Page 59 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 59
INVITED SPEAKERS
References
[1] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Universality of Euler flows and flexi-
bility of Reeb embeddings, arXiv:1911.01963.
[2] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Constructing Turing com-
plete Euler flows in dimension 3. PNAS May 11, 2021 118 (19) e2026818118;
https://doi.org/10.1073/pnas.2026818118.
[3] R. Cardona, E. Miranda and D. Peralta-Salas, Turing universality of the incompressible
Euler equations and a conjecture of Moore, arXiv:2104.04356 .
[4] J. Etnyre, R. Ghrist. Contact topology and hydrodynamics I. Beltrami fields and the Seifert
conjecture. Nonlinearity 13 (2000) 441–458.
[5] C. Moore. Generalized shifts: unpredictability and undecidability in dynamical systems.
Nonlinearity 4 (1991) 199–230.
[6] T. Tao. On the universality of potential well dynamics. Dyn. PDE 14 (2017) 219–238.
[7] T. Tao. On the universality of the incompressible Euler equation on compact manifolds.
Discrete Cont. Dyn. Sys. A 38 (2018) 1553–1565.
[8] T. Tao. Searching for singularities in the Navier-Stokes equations. Nature Rev. Phys. 1
(2019) 418–419.
Bayesian inverse problems, Gaussian processes, and PDEs
Richard Nickl, nickl@maths.cam.ac.uk
University of Cambridge, United Kingdom
The Bayesian approach to inverse problems has become very popular in the last decade after
seminal work by A. Stuart (2010). Particularly in nonlinear applications with PDEs and when
using Gaussian process priors, this can leverage powerful MCMC algorithms to tackle difficult
high dimensional and nonconvex inference problems, with associated uncertainty quantification
methodology. We review the main ideas and then discuss recent progress on rigorous mathe-
matical performance guarantees for such algorithms. We will touch upon issues such as how
to prove posterior consistency theorems, how to objectively validate posterior based statistical
uncertainty quantification, as well as the polynomial time computability of posterior measures
in some nonconvex model examples arising with PDEs.
Topology of symplectic fillings of contact 3-manifolds
Burak Özbag˘ci, bozbagci@ku.edu.tr
Koç University, Turkey
Ever since Donaldson showed that every symplectic 4-manifold admits a Lefschetz pencil and
Giroux proved that every contact 3-manifold admits an adapted open book decomposition, at
the turn of the century, Lefschetz fibrations and open books have been used fruitfully to obtain
57
References
[1] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Universality of Euler flows and flexi-
bility of Reeb embeddings, arXiv:1911.01963.
[2] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Constructing Turing com-
plete Euler flows in dimension 3. PNAS May 11, 2021 118 (19) e2026818118;
https://doi.org/10.1073/pnas.2026818118.
[3] R. Cardona, E. Miranda and D. Peralta-Salas, Turing universality of the incompressible
Euler equations and a conjecture of Moore, arXiv:2104.04356 .
[4] J. Etnyre, R. Ghrist. Contact topology and hydrodynamics I. Beltrami fields and the Seifert
conjecture. Nonlinearity 13 (2000) 441–458.
[5] C. Moore. Generalized shifts: unpredictability and undecidability in dynamical systems.
Nonlinearity 4 (1991) 199–230.
[6] T. Tao. On the universality of potential well dynamics. Dyn. PDE 14 (2017) 219–238.
[7] T. Tao. On the universality of the incompressible Euler equation on compact manifolds.
Discrete Cont. Dyn. Sys. A 38 (2018) 1553–1565.
[8] T. Tao. Searching for singularities in the Navier-Stokes equations. Nature Rev. Phys. 1
(2019) 418–419.
Bayesian inverse problems, Gaussian processes, and PDEs
Richard Nickl, nickl@maths.cam.ac.uk
University of Cambridge, United Kingdom
The Bayesian approach to inverse problems has become very popular in the last decade after
seminal work by A. Stuart (2010). Particularly in nonlinear applications with PDEs and when
using Gaussian process priors, this can leverage powerful MCMC algorithms to tackle difficult
high dimensional and nonconvex inference problems, with associated uncertainty quantification
methodology. We review the main ideas and then discuss recent progress on rigorous mathe-
matical performance guarantees for such algorithms. We will touch upon issues such as how
to prove posterior consistency theorems, how to objectively validate posterior based statistical
uncertainty quantification, as well as the polynomial time computability of posterior measures
in some nonconvex model examples arising with PDEs.
Topology of symplectic fillings of contact 3-manifolds
Burak Özbag˘ci, bozbagci@ku.edu.tr
Koç University, Turkey
Ever since Donaldson showed that every symplectic 4-manifold admits a Lefschetz pencil and
Giroux proved that every contact 3-manifold admits an adapted open book decomposition, at
the turn of the century, Lefschetz fibrations and open books have been used fruitfully to obtain
57
