Function spaces meet materials science: recent developments in spectral theory and scattering
Venue: Room SUM K201, CIMAT, Guanajuato.
The meeting will feature talks highlighting recent progress in the analysis of PDEs and operators of mathematical physics by members of the mathematics departments of the three founding institutions of the series: University of Bath, CIMAT, and UNAM.
The last 10-15 years have been a period of growing intensity in applying (and developing modifications of) abstract methods of function and spectral theory in the context of problems of continuous mechanics, wave propagation and scattering. For example, powerful tools of the analysis of abstract boundary-value problems have recently found an exciting application to the theory of "metamaterials", as media whose non-classical macroscopic behavior is understood in a constructuve way, on the basis of the analysis of resonance effects on the microscale. The abstract functional models for non-self-adjoint operators in a Hilbert space, complemented by asymptotic analysis with respect to length-scale parametres lead to new, quantitatively precise, statements about the behaviour of operator families, and hence prectically relevant models of continuous media.
The goals of the meeting are: a) to give a summary of the progress since the previous BUC in applied analysis in March 2018; b) to introduce new participants of the series to the relevant mathematical background; c) to develop a strategy for the future work and identify potentially fruitful ideas for widening the scope of the existing activity.
Talk schedule
Sunday 16 September:
17:00-19:00: Introduction. Open research discussion.
Monday 17 September
9:30--11:00: Kirill Cherednichenko "Unified approach to critical-contrast homogenisation of PDEs with explicit links to time-dispersive media"
11:00--11:30: Coffee
11:30--13:00: Iván Naumkin "Regularity of solutions and scattering for the nonlinear Schrödinger equation"
13:10-14:20: Lunch at CIMAT
14:30--16:00: Héctor Chang Lara "Further time regularity for parabolic equations"
16:00--16:30: Coffee
16:30--18:30: Open research discussion
Tuesday 18 September
9:30--11:00: Josué Cangas "Spectral characterisation of dissipative extensions of the operator of multiplication in de Branges' spaces"
11:00--11:30: Coffee
11:30--13:00: Luis Silva "Extremal properties of spectral measures"
13:10-14:20: Lunch at CIMAT
14:30--16:00: Isidro Munive "Boundary-value problems: The Neumann problem in the Heisenberg group"
16:00--16:30: Coffee
16:30--18:30: Open research discussion
Wednesday 19 September
9:30--13:00: Open research discussion.
13:10-14:20: Lunch at CIMAT. Closure.
Participants
| Bath | CIMAT | UNAM |
|---|---|---|
|
Kirill Cherednichenko
|
Héctor Chang Lara
Isidro Munive
Stephen Bruce Sontz
|
Josué Cangas
Asaf Levi Franco Arellano
Ivan Naumkin
Luis Octavio Silva
|
Participants of BUC-XV, with a view to Guanajuato from CIMAT