STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

Bott–Thom isomorphism, Hopf bundles and Morse theory

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable range, to mapping spaces associated to orthogonal Clifford representations. Given an oriented Euclidean bundle $$V \rightarrow X$$ V → X of rank divisible by four over a finite complex X we derive a stable decomposition result for vector bundles over the sphere bundle $$\mathord {{\mathbb {S}}}( \mathord {{\mathbb {R}}}\oplus V)$$ S ( R ⊕ V ) in terms of vector bundles and Clifford module bundles over X. After passing to topological K-theory these results imply classical Bott–Thom isomorphism theorems.

Microwave-assisted Automated Glycan Assembly

Automated synthesis of DNA, RNA, and peptides provides quickly and reliably important tools for biomedical research. Automated glycan assembly (AGA) is significantly more challenging as highly branched carbohydrates require strict regio- and stereocontrol during synthesis. A new AGA synthesizer enables rapid temperature adjustment from -40 °C to +100 °C to control glycosylations at low temperature and accelerates capping, protecting group removal, and glycan modifications by using elevated temperatures. Thereby, the temporary protecting group portfolio is extended from two to four orthogonal groups that give rise to oligosaccharides with up to four branches. In addition, sulfated glycans and unprotected glycans can be prepared. The new design reduces the typical coupling cycles from 100 min to 60 min while expanding the range of accessible glycans. The instrument drastically shorten and generalizes the synthesis of carbohydrates for use in biomedical and material science.<br>

Microwave-assisted Automated Glycan Assembly

Automated synthesis of DNA, RNA, and peptides provides quickly and reliably important tools for biomedical research. Automated glycan assembly (AGA) is significantly more challenging as highly branched carbohydrates require strict regio- and stereocontrol during synthesis. A new AGA synthesizer enables rapid temperature adjustment from -40 °C to +100 °C to control glycosylations at low temperature and accelerates capping, protecting group removal, and glycan modifications by using elevated temperatures. Thereby, the temporary protecting group portfolio is extended from two to four orthogonal groups that give rise to oligosaccharides with up to four branches. In addition, sulfated glycans and unprotected glycans can be prepared. The new design reduces the typical coupling cycles from 100 min to 60 min while expanding the range of accessible glycans. The instrument drastically shorten and generalizes the synthesis of carbohydrates for use in biomedical and material science.<br>

Microwave-assisted Automated Glycan Assembly

Automated synthesis of DNA, RNA, and peptides provides quickly and reliably important tools for biomedical research. Automated glycan assembly (AGA) is significantly more challenging as highly branched carbohydrates require strict regio- and stereocontrol during synthesis. A new AGA synthesizer enables rapid temperature adjustment from -40 °C to +100 °C to control glycosylations at low temperature and accelerates capping, protecting group removal, and glycan modifications by using elevated temperatures. Thereby, the temporary protecting group portfolio is extended from two to four orthogonal groups that give rise to oligosaccharides with up to four branches. In addition, sulfated glycans and unprotected glycans can be prepared. The new design reduces the typical coupling cycles from 100 min to 60 min while expanding the range of accessible glycans. The instrument drastically shorten and generalizes the synthesis of carbohydrates for use in biomedical and material science.<br>