Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...
Alkynes and nitriles are valuable building blocks in organic synthesis and also have multiple applications in chemical biology and materials science. Due to the high availability of tertiary alcohols, developing methods for their conversion into alkynes an ...
The recent discovery of an N2O-based synthesis of triazenes in our group has enabled the synthesis and investigation of 1-alkynyl triazenes. Early studies showed their potential for a functional group tolerant synthesis of 1-vinyl triazenes, which is furth ...
In a group, the collective dynamics is governed by the inter- actions between individuals, which can manifest differently depending on the available means of communication. In this paper, we compare 3 conditions of communication affordances (global chat, l ...
We prove some new cases of the Grothendieck-Serre conjecture for classical groups. This is based on a new construction of the Gersten-Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue ...
Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...
Cyclic peptides are ring-shaped molecules that emerged as a promising class of therapeutics. While it is often difficult to find small molecule binders for challenging disease targets, cyclic peptides can bind to featureless surfaces or inhibit protein-pro ...
In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...
