** The PDEs and Applications seminar**

Tuesdays 10.15, room 64119, Ångström

Supported by the Swedish Research Council

**Next seminar(s):**

15/10: * Per Sjölin, KTH: * Convergence and localization of Schrödinger means.

22/10: * Douglas Lundholm, Uppsala: * Mathematical methods for uncertainty and exclusion in quantum mechanics

5/11: * Nikos Katzourakis, University of Reading: * TBA

12/11: * Andrew Morris, University of Birmingham: * TBA

19/11: * David Maxwell, University of Alaska Fairbanks : * TBA

26/11: * Irina Mitrea, Temple University: * TBA

3/12: * Alan Sola, SU: * TBA

10/12: * Iwona Chlebicka, University of Warsaw: * TBA

8/10: * Oliver Lindblad Petersen, University of Hamburg: * Wave equations close to Cauchy and event horizons and applications in general relativity

Is there a general mathematical obstruction to time travel?

Is the known model for a stationary black hole the only one mathematically possible?

1/10: * Anders Israelsson, Uppsala: * Boundedness of Schrödinger Integral Operators in Sobolev Spaces

24/9: * Anton Savostianov, Uppsala: * Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations

17/9: * Rostyslav Kozhan, Uppsala: * Central Limit Theorem for linear statistics for orthogonal polynomial ensembles on the unit circle

10/9: * Erik Ekström, Uppsala: * Degenerate Equations and Boundary Conditions in Finance

3/9: * Andreas Strömbergsson, Uppsala: * Kinetic theory for the low-density Lorentz gas

11/6: Felix del Teso, BCAM, Bilbao: * The Liouville Theorem for Nonlocal Operator (and its relation to irrational numbers and subgroups of R^N. *

First, we will treat the one dimensional case. Here we give a precise classification for which the Liouville Theorem holds. The condition will be related to irrational numbers ([1]).

In the multi dimensional case such a characterization is also proved. This time it will be given in terms of additives subgroups of R^N ([1]).

This nonlocal result will allow us ([2]) to give a full characterization of the Liouville property for any linear operator (local + nonlocal, and not necessarily symmetric) with constant coefficients satisfying the maximum principle (see [3]).

References:

[1] N. Alibaud, F. del Teso, J. Endal, and E. R. Jakobsen. Characterization of nonlocal diffusion operators satisfying the Liouville theorem. Irrational numbers and subgroups of R^d. Preprint: arXiv:1807.01843.

[2] N. Alibaud, F. del Teso, J. Endal, and E. R. Jakobsen. The Liouville theorem and linear operators satisfying the maximum principle. A complete characterization in the constant coefficient case. Work in progress.

[3] P. Courrege. Generateur infinitesimal d'un semi-groupe de convolution sur R^n, et formule de Levy-Khinchine. Bull. Sci. Math. (2), 88:3-30, 1964. Joint work with N. Alibaud (Laboratorie de Mathematiques de Besancon), J. Endal and E. R. Jakobsen (Norwegian University of Science and Technology).

21/5: * Kaj Nyström, Uppsala: * On a strongly degenerate parabolic equation of Kolmogorov.

21/5: * Julie Rowlett, Göteborg: * Analysis and geometry on asymptotically hyperbolic manifolds and convex-cocompact manifolds with variable negative curvature

14/5: KTH-Uppsala PDE-Day, UU

7/5: Eric Schippers: * Schiffer operators on Riemann surfaces and the jump formula for quasicircles *

23/4, 10.15: * Erik Lindgren, Uppsala: * Infinity-harmonic potentials in convex rings

9/4, 10.15: Stephen McCormick: * Quasi-local mass in general relativity and some recent developments on Bartnik's definition *

2/4, 10.15: Benny Avelin, Uppsala: * Introduction to deep learning, continued *

26/3, 10.15: Alejandro Luque, Uppsala: * Oscillatory integrals and the problem of splitting of separatrices *

26/3, 11.15: Benny Avelin, Uppsala: * Introduction to deep learning, continued *

19/3: 10.15: Anna Sakovich, Uppsala: * On zero mass limit in mathematical general relativity *

19/3, 11.15: Benny Avelin, Uppsala: * Introduction to deep learning, continued *

12/3, 10.15: Linnea Gyllingberg, Uppsala: * Deriving macroscopic equations for complex systems *

12/3, 11.15: Benny Avelin, Uppsala: * Introduction to deep learning, continued *

26/2: Vesa Julin, Jyväskylä: * The Gaussian Isoperimetric Problem for Symmetric Sets *

19/2, 10.15: Benny Avelin, Uppsala: * Introduction to deep learning. *

19/2, 11.15: Avner Kiro, Tel Aviv: * Power substitution in quasianalytic Carleman classes. *

12/2: Stefano Borghini, Uppsala: * Riemannian methods in potential theory. *

29/1: Wolfgang Staubach, Uppsala: * Oscillatory integrals and partial differential equations*

5/2: Bruno Vergara, ICMAT: *Convexity of Whitam's wave of extreme form. *

**Organizers:** Benny Avelin, Erik Lindgren and Kaj Nyström