## Graduate Seminar on New Developments in PDE (S5B3)

In this research-oriented seminar we will discuss recent topics in Calculus of Variations and Inverse Problems.

This semester, we will mainly have student and internal speakers with some external guests.

**Info:** All the talks take place on **Friday** in room **SR 0.008**, **from 14 (c.t.) to 16**, unless otherwise specified (have a look at the news section below).

You found information of past semesters seminar in the corresponding subpages (on left navigation bar).

**News:** none.

## Calendar

- 12.04.2024:
**Preliminary organizational meeting**

- 19.04.2024:
**Camillo Tissot**In this talk we compare lower scaling estimates for a sharp and diffuse interface penalization of a double-well elastic energy.

Comparing lower scaling estimates for different surface penalizations

Abstract:

The results presented in this talk are based on [B. Zwicknagl, ARMA 2014].

- 26.04.2024:
**Hendrik Baers**

**Instability of the Fractional 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. We consider the fractional formulation of the problem and prove exponential instability.

- 03.05.2024:
**Lena Siemer**

**Sets of finite perimeter and the Direct Method**the results presented in this talk come from Chapter 12 of the book "Sets of Finite Perimeter and Geometric Variational Problems" by Francesco Maggi (2012)

Note^{1}:

**Note**this talk takes place in room N 0.007 (Neubau), due to the unavailability of the usual room^{2}:

- 10.05.2024:
**Friederike Schmid**

**The influence of surface energy on stress-free microstructures in shape memory alloys**

**Note:**the results presented in this talk come from the homonymous paper from Georg Dolzmann and Stefan Müller (1995)

- 17.05.2024:
**Oskar Engelfried**

**Energy scaling law for a singularly perturbed four-gradient problem in helimagnets to martensites**the results presented in this talk come from the homonymous paper from Janusz Ginster and Barbara Zwicknagl (2023)

Note:

- 31.05.2024:
**Linus Engelfried**

**On scaling laws for multi-well nucleation problems without gauge invariances**

**Note:**the results presented in this talk come from the homonymous paper from Angkana Rüland and Antonio Tribuzio (2023)

- 07.06.2024:
**Xiaopeng Cheng**

**Uniform energy distribution for an isoperimetric problem with long-range interactions**

**Note:**the results presented in this talk come from the homonymous paper from Giovanni Alberti, Rustum Choksi, and Felix Otto (2009)

- 14.06.2024:
**Leon Hamann**

**Asymptotic shape of isolated magnetic domains**

**Note:**the results presented in this talk come from the homonymous paper from Hans Knüpfer and Dominik Stantejsky (2022)

- 21.06.2024:
**Amavin Pasindu Pereira**

**On an isoperimetric problem with a competing nonlocal term I: The planar case**

**Note:**the results presented in this talk come from the homonymous paper from Hans Knüpfer and Cyrill Muratov (2013)

- 05.07.2024:
**Michel Alexis**

**How to represent a function in a quantum computer?**Quantum Signal Processing (QSP) is a process by which one represents a signal $f: [0,1] \to [-1,1]$ as the imaginary part of the upper left entry of a product of $SU(2)$ matrices parametrized by the input variable $x \in [0,1]$ and some ``phase factors'' $\{\psi_k\}_{k \geq 0}$ depending on $f$. QSP was well-understood for polynomial signals $f$, but not for arbitrary signals $f :[0,1] \to (-1,1)$. Our recent work addresses more general classes of signals by using the $L^2$ theory of nonlinear Fourier analysis. Namely, after a change of variables, QSP is actually the $SU(2)$ model of the nonlinear Fourier transform, and the phase factors $\{\psi_k\}_k$ correspond to the nonlinear Fourier coefficients. Then, by exploiting a nonlinear Plancherel identity and a contraction mapping, we will show that QSP can be extended to all signals $f$ bounded in absolute value by $\frac{1}{\sqrt{2}}$. This is joint work with Gevorg Mnatsakanyan and Christoph Thiele.

Abstract:

**Note:**this will be a joint appointment with the groups of Quantum Signal Processing and Harmonic Analysis

- 12.07.2024:
**Linus Elias Münch**

**T5-Configurations and non-rigid sets of matrices**

**Note:**the results presented in this talk come from the homonymous paper from Clemens Förster and László Székelyhidi (2017)