Research

Lennart Meier

Teaching



I am an assistant professor at the University of Utrecht, specializing in algebraic topology
and related areas of arithmetic geometry. Here is my CV.

My research is part of the Utrecht Geometry Center. It has a growing number of algebraic
topologists, including Ieke Moerdijk, Gijs Heuts and Brice Le Grignou.

Contact information:

Mathematical Institute of Utrecht
Budapestlaan 6
Kamer 508
Utrecht, Nederland
E-Mail: f.l.m.meier at uu.nl


Teaching

Research


My Zentralblatt Reviews    My MathSciNet Reviews

Research interests

I am an algebraic topologist with a special interest in the spectrum of topological modular forms TMF. I am also interested in several related
and unrelated questions in abstract homotopy theory, stable and unstable chromatic homotopy theory and (derived) algebraic geometry.
Currently I am thinking mostly about the Bousfield-Kuhn functor, TMF with level structures, equivariant TMF and its applications to elliptic
genera and Brauer groups. This includes the following collaborations:

  • Understanding torus-equivariant TMF (joint with D. Gepner and T. Nikolaus)
  • Towards the Brauer group of TMF (joint with B. Antieau and V. Stojanoska)

  • Preprints and Publications

  • Rings of modular forms and a splitting of TMF0(7) (joint with Viktoriya Ozornova)

  • A Whitehead theorem for periodic homotopy groups, arXiv:1811.04030 (joint with Tobias Barthel and Gijs Heuts)

  • Topological modular forms with level structures: decompositions and duality, arXiv:1806.06709

  • Decomposition results for rings of modular forms, arXiv:1710.03461

  • Monadicity of the Bousfield-Kuhn functor, arXiv:1707.05986 (joint with Rosona Eldred, Gijs Heuts and Akhil Mathew)

  • The Brauer group of the moduli stack of elliptic curves, arXiv:1608.00851 (joint with Ben Antieau)

  • Gorenstein duality for Real spectra (joint with John Greenlees), Algebraic & Geometric Topology 17 (2017), 3547-3619 , Erratum to the published version

  • Appendix B: 'Descent for higher real K-theories' to 'Descent in algebraic K-theory and a conjecture of Ausoni-Rognes', arXiv:1606.03328
          (joint with Niko Naumann and Justin Noel, 2016)

  • The C2-spectrum Tmf1(3) and its invertible modules (joint with Mike Hill), Algebraic & Geometric Topology 17 (2017) 1953-2011 (arXiv)

  • Fibration Categories are Fibrant Relative Categories, arXiv:1503.02036 , Algebraic & Geometric Topology 16 (2016), 3271-3300. (arXiv)

  • Fibrancy of Partial Model Categories (joint with Viktoriya Ozornova, 2015) Homology, Homotopy and Appl Volume 17.2 (2015), 53-80 (arXiv)

  • Affineness and Chromatic Homotopy Theory (joint with Akhil Mathew) J Topology (2015) 8 (2): 476-528 (arXiv, Erratum to the published version)

  • Vector Bundles on the Moduli Stack of Elliptic Curves, Journal of Algebra Volume 428 (2015), 425-456. (arXiv)

  • Hilbert Manifolds, Bulletin of the Manifold Atlas (2014, expository)

  • Spectral Sequences in String Topology, Algebraic & Geometric Topology 11 (2011), 2829-2860. (arXiv)


  • Other Documents and Non-arXived Preprints

    Theses

    Talks

    Academic Year 2018/19

  • Block 3, Topologie en Meetkunde
  • Spring, Mastermath Algebraic Topology II (jointly with Gijs Heuts)
  • Spring, Master seminar on a rational homotopy theory (jointly with Gijs Heuts)
  • Academic Year 2017/18

  • Block 3, Topologie en Meetkunde
  • Spring, Master seminar seminar on topological K-theory (jointly with Gijs Heuts)

  • Previously, courses at the University of Virginia and the University of Bonn on linear algebra, multivariable calculus, algebra, homology theories and elliptic cohomology.

    Students

  • Currently I supervise the master theses of Joost van Geffen, Jorge Becerra and Jeroen van der Meer and the PhD thesis of Jack Davies.
  • I supervised the master thesis of Simone Fabbrizzi in Bonn on the computation of Brauer groups of moduli stacks of elliptic curves
  • I supervised three bachelor theses so far on the topics de Rham cohomology, homology with local coefficients and genus formulae of modular curves. Generally I am happy to supervise bachelor theses in topology or on topics related to modular forms or elliptic curves.

  • If you are student interested in a thesis or reading project, please contact me!

    Topologie en meetkunde 2019

    General information

    This is a Blok 3 course meeting on Tuesdays and Thursdays. The precise times and the room will be fixed in the near future.

    Content

    The general aim of the course will be to apply algebraic tools to topological questions. In more detail:

  • We will start with a discussion, what topology is about. Can we classify spaces up to homeomorphism? Can we apply topology in analysis or algebra? This will quickly lead to the notion of a homotopy, a central concept for our course.

  • Using this notion, we will define the fundamental group of a space. Our first aim is to calculate it for the circle using the basics of covering space theory. Later we will give a beautiful classification of coverings of a space in terms of the fundamental group.

  • We will describe a way to calculate the fundamental group of CW-complexes, i.e. spaces build from spheres and disks (which includes most manifolds). The central tool is the van Kampen theorem that allows us to compute the fundamental group of a union of two spaces.

  • In the middle of the course, we will prove our first classification results. More precisely, we will classify closed one-dimensional manifolds (which is easy) and closed two-dimensional manifolds.

  • In the last weeks we will introduce the concept of homology. This can be used to solve higher-dimensional problems the fundamental group cannot deal with. Moreover it provides a way to show the topological invariance of the Euler characteristic, a number that first arose in Eulers's theorem on polyhedra. This opens the road to further applications.

    Recommended sources

    Our main source is the book Algebraic Topology by Hatcher. We will cover most material up to Chapter 2.2. The only part that is not covered in Hatcher's book is the classification of surfaces. For this I recommend Massey's A basic course in algebraic topology or Zeeman's The classification theorem for surfaces.

    Prerequisites

    Inleiding Topologie provides more than enough background for this course.
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