

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 twoway communication protocol but no efficient classical
twoway protocol and asked, whether there existed a function with an
efficient quantum oneway protocol, but still no efficient classical
twoway protocol. In 2010 Klartag and Regev demonstrated such a
function and asked, whether there existed a function with an efficient
quantum simultaneousmessages protocol, but still no efficient
classical twoway 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 polylogarithmic
size, and whose classical twoway 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 nonsecond countable topology will be constructed.



September 26, 2018

S. Bardyla


Embedding of the bicyclic monoid with adjoined zero $\mathcal{C}^0(p,q)$ into compactlike topological semigroups

We study embedding of the bicyclic monoid $\mathcal{C}^0(p,q)=\mathcal{C}(p,q)\sqcup\{0\}$ with adjoined zero into compactlike 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 dcompact 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 shiftcontinuous 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 shiftcontinuous 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 shiftcontinuous topologies on the bicyclic monoid with adjoint zero.

