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enRational Reconstructions. Making Sense of Proofs with Inconsistent Premises [Math. Logic]
http://cmafcio.ciencias.ulisboa.pt/node/52
<span>Rational Reconstructions. Making Sense of Proofs with Inconsistent Premises [Math. Logic]</span>
<div><time datetime="2017-03-31T15:00:00Z">Fri, 03/31/2017 - 15:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 03/27/2017 - 09:40</span>
<div><p><strong>Michèle Friend</strong> (The George Washington University)</p>
<p>Most mathematicians are classical or constructivist reasoners, so they think that contradictions lead to trivial theories, and the latter are disasters. Modern Western mathematicians make proofs. Often, these are only partly formal. Some of them use sets of premises that belong to theories that are inconsistent with each other. Some of them even use sets of premises that are inconsistent with each other in the stronger sense that it is possible to derive a contradiction from the premises. Even worse, few mathematicians seem perturbed by this. How do we explain the lack of concern?</p>
<p>First note that almost none of these proofs use an ex contradictione quodlibet proof or sub-proof, since this would explicitly bring disaster. We could use a paraconsistent logic to reconstruct the reasoning, but this would be disingenuous towards the beliefs and practices of working mathematicians. As an alternative, we can use a proof reconstruction strategy called ‘chunk and permeate’, developed by Brown (2004, 2016). The proof is divided into several consistent chunks, and only some information from one chunk permeates to the next chunk. I explain the strategy in more detail.</p>
<p>One problem that is still outstanding in the strategy is how to individuate consistent chunks. So far, this has been done intuitively. Following a suggestion by Abramsky et. al. (2015), we propose to make this less of an intuitive exercise by using bundle theory to represent chunks. In the conclusion, we discuss the limitations of this proposed solution to the outstanding problem. We then extend the method to include scientific reasoning. Finally, we draw some conclusions about the limitations of the method.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.38</a> [⤴]</p></div>
Mon, 27 Mar 2017 09:40:34 +0000pjmendes@fc.ul.pt52 at http://cmafcio.ciencias.ulisboa.ptGlobal solutions to random 3D vorticity equations for small initial data [Analysis & Diff. Eqs.]
http://cmafcio.ciencias.ulisboa.pt/node/51
<span>Global solutions to random 3D vorticity equations for small initial data [Analysis & Diff. Eqs.]</span>
<div><time datetime="2017-03-31T11:00:00Z">Fri, 03/31/2017 - 11:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Wed, 03/22/2017 - 09:18</span>
<div><p><strong>Michael Röckner</strong> (Bielefeld University)</p>
<p>One proves the existence and uniqueness in <span><span><span><span><span><span><span><span><span>(</span></span></span></span><span><span><span><em>L<sup>p</sup></em></span></span></span><span>(</span><span><span><span><span><span><span>R</span></span></span></span><sup><span><span>3</span></span></sup></span></span><span>)</span><span><span><span><span><span><span><span>)</span></span></span></span></span><sup><span><span>3</span></span></sup></span></span></span></span></span></span></span>, <span><span><span><span><span><span><span><span><span>3/</span></span><span><span>2 </span></span></span></span><span>< </span><em>p </em><span>< </span><span>2</span></span></span></span></span></span>, of a global mild solution to random vorticity equations associated to stochastic 3D Navier-Stokes equations with linear multiplicative Gaussian noise of convolution type, for sufficiently small initial vorticity. This resembles some earlier deterministic results of T. Kato and are obtained by treating the equation in vorticity form and reducing the latter to a random nonlinear parabolic equation. The solution has maximal regularity in the spatial variables and is weakly continuous in <span><span><span><span><span><span><span><span><span>(</span></span></span></span><span><span><span><em>L</em></span><sup><span><span>3</span></span></sup></span></span><span> ∩ </span><span><span><span><em>L</em></span><sup><span><span><span><span><span><span><span><span>3</span><em>p</em></span></span><span><span><span>/(4</span><em>p</em><span>−</span><span>6)</span></span></span></span></span></span></span></span></sup></span></span><span><span><span><span><span><span><span>)</span></span></span></span></span><sup><span><span>3</span></span></sup></span></span></span></span></span></span></span> with respect to the time variable. Furthermore, we obtain the pathwise continuous dependence of solutions with respect to the initial data.</p>
<p>[Event co-organized by the <a href="http://gfm.cii.fc.ul.pt">Group of Matematical Physics</a> of the University of Lisbon.]</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.38</a> [⤴]</p></div>
Wed, 22 Mar 2017 09:18:44 +0000pjmendes@fc.ul.pt51 at http://cmafcio.ciencias.ulisboa.ptAnalytic determinacy (part 5 and last) [Math. Logic]
http://cmafcio.ciencias.ulisboa.pt/node/50
