Past Inverse problems talks
Past Inverse problems talks
Time & Location: Tuesday, 2 December at 15:00, room MaD245
Speaker: Shubham Jaiswal
Slides:📄
Title: An inverse source problem for a quasilinear elliptic equation
Abstract: We study inverse source problems for quasilinear elliptic equations i.e. div( γ(x, u, ∇u ) · ∇u ) = F in Ω, u = f on ∂Ω, on a bounded domain Ω in ℝⁿ, n ≥ 2. We consider the nonlinearity of the form γ(x, u, ∇u) = σ + qu, and use nonlinearity to break the gauge invariance of the inverse source problem for this type. For this, we try to recover the γ(x, u, ∇u) and F(x) uniquely from the related Dirichlet-to-Neumann (DN) map. Here, nonlinearity helps, since for a linear equation it is not possible to recover both the conductivity and the source term. The method we use is the higher order linearization method. The key idea is to use unique continuation results for a coupled elliptic system.
Speaker: Pieti Kirkkopelto
Slides:📄
Title: Horizontal and vertical regularity of elastic wave geometry
Abstract: The elastic properties of a material are encoded in a stiffness tensor field and the propagation of elastic waves is modeled by the elastic wave equation. We characterize analytic and algebraic properties a general anisotropic stiffness tensor field has to satisfy in order for Finsler-geometric methods to be applicable in studying inverse problems related to imaging with elastic waves.
Time & Location: Tuesday, 25 November at 15:00, room MaD245
Speaker: Divyansh Agrawal
Slides:📄
Title: Unique and non-unique continuation of the d-plane transform
Abstract: The d-plane transform maps functions to their integrals over d-planes (d-dimensional affine subspaces) in ℝⁿ. For d = n − 1 and d = 1, it coincides with the classical Radon and X-ray transforms respectively. We consider the following question: If a function vanishes in a bounded open set, and its d-plane transform vanishes on all d-planes intersecting the same set, does the function vanish identically? We give a complete answer to the above question. It turns out, surprisingly, (or not!) that the answer depends on the parity of d. For d an even integer, we show by producing an explicit counterexample that neither the d-plane transform nor its normal operator has this property. On the other hand, for d odd, the question above has an affirmative answer. The proofs use some classical tools from Harmonic analysis and integral geometry, together with some geometric and analytic tricks. Based on a joint work with Nisha Singhal.
Speaker: William Trad
Slides:📄
Title: Mean soujourn time and eigenvalue asymptotic expansions
Abstract: I will briefly describe how pseudo-differential operators can be used to derive the mean sojourn time for a Brownian motion on a Riemannian manifold. Methods used in the derivation of the mean sojourn time can also be used to derive eigenvalue asymptotic expansions. What appears ubiquitously throughout our results is the dependence on geometric quantities such as the mean and principal curvatures.
Time & Location: Tuesday, 18 November at 15:00, room MaD245
Speaker: Henri Hänninen
Slides:📄
Title: Towards indirect measurement of the gluonic structure of the proton
Abstract: I will discuss our recent theoretical physics paper where we formulated the inference of the dipole amplitude into a proper inverse problem for the first time. The dipole amplitude is related to the gluon density inside the proton at high energy. To give some context for the problem, I will begin with a crash course into high energy particle physics, what the proton is made of, and how inverse problems can help answer open questions about the structure of the proton and the strong nuclear force.
Time & Location: Tuesday, 11 November at 15:00, room MaD245
Speaker: Eetu Satukangas
Title: Tomography of 1-forms in gas giant geometry
Abstract: Gas giant geometry is a special type of Riemannian manifold with boundary that describes acoustic wave propagation in gas giant planets. In this presentation I will discuss some properties of the geometry and present a new result for the (solenoidal) injectivity of the geodesic ray transform of 1-forms in gas giant geometry.
Time & Location: Tuesday, 4 November at 14:45, room MaD245
Speaker: Ashwin Tarikere Ashok Kumar Nag
Title: Propagation of polarization sets
Abstract: We will study the concept of polarization sets for vector valued distributions, which is a refinement of wavefront sets introduced by Dencker in 1981. We will also look at how polarization sets propagate for solutions of systems of real principal type.
Time & Location: Tuesday, 28 October at 15:00, room MaD245
Speaker: Antonio Pop-Gorea
Title: Characterization of elastic reducibility in 2D
Abstract: It has been shown in dimension two that slowness polynomials are generically irreducible. We give a characterization in dimension two that a stiffness tensor has to satisfy so that its induced slowness polynomial is stably solvable. We thus define the notion of a rectangular stiffness tensor and show that irreducibility of a slowness surface breaks down within this condition. Furthermore, we also show that uniqueness is no longer guaranteed and hence injectivity fails for rectangular stiffness tensors. In fact non-uniqueness is equivalent to rectangularity of a stiffness tensor. We also show that avoiding the rectangular stiffness tensors will lead to stability. All of these results then imply stable solvability for non-rectangular stiffness tensors.
Time & Location: Tuesday, 21 October at 15:00, room MaD245
Speaker: Joonas Ilmavirta
Slides:📄
Title: Spectral perturbation theory
Time & Location: Tuesday, 14 October at 15:00, room MaD245
Speaker: Inverse problems research group
Title: Meet the Inverse problems research group
Abstract: All the speakers of the seminar series shortly introduce themselves and their research.