Graduate Seminar on New Developments in PDE (S5B3)
In this research-oriented seminar we discussed recent topics in Calculus of Variations and Inverse Problems.
The seminar is held by Prof. Angkana Rüland and Antonio Tribuzio.
Find the schedule below.
At following link, you can have a look at the programs of the last semesters to get an idea
Info: the seminar will take place on Fridays from 14 c.t. to 16, in room N 0.003.
News: the next appointment on Friday, November 7 will take place from 13:00 (sharp) to 14:00, in room N 0.007 (Neubau).
Calendar
17.10.2025: Guillermo Pérez
The Calderón Problem for fractional Schrödinger operators with a drift term on closed manifold
Abstract: In this talk we will study an analog of the original Calderón problem for the case of a fractional Schrödinger operator with a gradient term. We will prove that under the right conditions, with only the Cauchy data given by the operator on an observable set, we can reconstruct an unknown closed Riemannian manifold up to a diffeomorphism.
The novelty of our result is that besides the reconstruction of the metric, we can also recover the potential and drift term up to a gauge transformation if time allows it we will also discuss how to generalize it to the case where we have higher order terms.
This results are in collaboration with Angkana Rüland and come from the work on my master thesis as well as the recent paper by T. Cai and X. Chen (2025).
24.10.2025: Hendrik Baers
Quantitative reduction of a nonlocal Calderón type problem to the local Calderón problem
Abstract: The Calderón problem is one of the classic examples of an inverse problem. It is about determining the conductivity of a medium by making voltage and current measurements on its boundary. Some of the main questions of interest are about uniqueness and stability of this reconstruction.
In this talk, we will consider the fractional (or nonlocal) and the local formulation of a Calderón type problem and discuss how these two are related. In particular, we will show that stability estimates for the local problem can be transferred to stability estimates for the nonlocal problem.
The results presented in this talk are based on joint work with Angkana Rüland.
31.10.2025: Alessandro Felisi
Subsampled inverse problems, sparsity, and compressed sensing
Abstract: In this talk, I will discuss a class of linear inverse problems in which severe ill-posedness arises from subsampling a more stable problem. Such settings are motivated, among others, by medical imaging applications such as Magnetic Resonance Imaging, Computed Tomography, and Photoacoustic Tomography. I will explain how certain sparsity priors - arising naturally in these applications - can be leveraged to regularize the inverse problem through suitable randomized measurements. Finally, I will show how tools from compressed sensing theory allow one to precisely quantify the relation between the number of measurements required to stabilize the problem and the intrinsic dimensionality of the sparsity prior.
- 07.11.2025: Timo Hofmann
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Abstract: tba
- 14.11.2025: Daniel Linn
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- 21.11.2025: Edvin Svenungsson
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- 28.11.2025: Christian Noaghiu & Mija Delija
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- 05.12.2025: Lennart Machill
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12.12.2025: Oskar Engelfried
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Abstract: tba- 19.12.2025: Merry Christmas (i.e. no meeting)
- 09.01.2026: Linus Engelfried
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- 16.01.2026: Antonio Tribuzio
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- 23.01.2026: Noah Piemontese-Fisher
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- 30.01.2026: tba
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