


I am College Associate Lecturer and Director of Studies in Mathematics at St John's College, University of Cambridge, affiliated with the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge.
Before that I was a Senior Research Associate in the Mathematics Department at Lancaster University, a Postdoctoral Fellow at the Max Planck Institute for Mathematics in Bonn and
a College Lecturer and Fellow of Christ's College.

Contact

Dr Julian VS Holstein
St John's College
Cambridge, CB2 3BUF
United Kingdom
Email: jvsh2, cam.ac.uk

Research

My research interests lie at the intersection of algebraic geometry and algebraic topology with higher category theory and homotopical algebra
Here is a list of my papers and preprints in reverese chronological order:
 Analytification of mapping stacks examines the interplay between the analytification functor and the mapping stack functor in derived geometry. In particular we show that in good cases the mapping stack between two analytifications is the analytification of the mapping stack. Along the way we prove a number of very useful technical results about analytic perfect complexes, analytic Tannaka duality and working with the derived analytification functor. This is joint work with Mauro Porta.
 Homotopy theory of monoids and derived localization derives a number of interesting consequences from the close relationship between the algebraic bar construction and the nerve construction on monoids. We prove that Adams' cobar construction is the analogue of the loop space even for nonsimply connected spaces, and we model topological spaces by an infinity category of discrete monoids. This is joint work with Joe Chuang and Andrey Lazrev.
 MaurerCartan moduli and theorems of RiemannHilbert type considers different notions of equivalence for MaurerCartan elements in dg algebras. As an application we compute some categories of twisted modules and give new descriptions of infinity local systems. This is joint work with Joe Chuang and Andrey Lazrev.
 The global derived period map constructs an analogue of Griffiths' period map in derived geometry. This is joint work with Carmelo di Natale.
 Explicity homotopy limits of dgcategories and twisted complexes constructs some explicit homotopy limits of dgcategories and thus gives a description of the twisted complexes of Toledo and Tong. This is joint work with Zhaoting Wei and Jonathan Block.
Published in Homology, Homotopy ond Applications, Volume 19 (2017), Number 2.
 Morita Cohomology constructs cohomology of a topological space X with coefficients in the dgcategory of perfect complexes in two different ways. The results agree and may be characterized as the dg category of infinity local systems on X.
Published in
Mathematical Proceedings of the Cambridge Philosophical Society, Volume 158, Issue 01.
 Morita Cohomology and homotopy locally constant presheaves shows that Morita cohomology is moreover equivalent to the dgcategory of homotopy locally constant sheaves of perfect complexes on X.
Published in
Mathematical Proceedings of the Cambridge Philosophical Society, Volume 158, Issue 01.
 Properness and simplicial resolutions for the model category dgCat proves two technical results about the category of dgcategories. When defined over a ring of flat dimension 0 dgCat is a left proper model category. Simplicial resolutions in dgCat are explicitly given by categories of MaurerCartan elements.
Published in Homology, Homotopy ond Applications, Volume 16 (2014), Number 2.
The paper title links to the arxiv, the journal title links to the published versions; there are no differences in content.
The last three papers are based on my PhD thesis Morita Cohomology.
My advisor was Ian Grojnowski.

Teaching

In Lent Term 2015 I was lecturing a Part III course, Homological and Homotopical Algebra.
I am running pure maths examples classes for first year students, and some information on these classes and undergraduate maths in general can be found here.
Other courses I taught include Algebraic Geometry,
Algebraic Toplogy and
Representation Theory in Part II,
Analysis II,
Geometry,
Groups, Rings & Modules,
Linear Algebra and
Metric & Topological Spaces in Part IB and
Analysis I,
and
Numbers & Sets in Part IA.
I have also been a group leader at the Part III Seminar Series,
talked at the Adams Society and in the Archimedeans' SU(2) series (where SU(2) stands for "seminars for undergraduates, too"). In 2009 I gave a course at the Deutsche Schülerakademie.

Young Researchers in Maths

From 16 to 18 April 2009 a novel event happened in
Cambridge. For two days 200 young researchers from all areas of
mathematics took over the CMS.
Young Researchers in Maths became a yearly event, with conferences 2010 in Cambridge, 2011 in Warwick, 2012 in Bristol,
2013 in Edinburgh, 2014 in Warwick, 2015 in Oxford, 2016 in St Andrews and 2017 in Kent.
The aim of Young Researchers in Maths is to improve contacts between PhD students and other early career mathematicians. If you are interested in running one of these events in the future or have other ideas how to get young mathematicians together, please get involved by getting in contact with the current comittee!

Other

In my nonmathematical life I like improvised theatre, that is,
theatre without a script, without a director, without any idea what is
going to happen on stage in the next minute.
I was a member of the Cambridge Impronauts, formerly known as ICE, and I have taught some wokshops at summer schools, including a full one week course at the CdE Sommerakademie.
My mother is Susannne Holstein, she is an artist.
