# Mathematics Colloquium Fall 2019

For further information please call the Mathematics Department at 459-2969

**Tuesday, October 8th, 2019**

**Frederic Faure, Joseph Fourier University**

*Emergence of the quantum wave equation in classical deterministic hyperbolic dynamics*

In the 80's, D. Ruelle, D. Bowen and others have introduced probabilistic and spectral methods in order to study deterministic chaos ("Ruelle resonances"). For example, a geodesic flow on a strictly negative curvature Riemannian manifold is chaotic: each trajectory is strongly unstable and its behavior is unpredictable. A smooth probability distribution evolves also in a complicated way since it acquires higher and higher oscillations. Nevertheless this evolution is predictable in the sense of distributions and converges towards equilibrium. Following this approach and use of microlocal analysis, one obtains that long time fluctuations of classical probabilities are described by an effective quantum wave equation. This may be surprising because there is no added quantization procedure. We will explain the concepts and results using different simple models. Joint work with Masato Tsujii.

**Tuesday, October 15th, 2019**

**Eduardo Fuertes**

**Some new constructions for loops of Legendrians in the standard contact $3$--sphere.**

**Tuesday, October 22nd, 2019**

**Nikhil Savale, University of Cologne**

**Spectrum and Abnormals in Sub-Riemannian geometry: the 4D quasi-contact case**

We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional quasi-contact case. A key role in all results is played by the presence of abnormal geodesics and represents the first such appearance of these in sub-Riemannian spectral geometry

**Tuesday, October 29th, 2019**

**TBA**

**Tuesday, November 5th, 2019**

**Chris Kottke, New College of Florida**

**Tuesday, November 12th, 2019**

**TBA**

**Tuesday,November 19th, 2019**

**TBA**

**Tuesday, November 26th, 2019**

**Bo Guan, Ohio State University**

**Tuesday, December 3rd, 2019**

**TBA**