Scientific Seminar
at Geometry and Topology Department of
Ivan Franko National University of Lviv
Archive for (2018/2019) academic year



Topological
Algebra

September 5, 2018 O. Gutik
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    • Active participants of the seminar will present and discuss interesting open problems from various branches of the topological algebra.

September 12, 2018 D. Gavinsky
  • Entangled simultaneity versus classical interactivity in communication complexity
    • In 1999 Raz demonstrated a partial function that had an efficient quantum two-way communication protocol but no efficient classical two-way protocol and asked, whether there existed a function with an efficient quantum one-way protocol, but still no efficient classical two-way protocol. In 2010 Klartag and Regev demonstrated such a function and asked, whether there existed a function with an efficient quantum simultaneous-messages protocol, but still no efficient classical two-way protocol. In this work we answer the latter question affirmatively and present a partial function, which can be computed by a protocol sending entangled simultaneous messages of poly-logarithmic size, and whose classical two-way complexity is lower bounded by a polynomial.

September 19, 2018 S. Bardyla
  • Topologization of the polycyclic monoid $P_1$

    • We investigate shift continuous topologies on the polycyclic monoid $P_1$. Also, an example of an non-second countable topology will be constructed.

September 26, 2018 S. Bardyla
  • Embedding of the bicyclic monoid with adjoined zero $\mathcal{C}^0(p,q)$ into compact-like topological semigroups

    • We study embedding of the bicyclic monoid $\mathcal{C}^0(p,q)=\mathcal{C}(p,q)\sqcup\{0\}$ with adjoined zero into compact-like topological semigroups. More precisely, we give necessary and sufficient conditions which provide an embedding of the bicyclic monoid with adjoined zero $\mathcal{C}^0(p,q)$ into d-compact topological semigroups.

October 24, 2018 M. Khylynskyi
  • On an interassociativity of the $\lambda$-polycyclic monoid

    • We discuss on algebraic properties of interassociativities of the $\lambda$-polycyclic monoid. In particular the Green relations on an interassociativity of the $\lambda$-polycyclic monoid and their isomorphisms will be described.

October 31, 2018 M. Khylynskyi
  • On an interassociativity of the $\lambda$-polycyclic monoid, II

    • We discuss on algebraic properties of interassociativities of the $\lambda$-polycyclic monoid. In particular the Green relations on an interassociativity of the $\lambda$-polycyclic monoid and their isomorphisms will be described.

November 7, 2018 M. Khylynskyi
  • On an interassociativity of the $\lambda$-polycyclic monoid, III

    • We discuss on algebraic properties of interassociativities of the $\lambda$-polycyclic monoid. In particular the Green relations on an interassociativity of the $\lambda$-polycyclic monoid and their isomorphisms will be described.

November 14, 2018 M. Khylynskyi
  • On an interassociativity of the $\lambda$-polycyclic monoid, IV

    • We discuss on algebraic properties of interassociativities of the $\lambda$-polycyclic monoid. In particular the Green relations on an interassociativity of the $\lambda$-polycyclic monoid and their isomorphisms will be described.

November 21, 2018 S. Bardyla
  • On a semitopological bicyclic monoid with adjoint zero $\mathcal{C}(p,q)^{0}$ which semilattice of idempotents is compact

    • We describe minimal semigroup topologies on $\mathcal{C}(p,q)^{0}$ and investigate properties of the semilattice of shift-continuous topologies on the bicyclic monoid with adjoint zero.

December 5, 2018 S. Bardyla
  • On a semitopological bicyclic monoid with adjoint zero $\mathcal{C}(p,q)^{0}$ which semilattice of idempotents is compact, II

    • We describe minimal semigroup topologies on $\mathcal{C}(p,q)^{0}$ and investigate properties of the semilattice of shift-continuous topologies on the bicyclic monoid with adjoint zero.

December 12, 2018 S. Bardyla
  • On a semitopological bicyclic monoid with adjoint zero $\mathcal{C}(p,q)^{0}$ which semilattice of idempotents is compact, III

    • We describe minimal semigroup topologies on $\mathcal{C}(p,q)^{0}$ and investigate properties of the semilattice of shift-continuous topologies on the bicyclic monoid with adjoint zero.