### Dr. Holger Kammeyer

- Office Hours: nach Vereinbarung
- Room: 1.007
- Phone: +49 (0) 721 608-43707
- Fax: +49 (0) 721 608-42148
- holger kammeyer ∂kit edu

- Karlsruher Institut für Technologie

MATH | IAG | AG Topologie

Englerstr. 2 | Mathebau (20.30)

76131 Karlsruhe

I am a postdoc in the topology group of the Institute for Algebra and Geometry at KIT. My mathematical interests range around algebraic topology, ℓ²-invariants and arithmetic groups. I am member of the Priority Program 2026 "Geometry at Infinity" and of the RTG 2229 "Asymptotic Invariants and Limits of Groups and Spaces". Here you can find slides of a talk on *"The construction of the regular 65.537-gon with compass and straightedge"* at the Day of Mathematics 2019 (in German).

### Publications

# Introduction to ℓ²-invariants

An up-to-date and user-friendly introduction to the rapidly developing field of ℓ ²-invariants.

Title | Coauthors | Year |
---|---|---|

On the profinite rigidity of lattices in higher rank Lie groups | Steffen Kionke |
2020 |

Products of free groups in Lie groups | Caterina Campagnolo |
2020 |

A remark on torsion growth in homology and volume of 3-manifolds | - |
2018 |

Title | Coauthors | Journal |
---|---|---|

Profinite invariants of arithmetic groups | Steffen Kionke, Jean Raimbault, Roman Sauer |
to appear in Forum of Mathematics, Sigma |

Profinite commensurability of S-arithmetic groups | - |
to appear in Acta Arithmetica |

S-arithmetic spinor groups with the same finite quotients and distinct L²-cohomology | Roman Sauer |
to appear in Groups, Geometry, and Dynamics. |

Introduction to ℓ²-invariants | - |
Springer Lecture Notes in Mathematics, Vol. 2247, viii+181 pp. ISBN: 978-3-030-28296-7 |

The shrinkage type of knots | - |
Bull. Lond. Math. Soc., 49-3 (2017), 428–442 |

Approximating Novikov-Shubin numbers of virtually cyclic coverings | - |
Groups, Geometry, and Dynamics, 11-4 (2017), 1231–1251 |

The Farrell-Jones conjecture for arbitrary lattices in virtually connected Lie groups | Wolfgang Lück, Henrik Rüping |
Geometry & Topology,
20-3 (2016), 1275--1287 |

L²-invariants of nonuniform lattices in semisimple Lie groups | - |
Algebraic & Geometric Topology, 14 (2014), 2475-2509 |

An explicit rational structure for real semisimple Lie algebras | - |
Journal of Lie Theory, 24, No. 2 (2014), 307-319 |

Title | Coauthors | Journal |
---|---|---|

From Betti numbers to L²-Betti numbers | Roman Sauer |
to appear in Oberwolfach Snapshots of Modern Mathematics |

The Heston-Hull-White Model I: Finance and Analytics | Jörg Kienitz |
Wilmott Magazine, Issues 57, 58, 59, (Jan 2012, March 2012, May 2012), 46-53, 34-45, 44-49 |

Title | Type, University |
---|---|

L²-invariants of nonuniform lattices in semisimple Lie groups | doctoral thesis, University of Göttingen |

On Exotic Manifolds | diploma thesis, University of Göttingen |

### Travel

# Travel

- Arithmetic groups and 3-manifolds

March 2020, Hagen - RTG-Colloquium

Talk:*"Profinite properties of lattices in Lie groups"*

*February 2020, Göttingen* - Manifolds and groups

February 2020, Oberwolfach - L2-torsion and symmetric spaces

October 2019, Göttingen - Workshop: Riemannian and Simplicial Volume

April 2019, Karlsruhe - SPP Conference "Geometry at Infinity"

April 2019, Münster - SFB Vorlesung

Talk:*"Profinite invariants of arithmetic groups"*

November 2018, Regensburg - Growth in Topology and Number Theory: Volume, Entropy, and L2-torsion

Talk:*"Profiniteness questions for L2-Betti numbers of S-arithmetic groups"*

July 2018, Bonn - L2-invariants and their analogues in positive characteristic

Talk:*"Profiniteness questions for L2-Betti numbers of S-arithmetic groups"*

June 2018, Madrid, Spain - Joint annual convention GDMV 2018

Talk: "Profinite commensurability of S-arithmetic groups"

March 2018, Paderborn - Nacht der Wissenschaft (Night of Science)

