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<h1 class="display-4 fw-normal">Nonlinear Meeting 2021</h1>
<p class="h3">Zoom, March 22-23, 2021</p>
<p class="lead fw-normal">The NLM2021 is the 6th of a series of annual workshops focusing on nonlinear analysis and differential problems. This edition's common thread will cover theoretical topics on reaction-diffusion equations and dynamical systems with possible applications to biology or physics.</p>
<!--<a class="btn btn-danger" style="font-size:small" href="images/posterNLM21.pdf" target="_blank">REGISTER HERE</a>-->
</div>
<div class="col-12 col-sm-9 col-md-9 col-lg-9 mx-auto my-0 bg-light">
<h3 class="display-9 text-center">Invited speakers</h3>
<table class="table table-sm table-light table-borderless">
<tbody>
<tr>
<td width="100"><span class="lead fw-bold text-dark">Henri Berestycki</span></br>EHESS-CAMS-CNRS Paris</td>
<td width="100"><span class="lead fw-bold text-dark">Christian Kuehn</span></br>Technical University of Munich</td>
</tr>
<tr>
<td width="100"><span class="lead fw-bold text-dark">Elaine Crooks</span></br>Swansea University</td>
<td width="100"><span class="lead fw-bold text-dark">Peter Poláčik</span></br>University of Minnesota</td>
</tr>
<tr>
<td width="100"><span class="lead fw-bold text-dark">Frank Hilker</span></br>University of Osnabrück</td>
<td width="100"><span class="lead fw-bold text-dark">Pedro J. Torres</span></br>University of Granada</td>
</tr>
</tbody>
</table>
</div>
<div class="screenshot-card-2 shadow-sm d-none d-md-block"><img style="height:100%;width:100%" src="images/lot.png", class="mx-auto w-65 lg:w-81"></div>
<div class="screenshot-card-3 shadow-sm d-none d-md-block"><img style="height:100%;width:100%" src="images/brusselator.png", class="mx-auto w-65 lg:w-81"></div>
<!--<a class="btn btn-outline-dark" href="images/posterNLM21.pdf" download="posterNLM21.pdf" target="_blank">Poster</a>-->
</div>
<div id="program" class="position-relative overflow-hidden p-3 p-md-6 m-md-3 text-center bg-dark text-white">
<h3 class="display-9">Program</h3>
<p>Times are displayed in UTC+1 (currently <span id="theTime"></span>). Click <a href="http://www.timebie.com/std/centraleuropean.php" target="_blank" class="link-secondary">here</a> for time conversion.</p>
</div>
<div class="d-md-flex flex-md-equal w-100 my-md-1 ps-md-3">
<div class="bg-dark me-md-3 pt-3 px-3 pt-md-4 px-md-5 text-justify text-white overflow-hidden">
<div class="my-0 py-0">
<h4 class="display-9 text-danger">Monday, March 22</h4>
<table class="table table-sm table-dark table-borderless">
<tbody>
<tr>
<th scope="row" rowspan="2" width="10%">15:30</th>
<td>Henri Berestycki</br><i>Reaction-diffusion systems in epidemiology</i></br></td>
</tr>
<tr>
<td><!--<div class="btn-links"><a class="btn btn-outline-light my-1 btn-sm" href="#" target="_blank" real="noopener">
<i class="fas fa-images mr-1"> </i>slides</a></div>-->
<button type="button" class="btn btn-outline-light btn-sm" data-toggle="collapse" data-target="#abs1">Abstract</button><p></p>
<div id="abs1" class="collapse"><p style="font-size:small" class="text-left">The classical SIR type equations of epidemiology that take into consideration
spatial spreading lead to reaction-diffusion systems. Such systems also arise in the study of collective behaviors such as riots.
In this lecture, I will first recall the classical setting and then discuss a general framework for this type of systems that we call
''Activity / Susceptibility'' systems. In the second part of my talk, I will present a new model that describes the influence of roads
on the spread of epidemics. If time permits I will also show applications of these ideas to data of the current Covid-19 epidemics. </br>
I report here on joint work with Samuel Nordmann and Luca Rossi for the first part, with Jean-Michel Roquejoffre and Luca Rossi for the model with roads
and with Lionel Roques et al. for the study of data.</p>
</div>
</td>
</tr>
<tr>
<th scope="row" rowspan="2" width="10%">16:30</th>
<td>Elaine Crooks</br><i>Travelling waves and minimality exchange in smectic C<sup>*</sup> liquid crystals</i></br></td>
</tr>
<tr>
<td><!--<div class="btn-links"><a class="btn btn-outline-light my-1 btn-sm" href="#" target="_blank" real="noopener">
<i class="fas fa-images mr-1"> </i>slides</a></div>-->
<button type="button" class="btn btn-outline-light btn-sm" data-toggle="collapse" data-target="#abs2">Abstract</button><p></p>
<div id="abs2" class="collapse"><p style="font-size:small" class="text-left">We consider minimality conditions for the speed of monotone travelling waves
in a model of a sample of smectic C<sup>*</sup> liquid crystal subject to a constant electric field, dealing with both isotropic and anisotropic cases.
