Seminar of the Faculty

• Invariant random subgroups of C*-simple groups
  dr Tattwamasi Amrutam, IMPAN, Warszawa
  2026-10-07 godz. 13:15 - 14:15
  Let G be a countable discrete C*-simple group, i.e. the reduced group C*-algebra of G is simple. We show that for any G-invariant probability measure on the space of subgroups of G, almost every subgroup is C*-simple. This is a very recent joint work with Mehrdad Kalantar.
• The maximal dimensions of path and graph algebras
  prof. dr hab. Piotr M. Hajac, IMPAN, Warszawa
  2026-10-28 godz. 13:15 - 14:15
  Graph theory is one of the most accessible parts of combinatorics, and one often uses graphs to visualize and study abstract objects in a plethora of mathematical contexts ranging from algebra and functional analysis to K-theory. Better still, the ubiquity of graphs goes beyond mathematics, e.g., Dijkstra’s graph-search algorithm is used in Google Maps. This talk will commence with an abridged hitchhiker's guide to the galaxy of applications of directed graphs. Then we will focus on solving a concrete optimization problem concerning the maximal dimension of both the path algebra and the graph algebra of a connected acyclic directed graph with N edges. The former is a broadly studied universal object, like the tensor algebra, and the latter is simply a matrix algebra. Finally, we will pose some reverse optimization problems: Given a dimension, what is the minimal sufficient number of edges? In particular, we will discuss the optimization-gap problem for matrix algebras, and speculate on its relation with the Cunningham chains of the first kind of prime numbers. (Based on joint work with Ł. Kaczmarczyk, M. Lowiel, and E. A. Pacheco.)

Department seminars

• Unique equivariant pseudo expectation and generalized powers averaging for crossed product
  Tattwamasi Amrutam,
  Laboratory of Functional Analysis, 2026-10-09 godz. 11:30
  Let $\Gamma$ be a countable discrete group and let $A$ be a unital $\Gamma$-simple $\Gamma$-$C^*$-algebra. We prove that $A\rtimes_r\Gamma$ has the generalized Powers averaging property if and only if the canonical map $A\rtimes_r\Gamma\to I_\Gamma(A)$ is the unique $\Gamma$-equivariant pseudo-expectation. We also show that this averaging property lifts to $I_\Gamma(A)\rtimes_r\Gamma$, with the averaging coefficients still belonging to $A$. This is a joint work with Fatemeh Khosravi and Zahra Naghavi.

Recently published

1. J.-P. Gazeau
   Electromagnetic Field From Affine Symmetry of Punctured Plane
   Geometric Methods in Physics XLII, Workshop, Białystok, Poland, 2025, (A. Dobrogowska, D. Fernández, T. Goliński, P. Kielanowski Ed(s).), Trends in Mathematics , (publ. by) Birkhauser Verlag, 2026, pp. 69-76.
   DOI: 10.1007/978-3-032-21578-9_8
2. T. Goliński
   A Note on Precotangent Bundles: The Example of Grassmannians
   Geometric Methods in Physics XLII, Workshop, Białystok, Poland, 2025, (A. Dobrogowska, D. Fernández, T. Goliński, P. Kielanowski Ed(s).), Trends in Mathematics , (publ. by) Birkhauser Verlag, 2026, pp. 193-201.
   DOI: 10.1007/978-3-032-21578-9_17
3. A. Dobrogowska, G. Jakimowicz
   Eigenvalue Problem and the Description of Lie Algebras
   Geometric Methods in Physics XLII, Workshop, Białystok, Poland, 2025, (A. Dobrogowska, D. Fernández, T. Goliński, P. Kielanowski Ed(s).), Trends in Mathematics , (publ. by) Birkhauser Verlag, 2026, pp. 219-228.
   DOI: 10.1007/978-3-032-21578-9_19
4. K. Bardadyn, B. Kwaśniewski
   Banach Algebra Crossed Products by Inverse Semigroup Actions
   Geometric Methods in Physics XLII, Workshop, Białystok, Poland, 2025, (A. Dobrogowska, D. Fernández, T. Goliński, P. Kielanowski Ed(s).), Trends in Mathematics , (publ. by) Birkhauser Verlag, 2026, pp. 317-333.
   DOI: 10.1007/978-3-032-21578-9_27
5. J.-P. Gazeau
   Quantum Formalism in Lower-Dimensional Real and Complex Hilbert Spaces
   Geometric Methods in Physics XLII, Workshop, Białystok, Poland, 2025, (A. Dobrogowska, D. Fernández, T. Goliński, P. Kielanowski Ed(s).), Trends in Mathematics , (publ. by) Birkhauser Verlag, 2026, pp. 337-344.
   DOI: 10.1007/978-3-032-21578-9_28