Marek Kaluba

Assistant Professor

Adam Mickiewicz University

Biography

I am an assistant professor at the Adam Mickiewicz University from 2014. The Mathematical Institute of Polish Academy of Sciences hosted me as a Post-Doc between 2015 and 2017, where I worked with Piotr Nowak on Kazhdan’s property (T). My research interests include also group actions, topology of high-dimensional manifolds (surgery and equivariant surgery theory), applied topology (persistence and others) and symbolic computation. From time to time I like to code – the effects may be (rarely) found on github or else (see links on the left).

Programming: Julia, Python
Sport: Climbing, Yoga

Interests

Group actions
Topology of manifolds
Applied topology

Education

PhD in Mathematics, 2014

Adam Mickiewicz University, Poznań
MSc in Mathematics, 2010

Adam Mickiewicz University, Poznań

Selected Publications

$\operatorname{Aut}(\mathbb{F}_5)$ has property (T)

We give a constructive, computer-assisted proof that $\operatorname{Aut}(\mathbb{F}_5)$, the automorphism group of the free group on $5$ generators, has Kazhdan’s property (T).

Marek Kaluba, Piotr W. Nowak, Narutaka Ozawa

Preprint, 2017.

Code Dataset ArXiv

Certifying Numerical Estimates of Spectral Gaps

We establish a lower bound on the spectral gap of the Laplace operator on special linear groups using conic optimisation. In particular, this provides a constructive (but computer assisted) proof that these groups have Kazhdan property (T).

Marek Kaluba, Piotr W. Nowak

Accepted in Groups Complexity Cryptology, 2017.

Code Slides ArXiv

Constructions of exotic actions on product manifolds with an asymmetric factor

Given $M\times S^n$, where $M$ is an asymmetric manifold, i.e. a manifold which does not admit any non-trivial action of a finite group, we try to answer how many (non-product) actions are there on such oddities?

Zbigniew Błaszczyk, Marek Kaluba

In review, 2016.

ArXiv

Publications

Effective topological complexity of spaces with symmetries

Zbigniew Błaszczyk, Marek Kaluba

Accepted in Publicacions Matemàtiques

ArXiv

On equivariant and invariant topological complexity of smooth $\mathbb{Z}/p$-spheres

Zbigniew Błaszczyk, Marek Kaluba

In Proceedings of American Mathematical Society Volume 145, Number 9 (2017), p. 4075-4086

PDF ArXiv

Group actions on complex projective spaces

Marek Kaluba, Krzysztof Pawałowski

In The Topology and the Algebraic Structures of Transformation Groups, Proceedings of RIMS – Kokyuroku, Volume 1922, (2014), p. 147-153

PDF

On Representation of the Reeb Graph as a Sub Complex of Manifold

Marek Kaluba, Wacław Marzantowicz, Nelson Silva

In Topological Methods in Nonlinear Analysis, Volume 45, Issue 1 (March 2015), p. 287-307

PDF ArXiv

Non Symplectic Actions on Complex Projective Spaces

Marek Kaluba, Wojciech Politarczyk

In Journal of Symplectic Geometry, Volume 10, Issue 1 (2012), p. 17-26

PDF ArXiv

Teaching

In the winter semester of 2017 I am teaching@AMU the following courses:

Introduction to Mathematics for CS (Mon 11:45 A2-10; Thu 11:45 A2-8)
Calculus 2 for CS (Thu 15:30 A2-22)
Elementary Mathematics (Mon 15:30 A2-24; Thu 13:45 A2-22)
Elements of Statistics (Tue 14:15; Tue 17:00; Fri 8:00)

In the summer semester of 2018 I will be teaching@AMU the following courses:

Abstract Algebra 2 (TBA)
Elements of Applied Mathematics (TBA)

Contact

kalmar@amu.edu.pl
(0048 61 829) 5497
Room B1-30, Faculty of Mathematics and Computer Science, ul. Umultowska 87, 61-614 Poznań, Poland
Tuesday 10:30 – 12:00, or appointment by email