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Besides the standard seminar on Tuesday, we have also a special
seminar on Thursday afternoon this week.<br>
<p>Thursday, 28 May 2026 - 15:00 to 16:30 <br>
Place: IM, konírna </p>
<p>Speaker: Jan Lang, Ohio State University, USA<br>
Title: Notes about modular-based topologies </p>
<p>Abstract <br>
</p>
<p>This talk concerns the topology generated by modular convergence
in vector spaces equipped with a convex modular $\rho$, with
particular emphasis on the case where $\rho$ does not satisfy the
$\Delta_2$-condition. We show that the modular topology is a
topological vector space topology precisely when $\rho$ satisfies
$\Delta_2$. In the absence of this condition, several familiar
features of normed spaces break down: modular balls need not be
open, they may have empty interior, and modular convergence may be
strictly weaker than Luxemburg norm convergence.</p>
<p>The general theory is illustrated in the variable exponent spaces
$\ell^{(p_n)}$ and $L^{p(.)}(\Omega)$, where unbounded exponents
lead to genuinely non-normable modular phenomena. We also discuss
applications to Dirichlet energy minimization and weak solutions
of boundary value problems for the p(x)-Laplacian with unbounded
exponent.</p>
<p></p>
<p> For more information see the seminar web page at <br>
<a href="https://www.math.cas.cz/index.php/events/seminar/6"
target="_blank"
data-saferedirecturl="https://www.google.com/url?q=https://www.math.cas.cz/index.php/events/seminar/6&source=gmail&ust=1779644487905000&usg=AOvVaw3WZM4TtOjtMHnlrncLjafv">https://www.math.cas.cz/index.<wbr>php/events/seminar/6</a>
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