The unification of Quantum Field Theory and Statistical Mechanics is one of the major's achievements of modern physics. This unification is mostly not understood in a mathematically rigorous way.
My goal is to understand how lattice models in statistical mechanics are connected with field theories. For the 2D Ising model, we have recently made significant progress towards the goal; in particular we have successfully proven a number of conjectures from Conformally Symmetric Quantum Field Theory. We are now working to obtaining a complete correspondence and to extend it to other models and field theories. This will bring much insight to the understanding of lattice models, which in turn are connected to many other fields, such as magnetism, ecology or image processing.
2006: B.Sc. Math, EPFL
2008: M.Sc. Math, EPFL
2010: Ph.D. Math, Université de Genève
2010-2014: Ritt Assistant Professor, Columbia University
2014-...: Tenure-Track Assistant Professor, EPFL
Awards and grants (main)
2011: NSF Grant DMS-1106588
2014: Blavatnik Award for Young Scientists
2016: Erc Starting Grant CONSTAMIS
2017: Latsis University Prize
Teaching & PhD
- Doctoral Program in Mathematics
- Doctoral Program in Electrical Engineering
Lattice models consist of (typically random) objects living on a periodic graph. We will study some models that are mathematically interesting and representative of physical phenomena seen in the real world.
Scheme: an intro, a key theorem, and key ideas of the proofs. Topics include: Dimers and Limit shapes, Ising model and Fermions, Conformal Field Theory and Moonshine, KdV and Inverse Scattering, Quantum Information and Measurement, Complex Dynamics and Ju...