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Workshop organised by Oliver Gregory, Christian Liedtke, Alexei Skorobogatov and funded by the TUM-ICL Mathematical Sciences Hub

To personalize cancer radiation therapy, we must give the right dose and dose fractionation, at the right time, dynamically adapted, to best harness the radiobiological effects of radiation as well as synergy with the patient’s immune system. I present latest developments in the mathematical and computational modelling in radiation oncology to develop digital twins – constructs that mimic the structure and behavior of the patient and the tumor to make predictions and inform decisions that realize value. I present different simple approaches to build predictive pipelines and how to integrate those into clinical decision making towards the concept of real-time adaptive personalized radiation treatments.

A central issue in modern Galois theory is the profinite inverse Galois problem, which asks how to characterize absolute Galois groups of fields among all profinite groups. While an answer to this question is unknown, even conjecturally, several necessary conditions for a profinite group to qualify as an absolute Galois group have been established. The most classical result in this direction is due to Artin and Schreier, who proved that every non-trivial finite subgroup of an absolute Galois group is cyclic of order 2. A much deeper necessary condition is the Bloch-Kato conjecture, now a theorem due to Voevodsky and Rost, which in particular implies that the mod p cohomology ring of an absolute Galois group of a field containing a primitive p-th root of unity is generated in degree 1 with relations in degree 2. In the lecture, we will discuss restrictions to the profinite inverse Galois problem coming from the embedding problem with abelian kernel. This is a joint work with Federico Scavia. _______________ Invited by Prof. Nikita Geldhauser