Address Research Notes Ph.D. Students Talks

Sabrina Pauli

I am a professor at the TU Darmstadt. Before that, I was a substitute professor in Düsseldorf and a postdoc at the University of Duisburg-Essen, working with Marc Levine. I received my Ph.D. in September 2020 from the University of Oslo, supervised by Paul Arne Østvær and Kirsten Wickelgren.
My research area is A1-homotopy theory, especially applications to enumerative geometry. For this I also use tropical geometry. I am also working on some computations in equivariant parametrized homotopy theory with my WIT group.

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TU Darmstadt
Schlossgartenstraße 7
64289 Darmstadt

Gebäude: S2 15 Raum: 442

E-Mail: pauli - at - mathematik.tu-darmstadt.de
Webpage

Research

A1-homotopy theory, also known as motivic homotopy theory developed by Morel-Voevodsky, is an emerging area of mathematics that unites the two worlds of algebraic geometry and algebraic topology by applying tools from algebraic topology, in particular homotopy theory, to algebraic varieties. This provides new tools for attacking classical problems in algebraic geometry and related areas.
I started my research by studying examples of algebraic varieties that are A1-contractible, i.e., algebraic varieties that look like a point in this A1-homotopy category. Currently, my research focuses on the application of A1-homotopy theory to enumerative geometry, leading to the new and rapidly growing field of A1-enumerative geometry, which allows to study questions in enumerative geometry over an arbitrary base field. I also use methods from tropical geometry for this.
Recently, with my WIT group, I have started to study and compute equivariant parametrized cohomology for G a finite group. This is cohomology with extended grading, which can be seen as an equivariant version of cohomology with local coefficients and was developed by Costenoble-Waner.

Publications

Preprints

Code

Other writing and notes

I gave a mini-workshop at PCMI 2024 titled Motivic explorations in enumerative geometry in which I explain how to do enumerative geometry over an arbitrary field and how to use tropical geometry to solve questions in this direction. Here are my lecture notes for the mini-workshop.

Here are some notes for the talks I gave at the Motives and Research Seminar in Essen.

Ph.D. Students

Talks

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