S5B3: Graduate Seminar on New Developments in PDE - Advances in Inverse Problems and the Calculus of Variations
This is a research-oriented seminar focusing on the research interests of the group supervised by Prof. Dr. Angkana Rüland, in particular inverse problems and topics from the calculus of variations.
A preliminary meeting, during which seminar topics will be assigned, will take place in the room 0.011 on February 9 at 4:15 in the room 0.011. If you are unable to attend the preliminary meeting, please send a brief email to mailto:lmachill(at)uni-bonn.de. The seminar takes place on Thursday at 10:15 in N0.007, and the first meeting is on the 16.04.2026.
Calendar
- 16.04.2026: Hendrik Baers
Quantitative reduction of a fractional Calderón problem to the corresponding 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 problem and discuss their relation. We will prove that the fractional problem can be quantitatively reduced to the local one. In particular, 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.
- 23.04.2026: Sofia Raible
Bifurcation analysis of a nonlinear aggregation-diffusion equation
Abstract: In mathematical ecology, aggregation-diffusion equations can be used to model the spatial distribution of animal populations. In this talk, we discuss the bifurcation structure of one such aggregation-diffusion equation, a variant of Carrillo et al.’s McKean-Vlasov equation. We focus on the existence of local bifurcations from the trivial solution as the balance between aggregation and diffusion varies, and briefly touch on questions of stability. We further extend Carrillo et al.’s results for the McKean-Vlasov equation by studying specific scenarios where we can show the existence of multiple bifurcating branches - a phenomenon which had previously only been observed numerically. This talk is based on the speaker's master thesis supervised by Yurij Salmaniw and Ilka Agricola.
- 30.04.2026: Antonio Tribuzio
Homogenization, separation of scales, and examples for a nonlocal thin-film model
Abstract: After having presented a nonlocal model for dimension reduction in this group seminar, this talk will address the question of asymptotic homogenization. In this context, we will see how, when one of the two scale of the model is infinitesimal with respect to the other, a “separation of scales” effect emerges. We will also illustrate this phenomenon by means of a couple of examples. This work is in collaboration with Nadia Ansini (La Sapienza, Rome).
- 07.05.2026: Christian Noaghiu
$T_3$-structures and analysis of a numerical simulation
Abstract: In elasticity theory, a central problem is to describe deformations of a body minimising its elastic energy, i.e. functions minimising a functional $\int_\Omega W(\nabla u)$. In this talk, we first summarise some classical results on nontrivial pointwise exact and approximate minimisers. Notably, the Tartar square and $T_3$-structures are minimal settings in which nontrivial microstructures arise in approximate solutions. The second part of the talk is devoted to an iterative scheme by Kochmann, which is aimed at computing approximate minimisers in the setting of a $T_3$-structure numerically. The core of this scheme is the Euler–Lagrange equation for an entropy-regularised energy functional. Finally, we present some key results on the behaviour of Kochmann's scheme and compare it to a Hessian-regularised version.
Note: This is the defense of the Bachelor's thesis, written under the supervision of Angkana Rüland and Antonio Tribuzio.
- 14.05.2026: Christi Himmelfahrt (i.e. no meeting)
tba
- 21.05.2026: Timo Hofmann
tba
- 28.05.2026: Pfingsten (i.e. no meeting)
tba
- 4.06.2026: Fronleichnam (i.e. no meeting)
tba
- 5.06.2026: Linus Engelfried
Minimal energy for geometrically nonlinear elastic inclusions in two dimensions
Note: The talk takes place on Friday at 4pm (sharp) in room N0.003.
Note: This talk is based on the homonymous paper by I. Akramov, H. Knüpfer, M. Kružík, and A. Rüland from 2024
- 11.06.2026: Noah Piemontese-Fischer
tba
- 12.06.2026: Oscar Engelfried
Characterizations of Symmetric Polyconvexity
Note: The talk takes place on Friday at 4pm (sharp) in room N0.003.
Note: This talk is based on the homonymous paper by O. Boussaid, C. Kreisbeck, and A. Schlömerkemper from 2019
- 18.06.2026: Eske Bockelmann
Optimal fine-scale structures in compliance minimization for a uniaxial load
Note: This talk is based on the homonymous paper by R. V. Kohn and B. Wirth from 2014
- 25.06.2026: Toni Abi Aoun
Geometric rigidity for incompatible fields & an application to strain-gradient plasticity
Note: this talk is based on the homonymous paper by S. Müller, L. Scardia, and C. Zeppieri from 2014
- 2.07.2026: Christian Poggenburg
tba
- 09.07.2026: Daniel Linn
tba
- 16.07.2026: Tamar Bandzeladze
Crystallization in the Winterbottom shape and sharp fluctuation laws
Note: this talk is based on the homonymous paper by M. Friedrich, L. Kreutz, U. Stefanelli from 2025
- 23.07.2026: Jolanda Weygandt
Uniform stability estimates for the discrete Calderón problems
Note: this talk is based on the homonymous paper by S. Ervedoza, F. de Gournay from 2011