Fakultät für Mathematik

Universität Regensburg

93040 Regensburg

Deutschland

Universität Regensburg

93040 Regensburg

Deutschland

Zimmer M223

`denis DOT nardin AT ur DOT de`

- Hermitian K-theory via oriented Gorenstein algebras new!

with Marc Hoyois, Joachim Jelisiejew and Maria Yakerson. - Hermitian K-theory for stable ∞-categories I: Foundations

with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Markus Land, Thomas Nikolaus and Wolfgang Steimle. - Hermitian K-theory for stable ∞-categories II: Cobordism categories and additivity

with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Markus Land, Thomas Nikolaus and Wolfgang Steimle. - Hermitian K-theory for stable ∞-categories III: Grothendieck-Witt groups of rings

with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Markus Land, Thomas Nikolaus and Wolfgang Steimle. - The Hilbert scheme of infinite affine space and algebraic K-theory

with Marc Hoyois, Joachim Jelisiejew, Burt Totaro and Maria Yakerson. - Hermitian K-theory for stable ∞-categories IV: Poincaré motives and Karoubi-Grothendieck-Witt groups

with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Markus Land, Thomas Nikolaus and Wolfgang Steimle.*In preparation* - A descent view on Mitchell's theorem

with Elden Elmanto and Lucy Yang. - A comment on the vanishing of rational motivic Borel-Moore homology

with Clark Barwick. - Parametrized higher category theory and higher algebra: A general introduction

with Clark Barwick, Emanuele Dotto, Saul Glasman and Jay Shah. - PHCTHA: Exposé I -- Elements of parametrized higher category theory

with Clark Barwick, Emanuele Dotto, Saul Glasman and Jay Shah. - PHCTHA: Exposé IV -- Stability with respect to an orbital ∞-category

A slightly reworked version of the first half of my thesis - PHCTHA: Exposé V -- Parametrized monoidal structures

with Jay Shah.*In preparation* - Stability and distributivity over an orbital ∞-category

My ph.D. thesis - Categorifying rationalization (ArXiv)

with Clark Barwick, Marc Hoyois, Saul Glasman and Jay Shah. Published in*Forum of Mathematics, Sigma*. Volume 7, 2019 , e42. - Dualizing cartesian and cocartesian fibrations (ArXiv)

with Clark Barwick and Saul Glasman. Published in*Theory and Applications of Categories*Vol. 33, 2018, No. 4, pp 67-94

- Introduction to equivariant homotopy theory

An introduction to stable equivariant homotopy theory. To be revised. - Levine's Chow's moving lemma

An exposition of Marc Levine's proof of Chow's moving lemma for higher Chow groups. - Crossing Browder's bridge

Forthcoming. An explanation in modern language of Browder's original proof of his theorem relating the Kervaire invariant of framed manifolds and the 2-line of the Adams spectral sequence. - The purity theorem in motivic homotopy theory

A short discussion of the proof of the purity theorem in motivic homotopy theory. - Fundamental quandle of knots and the Alexander module

A short essay defining the fundamental quandle and proving some of its main properties. - Superfici di Riemann, teorema di Riemann-Roch e applicazioni

In italian. My bachelor thesis, about Riemann-Roch theorem for Riemann surfaces. Contains an elementary proof that every plane Riemann surface is algebraic. - Essential dimension of finite group schemes

My master thesis about the basic theory of essential dimension for finite group schemes. Contains a small improvement on a result by Ledet.