Asymptotics, Operators, and Functionals

Leading the discussion in 2016:

8 February Yulia Ershova (Topic: The inverse topology problem for quantum graphs)

22 February Shane Cooper (Topic: Results, shortcomings and recent developments in high-contrast periodic spectral problems I)

29 February Marcus Waurick (Topic: Invertibility of operators in space-time, and a new approach to the homogenisation of evolutionary equations) Abstract: We present a concept of solving partial differential equations via a space-time Hilbert space approach. Within the approach developed, we provide an operator-theoretic perspective to homogenisation theory and exemplify our findings with a 1+1-dimensional problem of mixed type. In this example, the change of type from hyperbolic to elliptic will be highly oscillatory and the effective equation is studied.

7 March Alexander Kiselev (Kyiv) (Topic: Uniqueness of reconstruction of the topology of a quantum graph from its spectrum, via the analysis of the behaviour of the M-matrix at zero I)

Away: [14 March Conference "Spectral Theory and Applications", Stockholm University, Sweden]

4 April Mikhail Cherdantsev (Cardiff) (Topic: Superexponential decay of defect eigenfunctions in one-dimensional high-contrast media)

11 April Yulia Ershova (Topic: The inverse topology problem for quantum graphs. Part II: Boundary triples and M-matrix)

Away: [18 April Conference "Spectral Theory of Novel Materials" , CIRM, Marseille, France]

25 April Sergey Naboko (St. Petersburg) (Topic: The functional model for maximal dissipative operators and the boundary triples)

Away: [ 9 May SIAM Conference on Mathematical Aspects of Materials Science , Philadelphia, USA]

Away: [ 16 May Conference "Operators, Operator Families and Asymptotics", University of Bath]

Away: [ 22 May Course High-Velocity Estimates, Inverse Scattering and Topological Effects by Ricardo Weder (IIMAS-UNAM, Mexico), at the University of Bath]

Away: [ 6 June Conference "Computational and Analytic Problems in Spectral Theory", Cardiff University, UK]

17 June (Friday) Fritz Gesztesy (Missouri) (Topic: A bound for the eigenvalue counting function for Krein-von Neumann extensions for elliptic second-order partial differential operators on bounded sets) Abstract

Away: [20 June Conference "New Trends in Nonlinear PDEs: from Theory to Applications", Cardiff University, UK]

27 June Kirill Cherednichenko (Topic: Microscale isometry constraint for thin heterogeneous plates with finite bending energy)

4 July Yulia Ershova (Topic: Theorem of Kurasov-Kostrykin-Schrader in the inverse topology problem for graphs, and its shortcomings)

Away: [11, 21 July EPSRC Durham Symposium Mathematical and Computational Aspects of Maxwell's Equations, Durham University, UK]

19 September Alexander Kiselev (Kyiv) (Topic: Uniqueness of reconstruction of the topology of a quantum graph from its spectrum, via the analysis of the behaviour of the M-matrix at zero II)

26 September Igor Velčić (Zagreb) (Topic: Homogenization of thin structures in nonlinear elasticity, periodic and non-periodic) Abstract: We will give the results on the models of thin plates and rods in nonlinear elasticity by doing simultaneous homogenization and dimensional reduction. In the case of bending plate we are able to obtain the models only under periodicity assumption and assuming some special relation between the periodicity of the material and thickness of the body. In the von Kármán regime of rods and plates and in the bending regime of rods we are able to obtain the models in the general non-periodic setting. In this talk we will focus on the derivation of the rod model in the bending regime without any assumption on periodicity.

3 October Kirill Cherednichenko (Topic: Asymptotic expansions as a heuristic and rigorous tool in the analysis of multiscale differential equations)

10 October Yulia Ershova (Topic: Homogenisation: the Krein resolvent formula and operator-norm convergence estimates)

17 October Davit Harutyunyan (EPFL) (Topic: Recent progress in the shell buckling theory) Abstract

31 October Yulia Meshkova (St. Petersburg) (Topic: Homogenization of elliptic and parabolic Dirichlet problems in a bounded domain) Abstract

14 November Yuri Antipov (Luisiana State) (Topic: Singular integral equations with two fixed singularities: theory and applications) Abstract: Motivated by model problems of fracture, the talk focuses on the solution of SIEs with the Cauchy kernel and kernels with fixed singularities at the endpoints. The method developed is based on solving an associated vector Riemann-Hilbert problem with a piece-wise constant matrix coefficient having three discontinuities. In a symmetric case, the number of the discontinuities reduces to two, and the general solution of the SIE is significantly simplified. For a specific right hand-side the solution is expressed in terms of some polynomials with weights, and a spectral relation for the singular integral operator with two fixed singularities is derived. This relation is employed for an approximate solution of the corresponding complete SIE. Applications to model problems of fracture and the theory of composites are discussed.

21 November Harsha Hutridurga (Imperial) (Topic: A new approach to study strong advection problems) Abstract

28 November Shane Cooper (Topic: Results, shortcomings and recent developments in high-contrast periodic spectral problems II)

5 December Marcus Waurick (Topic: Invertibility of operators in space-time, and a new approach to the homogenisation of evolutionary equations)

Away: [12, 19 December Conference "Mathematical and Numerical Modelling in Optics", IMA, Minnesota]