Talk: "Die Konstruktion des regelmäßigen 65.537-Ecks mit Zirkel und Lineal"

November 2017, Karlsruhe - Manifolds and groups

Talk:*"Cyclic knot coverings and transcendental numbers"*

September 2017, Regensburg - Summer school on "Growth in geometry and topology"

Mini course:*"Intro to L2-Betti numbers / L2-torsion and torsion growth in homology"*

August 2017, Les Diablerets, Switzerland - Group actions and cohomology in non-positive curvature

June 2017, Cambridge, UK - Groups, manifolds and K-theory

June 2017, Münster - Oberseminar Topologie

Talk:*"Secondary L2-invariants of groups and knots"*

May 2017, Münster - Compactifications of Buildings and Symmetric Spaces

May 2017, Heidelberg - School on Arithmetic groups

March 2017, Ein Gedi, Israel - Asymptotic geometry of groups and spaces

February 2017, Heidelberg - New directions in L2-invariants

October 2016, Bonn - Oberseminar Topologie

Talk:*"L²-invariants of groups and knots"*

September 2016, Bonn - Geometry Day

April 2016, Strasbourg, France - Young Geometric Group Theory

February 2016, Karlsruhe - Oberseminar Global Anlaysis

Talk:*"Approximating Novikov-Shubin numbers along finite coverings"*

January 2016, Regensburg - Geometry day

Talk:*"The Farrell-Jones conjecture and lattices in Lie groups"*

October 2015, Heidelberg - Topology Retreat

Talk:*"Introduction to L**²*-torsion"

September 2015, Bedlewo, Poland - Manifolds and Groups

September 2015, Ventotene, Italy - Oberseminar Topologie

Talk:*"L²-invariants and approximation along finite coverings"*

June 2015, Münster - Follow-up workshop to trimester program "Rigidity"

April 2015, Bonn - AG-Seminar Topologie

Talk:*"Local rigidity and the Farrell-Jones conjecture"*

February 2015, Karlsruhe - Workshop "Geometric Topology"

January 2015, Oberwolfach - Workshop "Topologie"

Short talk:*"The Farrell-Jones conjecture for lattices in Lie groups"*

September 2014, Oberwolfach - Oberseminar Differentialgeometrie

Talk:*"Local rigidity and the Farrell-Jones conjecture"*

June 2014, Augsburg - Seminario de Topología Algebraica

Talk:*"Rigidez local y la conjetura de Farrell-Jones"*

May 2014, Morelia, Mexico - Arbeitsgemeinschaft "Superrigidity"

Talk:*"Factor theorems for lattices in products of groups (Bader-Shalom)"*

March/April 2014, Oberwolfach - GK-Kolloquium Regensburg

Talk:*"L²-invariants and groups"*

October 2013, Regensburg - Oberseminar Regensburg

Talk:*"Novikov-Shubin numbers of arithmetic groups"*

October 2013, Regensburg - Oberseminar Topologie

Talk:*"L²-invariants of nonuniform lattices in semisimple Lie groups"*

October 2013, Bonn - Geometry, Groups and Topology

October 2013, Karlsruhe - Summer School: Topology of high-dimensional manifolds

August 2013, Bonn - Von Neumann Algebras and Measurable Group Theory

July 2013, Leuven, Belgium - Operator Algebra Seminar

Talk:*"On L²-invariants of lattices in semisimple Lie groups"*

January 2013, Copenhagen, Denmark - Topology Seminar

Talk:*"On L²-invariants of lattices in semisimple Lie groups"*

October 2012, Karlsruhe - Workshop "Topologie"

Short talk:*"On L²-invariants of lattices in semisimple Lie groups"*

September 2012, Oberwolfach - Topology and Groups

June 2012, Berlin - Young Topologists Meeting

Talk:*"Compactifications of locally symmetric spaces"*

June 2011, Lausanne, Switzerland - Von Neumann algebras and ergodic theory of group actions

April 2011, CIRM Marseille, France - Symplectic and Poisson Geometry in interaction with Algebra, Analysis and Topology

May 2010, MSRI Berkeley, California - Many cheerful facts

Talk:*"Fair and unfair prices of financial derivatives"*

April 2010, Berkeley, California - Eighth Annual Graduate Student Topology and Geometry Conference

