Klaus Mattis

Hi, I am Klaus Mattis, a second year PhD-student at JGU Mainz, under the supervision of Tom Bachmann.

For more information, consult my CV.

You can reach me via mail at klaus.mattis@uni-mainz.de.

Research Interests

Motivic homotopy theory is a branch of algebraic geometry and algebraic topology that studies schemes with tools inspired by classical homotopy theory. It blends techniques from both geometry and topology to study the so-called "motives" of varieties.

For more details, see Wikipedia: Motivic Homotopy Theory .

Higher category theory generalizes the notion of categories, functors, and natural transformations to "n-categories," capturing deeper homotopy-theoretic information. An (∞,1)-topos (or higher topos) is a higher-categorical version of a topos, providing a unifying framework for homotopy theories of various geometric contexts.

For more details, see Wikipedia: Topos (classical notion) and nLab: (∞,1)-Topos .

Algebraic K-theory is a tool used in both geometry and topology to study projective modules over a ring, vector bundles on a scheme, and more. It is closely tied to areas like motivic homotopy theory and is fundamental in exploring deep connections between number theory, geometry, and topology.

For more details, see Wikipedia: Algebraic K-theory .

Work

Talks

Academic service

I am a co-organizer of the winter school on unstable motivic homotopy theory in Mainz.
I am an organizer of the GAUS Junior AG on Maps between spherical group rings in Mainz.

Impressum

Angaben gem. § 5 TMG:
Klaus Mattis
Institut für Mathematik
Johannes Gutenberg-Universität
Staudingerweg 9
55128 Mainz