HSM Early Career Colloquium: Jan Bohr, Alessandro Felisi, Zahra Janbazi

Wednesday Nov 25, 2026, 3:15 PM → 4:30 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Jan Bohr

Electrical Impedance Tomography: from the Calderón problem to Finite Measurements 

Can we reconstruct the interior of an object by taking measurements only on its boundary? This question lies at the heart of Electrical Impedance Tomography, a non-invasive imaging technique that aims to recover the electrical conductivity of a body from voltage and current measurements at its surface. In this talk, we will introduce the mathematical foundations of this problem, known as the Calderón problem, and discuss some of the main challenges associated with instability issues. Finally, we will explore how the idealized mathematical setting relates to practical measurements performed using finitely many electrodes, and present some recent results on how many electrodes are sufficient for stable reconstruction.

Alessandro Felisi 

Electrical Impedance Tomography: from the Calderón problem to Finite Measurements

Can we reconstruct the interior of an object by taking measurements only on its boundary? This question lies at the heart of Electrical Impedance Tomography, a non-invasive imaging technique that aims to recover the electrical conductivity of a body from voltage and current measurements at its surface. In this talk, we will introduce the mathematical foundations of this problem, known as the Calderón problem, and discuss some of the main challenges associated with instability issues. Finally, we will explore how the idealized mathematical setting relates to practical measurements performed using finitely many electrodes, and present some recent results on how many electrodes are sufficient for stable reconstruction.

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Zahra Janbazi 

Boundedness of average rank of elliptic curves ordered by the coeddicients

In arithmetic statistics, elliptic curves E_{A,B}: y² = x³ + Ax + B are typically ordered by the naive height H(E_{A,B}) = max{4|A|³, 27B²}, which effectively orders them by the size of their roots. In this paper, we instead consider the height h(E_{A,B}) = max{|A|, |B|}, which orders curves by the magnitudes of their coefficients. We prove that the average size of the 2-Selmer group under this ordering is at most 3, matching the bound established by Bhargava and Shankar for the naive height. To study these 2-Selmer groups, we analyze integral binary quartic forms in non-uniformly expanding regions determined by the height function. We develop a new technique for counting lattice points and establishing their equidistribution in these regions, where standard methods do not suffice.