Such conditions are important in understanding switching properties of a liquid crystal, and our focus is on understanding how the presence of anisotropy
can affect the speed and nature of switching. Through a study of travelling-wave solutions of a quasilinear parabolic equation, we obtain an estimate
of the influence of anisotropy on the minimal speed, and sufficient conditions for linear and non-linear minimal speed selection mechanisms to hold
in different parameter regimes. We also discuss sufficient conditions for so-called “minimality exchange” in a general class of parameter-dependent
monostable reaction-diffusion equations with explicit travelling-wave solutions, when the minimal wave speed switches from the linearly determined value
to the speed of the explicitly determined front as a parameter changes. </br>
This is joint work with Michael Grinfeld and Geoff McKay (Strathclyde).</p>
</div>
</td>
</tr>
<tr><td></td><td class="text-left text-danger"><p>Break</p></td>
</tr>
<tr>
<th scope="row" rowspan="2" width="10%">17:40</th>
<td>Christian Kuehn</br><i>Geometric Singular Perturbation Theory for Fast-Slow PDEs</i></br></td>
</tr>
<tr>
<td><!--<div class="btn-links"><a class="btn btn-outline-light my-1 btn-sm" href="#" target="_blank" real="noopener">
<i class="fas fa-images mr-1"> </i>slides</a></div>-->
<button type="button" class="btn btn-outline-light btn-sm" data-toggle="collapse" data-target="#abs3">Abstract</button><p></p>
<div id="abs3" class="collapse"><p style="font-size:small" class="text-left">Systems with multiple time scales appear in a wide variety of
applications. Yet, their mathematical analysis is challenging already in
the context of ODEs, where about four decades were needed to develop a
more comprehensive theory based upon invariant manifolds,
desingularization, variational equations, and many other techniques.
Yet, for PDEs progress has been extremely slow due to many obstacles in
generalizing several ODE methods. In my talk, I shall report on two
recent advances for fast-slow PDEs, namely the extension of slow
manifold theory for unbounded operators driving the slow variables, and
the design of a blow-up method for PDEs, where normal hyperbolicity is
lost [1-2]. </br>
This is joint work with Maximilian Engel and Felix Hummel.
</br></br>
[1] "Blow-up analysis of fast-slow PDEs with loss of hyperbolicity", M.
Engel and C. Kuehn, <a class="link-secondary" href="https://arxiv.org/abs/2007.09973" target="_blank">https://arxiv.org/abs/2007.09973</a>
</br>
[2] "Slow manifolds for infinite-dimensional evolution equations", F.
Hummel and C. Kuehn, <a class="link-secondary" href="https://arxiv.org/abs/2008.10700" target="_blank">https://arxiv.org/abs/2008.10700</a></p>
</div>
</td>
</tr>
<tr>
</tbody>
</table>
</div>
</div>
<div class="bg-dark me-md-3 pt-3 px-3 pt-md-4 px-md-5 text-justify text-white overflow-hidden">
<div class="my-0 py-0">
<h4 class="display-9 text-primary">Tuesday, March 23</h4>
<table class="table table-sm table-dark table-borderless">
<tbody>
<tr>
<th scope="row" rowspan="2" width="10%">15:30</th>
<td>Pedro J. Torres</br><i>Periodic solutions of the Lorentz force equation</i></br></td>
</tr>
<tr>
<td><!--<div class="btn-links"><a class="btn btn-outline-light my-1 btn-sm" href="#" target="_blank" real="noopener">
<i class="fas fa-images mr-1"> </i>slides</a></div>-->
<button type="button" class="btn btn-outline-light btn-sm" data-toggle="collapse" data-target="#abs4">Abstract</button><p></p>
<div id="abs4" class="collapse"><p style="font-size:small" class="text-left">The Lorentz force equation governs the motion of a charged
particle under the effect of an electromagnetic field. In spite of that it plays a fundamental role in Classical Electromagnetism together
with Maxwell equations, the application of the most known methods in Nonlinear Analysis and Dynamical Systems is still under development.
The purpose of this talk is to present some recent results on the existence of periodic solutions when the electromagnetic field is periodic
in time, and to identify several open problems.</p>
</div>
</td>
</tr>
<tr>
<th scope="row" rowspan="2" width="10%">16:30</th>
<td>Frank Hilker</br><i>Mathematical models of a social-ecological system: coupling lake pollution dynamics and human behavior</i></br></td>
</tr>
<tr>
<td><!--<div class="btn-links"><a class="btn btn-outline-light my-1 btn-sm" href="#" target="_blank" real="noopener">
<i class="fas fa-images mr-1"> </i>slides</a></div>-->
<button type="button" class="btn btn-outline-light btn-sm" data-toggle="collapse" data-target="#abs5">Abstract</button><p></p>
<div id="abs5" class="collapse"><p style="font-size:small" class="text-left">From global warming over land-use change to pollution, the world is facing many environmental problems. While the causes are mostly
well-known from a natural sciences point of view, the challenge is the implementation of possible solutions. Societal demands, human behavior, and economic aspects not only impact the environmental state, but are
reversely affected by the environment. Mathematical models can be helpful in better understanding mutual feedbacks in coupled human-environment systems. In this talk, I will introduce a system of
two nonlinear differential equations, one describing lake water pollution and the other one describing human behavior of discharging pollutants. The latter uses approaches from evolutionary game theory.