February 2010, Ann Arbor, Michigan - First National Forum of Young Topologists

November 2009, New Orleans, Louisiana - Young Topologists Meeting

Talk:*"Classification of 3-sphere bundles over the 4-sphere (Crowley-Escher)"*

May 2009, Le Châtelard, Switzerland

### Events

### Teaching

# Summer term 2020

- Lecture "Algebraic Topology" Thu 02:00-03:30 pm, -1.012 UG, Fr 09:45-11:15 am, -1.025 UG
- Seminar "Representation theory of finite groups" block seminar
- RG Seminar "Topology" Thu 03:45-05:15 pm, SR 2.059 (20.30)

# Summer term 2019

- Exercise class for Linear Algebra II Fr 02:00 - 03:30 pm, Fritz-Haller-Hörsaal
- RG-Seminar "Topology" Fr 09:45-11:15 am, Raum 2.059 (20.30)

# Winter term 2018/2019

- Exercise class for Linear Algebra and Analytic Geometry I Mon 03:45 - 05:15 pm, Carl-Benz-Hörsaal
- RG-Seminar "Topology" Thu 03:45-05:15 pm, 2.058 (20.30)
- Workshop on current developments around the Atiyah conjecture 19.11.18 - 21.11.18

# Summer term 2018

- Seminar "Projective Geometry" block course 07/23 - 07/25/2018, SR 0.016 (20.30) seminar announcement
- RG-Seminar "Topology" Thu 03:45-05:15 pm, 2.059 (20.30)

# Winter term 2017/2018

- Lecture "Mathematics for Natural Sciences" Tue 08:00-09:30 am, Fr 08:45-09:30 am, 30.46 Chemie Neuer Hörsaal
- RG-Seminar "Topology" Thu 03:45-05:15 pm, 2.058 (20.30)

# Summer term 2017

- Seminar: "Differential topology" Thu 09:45-11:15 am, -1.009(UG) (20.30) seminar announcement
- Proseminar: "Proofs from THE BOOK" Thu 02:00-03:30 pm, 2.059 (20.30) proseminar announcement
- RG-Seminar "Arithmetic hyperbolic 3-manifolds" Thu 03:45-05:15 pm 2.059 (20.30) seminar announcement

# Summer term 2016

- Lecture "Algebraic Topology" Tue 11:30 am-01:00 pm, 2.058 (20.30), Thu 11:30 am-01:00 pm, 0.014 (20.30)
- Tutorial "Algebraic Topology" Wed 05:30-07:00 pm, 2.059 (20.30)

tutor: Jakob Albers - RG-Seminar "Topology" Thu 02:00-03:30pm, 2.058 (20.30)

# Winter term 2015/2016

- Lecture "L²-invariants" Thu 03:45-05:15 pm, room 2.058 (20.30)
- Problem class "L²-invariants" Mon 02:00-03:30 pm, room 2.059 (20.30)

Teaching assistant: Sabine Braun;**Starts 10/26/2015** - RG Seminar "Topology" Thu 05:30-07:00 pm, room 2.058 (20.30)

More information on the lecture "L²-invariants" is given in the course announcement.

# Summer term 2015

- Exercise class: "Algebraic Topology" Fri 11:30-01:00 pm, room 2.059 (20.30)
- Seminar: "Projektive Geometrie" Thu 05:30-07:00 pm, room 3.060 (20.30)
- RG Seminar: "Topology" Thu 02:00-03:30 pm, room 2.058 (20.30)

### Supervision

Title | Type | Student |
---|---|---|

The Lefschetz fixed point theorem: from simplicial to CW complexes | Masterarbeit | Gotami Heller |

Homologies and elations in the projective and Euclidean plane | Bachelorarbeit | Cédric Dujardin |

L2-Betti numbers and profinite completions of groups | Master thesis | Nico Stucki |

Construction of Thom spectra for bordism with G-structure | Bachelor thesis | Amelie Flatt |

### Short CV

Since April 2015 | Postdoc at Institute for Algebra and Geometry (working with Roman Sauer) |
Karlsruhe Institute of Technology |

July 2013 - March 2015 | Postdoc at Mathematical Institute (working with Wolfgang Lück) |
University of Bonn |

July 2010 - May 2013 | Doctoral studies at Mathematical Institute (working with Thomas Schick) |
University of Göttingen |

August 2009 - June 2010 | Fulbright scholar at Department of Mathematics | University of California Berkeley |

July 2008 - October 2008 | Internship in team "Quantitative Analysis" | Deutsche Postbank, Bonn |

October 2004 - July 2009 | Diploma studies in mathematics with minor theoretical physics | University of Göttingen |