Jonte Gödicke (he/him)

Jonte Gödicke

About

I am a Ph.D. student at the Department of Mathematics at the University of Hamburg advised by Tobias Dyckerhoff and funded by the Excellence Cluster Quantum Universe.

Starting in October 2025 I will be a postdoctoral fellow at the MPIM in Bonn. Furthermore, I am an affiliated researcher of the CRC 1624 "Higher Structures, Moduli Spaces and Integrability".

This is my CV. For a letter of reference, please contact Tobias Dyckerhoff, Paul Wedrich, Julian Holstein and Joachim Kock.

Research

My research lies in the area of Higher Category Theory and Topological Field Theories. In particular, I am currently interested in applying lax constructions (e.g. lax algebraic structures, gluing constructions) to problems in Higher Representation Theory and Topological Field Theories.

Preprints and other scientific writings appear in order of first arXiv appearing in the following list.

1. An ∞-category of 2-Segal spaces:

   Arxiv , Author: Jonte Gödicke

   Abstract: Algebra objects in ∞-categories of spans admit a description in terms of 2-Segal objects. We introduce a notion of span between 2-Segal objects and extend this correspondence to an equivalence of ∞-categories. Additionally, for every ∞-category with finite limits C, we introduce a notion of a birelative 2-Segal object in C and establish a similar equivalence with the ∞-category of bimodule objects in spans. Examples of these concepts arise from algebraic and hermitian K-theory through the corresponding Waldhausen S-construction. Apart from their categorical relevance, these concepts can be used to construct homotopy coherent representations of Hall algebras.

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2. Simons Lectures on Categorical Symmetries:

   Arxiv
   Davi Costa, Clay Córdova, Michele Del Zotto, Dan Freed, Jonte Gödicke, Aaron Hofer, David Jordan, Davide Morgante, Robert Moscrop, Kantaro Ohmori, Elias Riedel Gårding, Claudia Scheimbauer, Anja Švraka

   Abstract: Global Categorical Symmetries are a powerful new tool for analyzing quantum field theories. This volume compiles lecture notes from the 2022 and 2023 summer schools on Global Categorical Symmetries, held at the Perimeter Institute for Theoretical Physics and at the Swiss Map Research Station in Les Diableret. Specifically, this volume collects the lectures:
   * An introduction to symmetries in quantum field theory, Kantaro Ohmori
   * Introduction to anomalies in quantum field theory, Clay Córdova
   * Symmetry Categories 101, Michele Del Zotto
   * Applied Cobordism Hypothesis, David Jordan
   * Finite symmetry in QFT, Daniel S. Freed
   These volumes are devoted to interested newcomers: we only assume (basic) knowledge of quantum field theory (QFT) and some relevant maths. We try to give appropriate references for non-standard materials that are not covered. Our aim in this first volume is to illustrate some of the main questions and ideas together with some of the methods and the techniques necessary to begin exploring global categorical symmetries of QFTs.

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Thesis: Rigid Convolution Structures

Ediss.sub.uni-hamburg , Author: Jonte Gödicke

This is my Thesis written under the supervision of Tobias Dyckerhoff. The content of sections 6,7,8 and 9 already appears in Preprint 1 . The content of the remaining Sections will appear soon in a separate Preprint.

Abstract: A monoidal category is called a convolution monoidal category if it arises from linearizing a 2-Segal space. The goal of this thesis is to study for which 2-Segal spaces the induced convolution monoidal category is a multi-fusion category.
With this aim, we show that multi-fusion categories admit an intrinsic description as rigid algebras in the symmetric monoidal 2-category of ℂ-linear additive categories. We use this observation to define, by analogy, a derived version of a multi-fusion category as a rigid algebra in the symmetric monoidal (∞,2)-category of stable ∞-categories. We show that examples of these arise as derived categories of multi-fusion categories and as categories of modules over smooth and proper 𝔼2-algebras.
Afterward, we show that rigid algebras in the (∞,2)-category of spans are precisely given by those 2-Segal objects that are Čech-nerves. Together with our previous result, we use this to provide an answer to our initial question. To prove this result, we provide a description of bimodules in the ∞-category of spans as birelative 2-Segal objects. Furthermore, we introduce a notion of morphism between birelative 2-Segal objects that extends this classification to an equivalence of ∞-categories.
We use this classification to construct examples of convolution monoidal structures that form derived multi-fusion categories and discuss some aspects of the associated fully extended TFTs. We finish by studying Grothendieck–Verdier-structures on convolution monoidal ∞-categories and by comparing them with rigid dualities

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Notes

Here is a collection of Notes if I have written that did not make it onto the arXiv. None of them has been revised so use them with care. I am happy about any feedback or comments.

1. Poster, Derived TQFT's: Quantum Mechanics

   Poster Quantum Universe Graduate School, Author: Jonte Gödicke

   Abstract: We illustrate the advantage of derived TFT's over classical TFT's on the example of Quantum Mechanics. Therefore, we first explicitly describe Quantum Mechanics as an ordinary 1-dimensional TFT with values in vector spaces. After introducing basic terminology from homological algebra, we then extend this theory to a derived 1-dimensional TFT.

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