My wife Danica Kosanović is a mathematician at ETH.

News

22.01.2025 Given two hyperbolic metrics g_1 and g_2 on a surface M, is there an Anosov flow whose marked length spectrum is precisely the arithmetic mean of the geodesic flows of g_1 and g_2? Yes! In my preprint with G.P. Paternain, we revisit the family of Anosov flows with smooth weak bundles constructed by Ghys in 1992 from a completely different PDE-like point of view.
24.05.2025 With T. Lefeuvre, I just completed (after much effort!) a Monograph on Semiclassical Analysis on Principal Bundles. We develop a semiclassical calculus on G-principal bundles P which enables us to study right-invariant differential operators on P. To give a flavour of the theory, the operators in the calculus are pseudodifferential operators on the base and Toeplitz operators on the fibres of the flag bundle F = P/T (where T is a maximal torus of G). We give two main applications:
  1. Dynamical Systems: we show rapid mixing (faster than polynomial) for extensions of Anosov flows to P under suitable conditions; in particular, we show that ergodicity implies rapid mixing for the frame flow in negative curvature .
  2. Spectral Theory: we give explicit conditions under which the horizontal Laplacian defined by a connection on P is hypoelliptic, compute the bottom of the spectrum, and show quantum ergodicity.
9-13.9.2024 With C. Ulcigrai, I am organizing a Workshop on Rigidity phenomena in Dynamics and Spectral Theory at the University of Zurich. We are pleased to confirm there will be four mini-courses:
  1. Marked Length Spectrum Rigidity by T. Lefeuvre
  2. Fractal Uncertainty Principle and Applications by S. Nonnenmacher
  3. Convex Billiards by A. Sorrentino
  4. Poincaré series and Counting Problems by G. Rivière

Upcoming and Recent Talks

4.2.2025   Analysis seminar, IIT Bombay
8-10.1.2025 Workshop on Special Structures in Geometry and Dynamics, Paris