Stability analysis reveals up to four alternative attractors as well as limit cycle oscillations. Numerical bifurcation analysis suggests the existence of Bogdanov-Takens and saddle-node homoclinic bifurcations.
In addition, some very preliminary results will be shown to indicate potential effects of discontinuous policy instruments.</br>
(Joint work with Anthony Sun.)</p>
</div>
</td>
</tr>
<tr><td></td><td class="text-left text-primary"><p>Break</p></td>
</tr>
<tr>
<th scope="row" rowspan="2" width="10%">17:40</th>
<td>Peter Poláčik</br><i>Quasiperiodic partially localized solutions of nonlinear elliptic equations on the entire space</i></br></td>
</tr>
<tr>
<td><!--<div class="btn-links"><a class="btn btn-outline-light my-1 btn-sm" href="#" target="_blank" real="noopener">
<i class="fas fa-images mr-1"> </i>slides</a></div>-->
<button type="button" class="btn btn-outline-light btn-sm" data-toggle="collapse" data-target="#abs6">Abstract</button><p></p>
<div id="abs6" class="collapse"><p style="font-size:small" class="text-left">In this joint project with Dario Valdebenito, we study positive partially localized solutions of elliptic equations on the entire space. "Partially localized" means that the solutions decay to zero in all but one variable;
we examine their behavior in the remaining variable. Our goal is to prove the existence of solutions which are quasiperiodic in the nondecay variable.
In the lecture, I will discuss our techniques and report on recent progress.</p>
</div>
</td>
</tr>
<tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="position-relative text-center d-md-flex flex-md-equal w-100 my-md-3 ps-md-3">
<div id="registration" class="bg-light me-md-3 pt-3 px-3 pt-md-4 px-md-5 text-center overflow-hidden">
<div class="my-0 p-0">
<h3 class="display-9">Registration</h3>
<p><b>Participation in the meeting is free upon registration.</b></br>The registration for the NLM2021 is open!</p>
<a class="btn btn-danger" style="font-size:small" href="https://cesnet.zoom.us/meeting/register/tJUldempqz0tH9HmH5uTK0an4tIt3JsmlR4i" target="_blank">REGISTER HERE</a>
<p></br>For more information, please write to <code>gidoni[at]utia[dot]cas[dot]cz</code>.</p>
<p></p>
</div>
</div>
<div id="registration" class="bg-light me-md-3 pt-3 px-3 pt-md-4 px-md-5 text-center overflow-hidden">
<div class="my-0 p-0">
<h3 class="display-9">Information</h3>
<p>As it is not possible to attend Zoom meetings with registration through the web client,</br>
<span class="text-danger">to join this meeting the use of the desktop client or mobile app is required.</span></p>
<p>If you have not already installed it, you can download it at this <a class="link-secondary text-danger" href="https://zoom.us/download" target="_blank">link</a>.</p>
</div>
</div>
<div id="archive" class="bg-light me-md-3 pt-3 px-3 pt-md-4 px-md-5 text-center overflow-hidden ">
<div class="my-0 py-0">
<h3 class="display-9">Past NLMs</h3>
<p>The workshop continues the series of Nonlinear Meetings, which started in Turin (2015).</p>
<p>Visit the websites of the past editions:</br>
<a href="https://sites.google.com/site/nlmt2015/" target="_blank">Turin-2015</a>, <a href="https://sites.google.com/site/nonmil16/" target="_blank">Milan-2016</a>,
<a href="https://sites.google.com/site/2017nlmu/" target="_blank">Udine-2017</a>, <a href="https://sites.google.com/view/nlmt2019" target="_blank">Turin-2019</a>,
<a href="https://sites.google.com/view/nonlinear-meeting-milan-2020" target="_blank">Milan-2020</a>.</p>
</div>
</div>
</div>
</main>
<div class="position-relative overflow-hidden p-12 p-md-12 m-md-12 my-10 pt-3 text-center">
<div class="column">
<h5>Organizers</h5>
<p>
<a class="link-secondary text-dark" href="https://users.dimi.uniud.it/~guglielmo.feltrin/" target="_blank">Guglielmo Feltrin</a> <span style="font-size: 100%">|</span>
<a class="link-secondary text-dark" href="http://www.paologidoni.com/" target="_blank">Paolo Gidoni</a> <span style="font-size: 100%">|</span>
<a class="link-secondary text-dark" href="https://www.elisasovrano.it/" target="_blank">Elisa Sovrano</a> <span style="font-size: 100%">|</span>
<a class="link-secondary text-dark" href="http://andreatellini.weebly.com/" target="_blank">Andrea Tellini</a>
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