Damian Sawicki

email

I am interested in analytic and geometric group theory and non-commutative geometry, including large scale geometry. My advisor is dr hab. Piotr W. Nowak from the Warsaw GGT research group.

A considerable part of my PhD work has been devoted to the warped cone construction, providing a bridge between dynamical systems of finitely generated groups and metric geometry.
Keywords: spectral gap; Baum–Connes conjecture; amenability and dimension for dynamical systems, metric spaces, etc.; metric embeddings; super-expander graphs; Kazhdan and Haagerup properties.

Publications and preprints

1. Warped cones violating the coarse Baum–Connes conjecture
   (pdf)

2. Warped cones, (non-)rigidity, and piecewise properties
   with a joint appendix with Dawid Kielak
   Proceedings of the London Mathematical Society 118 (2019), no. 4, 753-786 (journal | arxiv)

3. Straightening warped cones
   with Jianchao Wu (arxiv)

4. Super-expanders and warped cones
   Annales de l'Institut Fourier, to appear (arxiv)

5. Warped cones and spectral gaps
   with Piotr W. Nowak
   Proceedings of the American Mathematical Society 145 (2017), no. 2, 817–823 (journal | arxiv)

6. Warped cones over profinite completions
   Journal of Topology and Analysis 10 (2018), no. 3, 563–584 (journal | arxiv)

7. On equivariant asymptotic dimension
   Groups, Geometry, and Dynamics 11 (2017), no. 3, 977–1002 (journal | arxiv)

8. Remarks on coarse triviality of asymptotic Assouad–Nagata dimension
   Topology and its Applications 167 (2014), 69–75 (journal | arxiv)

Theses

1. Equivariant asymptotic dimension
   Master's thesis, MIMUW, 2014.

2. Funkcje liniowe w geometrii wielkiej skali: quasi-izometrie i wymiar asymptotyczny Assouada-Nagaty
   English title: Linear functions in large scale geometry: quasi-isometries and asymptotic Assouad-Nagata dimension
   Bachelor's thesis (in Polish), MIMUW, 2012.

Metric spaces defined by group actions (abstract)
Geometry and Topology Seminar, Adam Mickiewicz University, May 2018

Warped cones violating the coarse Baum–Connes conjecture (abstract)
Mini-Workshop: Superexpanders and their coarse geometry, Oberwolfach, April 2018

Counterexamples to the coarse Baum–Connes conjecture from spectral-gap actions (abstract)
Operator algebra seminar, University of Copenhagen, February 2018

Large scale geometry of actions on compact spaces (abstract | lecture notes by Professor Pierre Pansu)
Workshop: Asymptotic decomposition methods in geometry, dynamics and operator algebras, University of Southampton, Isaac Newton Institute Satellite event, March 2017

Large scale geometry of group actions (abstract)
Dynamical Systems Seminar, IMPAN, February 2017

View on geometric group theory from the perspective of a warped cone (abstract)
Young Researchers' Colloquium, IMPAN, March 2016

Warped cones, profinite completions, coarse embeddings and property A (abstract | slides)
Séminaire Groupes et Analyse, Université de Neuchâtel, October 2015

Amenability and coarse embeddings of warped cones (abstract | slides)
Summer School: Probability on graphs and groups, CIB, EPFL, August 2015

Zgrupowane stożki i zgrubne zanurzenia (abstract)
Seminarium Geometrów (Geometry Seminar), University of Wrocław, May 2015