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SUMMARY:HSM Early Career Colloquium: Jan Bohr\, Alessandro Felisi\, Zahra 
 Janbazi
DTSTART:20261125T141500Z
DTEND:20261125T153000Z
DTSTAMP:20261109T222000Z
UID:indico-event-1760@math-events.uni-bonn.de
CONTACT:hsm-contact@uni-bonn.de
DESCRIPTION:Jan Bohr\nElectrical Impedance Tomography: from the Calderón 
 problem to Finite Measurements \nCan we reconstruct the interior of an ob
 ject by taking measurements only on its boundary? This question lies at th
 e heart of Electrical Impedance Tomography\, a non-invasive imaging techni
 que that aims to recover the electrical conductivity of a body from voltag
 e and current measurements at its surface. In this talk\, we will introduc
 e the mathematical foundations of this problem\, known as the Calderón pr
 oblem\, and discuss some of the main challenges associated with instabilit
 y issues. Finally\, we will explore how the idealized mathematical setting
  relates to practical measurements performed using finitely many electrode
 s\, and present some recent results on how many electrodes are sufficient 
 for stable reconstruction.\nAlessandro Felisi \nElectrical Impedance Tomo
 graphy: from the Calderón problem to Finite Measurements\nCan we reconstr
 uct the interior of an object by taking measurements only on its boundary?
  This question lies at the heart of Electrical Impedance Tomography\, a no
 n-invasive imaging technique that aims to recover the electrical conductiv
 ity of a body from voltage and current measurements at its surface. In thi
 s talk\, we will introduce the mathematical foundations of this problem\, 
 known as the Calderón problem\, and discuss some of the main challenges a
 ssociated with instability issues. Finally\, we will explore how the ideal
 ized mathematical setting relates to practical measurements performed usin
 g finitely many electrodes\, and present some recent results on how many e
 lectrodes are sufficient for stable reconstruction.\n.\nZahra Janbazi \nB
 oundedness of average rank of elliptic curves ordered by the coeddicients 
 \nIn 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 pape
 r\, we instead consider the height h(E_{A\,B}) = max{|A|\, |B|}\, which or
 ders curves by the magnitudes of their coefficients. We prove that the ave
 rage size of the 2-Selmer group under this ordering is at most 3\, matchin
 g the bound established by Bhargava and Shankar for the naive height. To s
 tudy these 2-Selmer groups\, we analyze integral binary quartic forms in n
 on-uniformly expanding regions determined by the height function. We devel
 op a new technique for counting lattice points and establishing their equi
 distribution in these regions\, where standard methods do not suffice.\n\n
 https://math-events.uni-bonn.de/event/1760/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1760/
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