# Seminar za analizu i algebru Alpe-Jadran

lokacija:
PMF Matematički odsjek
vrijeme:
18.05.2019 - 10:00 - 13:30
Obavještavamo vas da će prvi sastanak hrvatsko-slovenskog Seminara
za analizu i algebru Alpe-Jadran biti u održan u subotu 18.5. na
PMF-MO u predavaoni 201, prema sljedećem rasporedu:

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10.00-10.45, Ilja Gogić: The cb-norm approximations by two-sided
multiplications and elementary operators

Abstract: We describe joint work with Richard M. Timoney on a problem
that asks when the set of two-sided multiplications
on a C*-algebra is closed in the completely bounded norm (cb-norm). We
also discuss the cb-norm approximations of derivations and automorphisms by
elementary operators.

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10.55-11.40, Aleksey Kostenko: Infinite Quantum Graphs

Abstract: We will review basic spectral properties of infinite quantum
graphs (graphs having infinitely many vertices and edges). In
particular, we will focus on recently discovered fruitful connections
between quantum graphs and discrete Laplacians on graphs.

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11.50-12.35, Vjekoslav Kovač: Variants of the Christ-Kiselev lemma and
an application to the maximal Fourier restriction

Abstract: Back in the year 2000, Christ and Kiselev introduced a useful "maximal
trick" in their study of spectral properties of Schro edinger operators.
The trick was completely abstract and only at the level of basic
functional analysis and measure theory. Over the years it was reproven,
generalized, and reused by many authors. We will present its recent
application in the theory of restriction of the Fourier transform to
surfaces in the Euclidean space.

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12.45-13.30, Primoz Moravec: Gaps in probabilities of satisfying some
commutator identities

Abstract: Let $w$ be a non-trivial word in a free group of rank $d$
and $w: G^d\to G$ a corresponding word map on a finite group $G$. Let
$P_{w=1}(G)=|w^{-1}(1)| / |G|^d$ be the probability that a randomly
chosen $d$-tuple of elements of $G$ evaluates to 1 under the map $w$.
There is an old result of Gustafson stating that if $G$ is a finite
non-abelian group, then the commuting probability $P_{[x,y]=1}(G) is bounded above by$5/8$. Dixon (2004) posed a question whether or not there exists a constant$\eta <1$depending on$w$only such that for every finite group$G$not satisfying the law$w=1$we have that$P_{w=1}(G)\le \eta$. We answer the question affirmatively for the 2-Engel word$w=[x,y,y]$and metabelian word$w=[[x,y],[z,w]]\$. We
also give an overview of related results and problems concerning word
probabilities.
This is joint work with Costantino Delizia and Chiara Nicotera
(University of Salerno, Italy), and Urban Jezernik (University of the
Basque Country, Spain).
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Pozivaju se članovi seminara i svi zainteresirani.

Ilja Gogić i Dijana Iliševic