<span>Analytic determinacy (part 5 and last) [Math. Logic]</span>
<div><time datetime="2017-03-24T15:00:00Z">Fri, 03/24/2017 - 15:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 03/20/2017 - 13:19</span>
<div><p><strong>António Fernandes</strong> (Instituto Superior Técnico, Universidade de Lisboa)</p>
<p>The purpose of this talk (eventually a series of talks) is to exhibit a proof (by Donald Martin) that analytic determinacy holds under a certain large cardinal hypothesis. In fact we intend to convey a little bit more than just the content of this proof, we will try to enlighten the deep connection between determinacy, which is a game related concept, and the theory of definable sets of reals.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]</p></div>
Mon, 20 Mar 2017 13:19:21 +0000pjmendes@fc.ul.pt50 at http://cmafcio.ciencias.ulisboa.ptTopological Lattice Models in Geometry and Physics [Geometry]
http://cmafcio.ciencias.ulisboa.pt/node/49
<span>Topological Lattice Models in Geometry and Physics [Geometry]</span>
<div><time datetime="2017-03-31T14:00:00Z">Fri, 03/31/2017 - 14:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 03/13/2017 - 14:55</span>
<div><p><strong>Björn Gohla</strong> (Group of Mathematical Physics - University of Lisbon)</p>
<p>Lattice models arise in physics as discrete approximations of quantum field theories (QFT). Topological quantum field theories (TQFT) on the other hand by definition are QFTs, that can be defined on smooth or topological space-times, as opposed to the usual pseudo-Riemannian space-times required by QFTs. Interesting TQFTs can be defined as lattice models, giving exactly solvable models in 2 dimensions for example. As an example in mathematics the Turaev-Viro TQFT gives a well defined topological invariant of 3-manifolds.</p>
<p>We will give an overview of these phenomena and present our work on a 4-dimensional gravitational lattice model.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.38</a> [⤴]</p></div>
Mon, 13 Mar 2017 14:55:07 +0000pjmendes@fc.ul.pt49 at http://cmafcio.ciencias.ulisboa.ptAnalytic determinacy (part 4) [Math. Logic]
http://cmafcio.ciencias.ulisboa.pt/node/48
<span>Analytic determinacy (part 4) [Math. Logic]</span>
<div><time datetime="2017-03-17T15:00:00Z">Fri, 03/17/2017 - 15:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 03/13/2017 - 10:48</span>
<div><p><strong>António Fernandes</strong> (Instituto Superior Técnico, Universidade de Lisboa)</p>
<p>The purpose of this talk (eventually a series of talks) is to exhibit a proof (by Donald Martin) that analytic determinacy holds under a certain large cardinal hypothesis. In fact we intend to convey a little bit more than just the content of this proof, we will try to enlighten the deep connection between determinacy, which is a game related concept, and the theory of definable sets of reals.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]</p></div>
Mon, 13 Mar 2017 10:48:20 +0000pjmendes@fc.ul.pt48 at http://cmafcio.ciencias.ulisboa.ptCharacterization of Sobolev Spaces Through Functionals without Derivatives Dependence [Analysis & Diff. Eqs.]
http://cmafcio.ciencias.ulisboa.pt/node/47
<span>Characterization of Sobolev Spaces Through Functionals without Derivatives Dependence [Analysis & Diff. Eqs.]</span>
<div><time datetime="2017-03-24T15:00:00Z">Fri, 03/24/2017 - 15:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Wed, 03/08/2017 - 11:45</span>
<div><p><strong>Ana Margarida Ribeiro</strong> (CMA - FCT, Universidade Nova de Lisboa)</p>
<p>Extending previous works due to Bourgain, Brézis, and Mironescu [J. Anal. Math. 87 (2002)] and Leoni and Spector [J. Funct. Anal. 261, 10 (2011)], we provide new characterizations of Sobolev spaces in terms of functionals involving difference quotients. These characterizations have their origin on the study of the limit behavior of the Gagliardo semi-norms taken by Bourgain, Brézis, and Mironescu and may have some applications to imaging problems. Our results include classical higher-order Sobolev spaces as well as the variable exponent case. More general spaces as Musielak-Orlicz spaces will also be discussed. This talk is a consequence of a joint work with C. Kreisbeck and R. Ferreira [Nonlinear Analysis: Theory, Methods & Applications (2015)] and with P. Hästö [Communications in Contemporary Mathematics (2016 online ready)].</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]</p></div>
Wed, 08 Mar 2017 11:45:41 +0000pjmendes@fc.ul.pt47 at http://cmafcio.ciencias.ulisboa.ptAnalytic determinacy (part 3) [Math. Logic]
http://cmafcio.ciencias.ulisboa.pt/node/46
<span>Analytic determinacy (part 3) [Math. Logic]</span>
<div><time datetime="2017-03-10T15:00:00Z">Fri, 03/10/2017 - 15:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 03/06/2017 - 09:51</span>
<div><p><strong>António Fernandes</strong> (Instituto Superior Técnico, Universidade de Lisboa)</p>
<p>The purpose of this talk (eventually a series of talks) is to exhibit a proof (by Donald Martin) that analytic determinacy holds under a certain large cardinal hypothesis. In fact we intend to convey a little bit more than just the content of this proof, we will try to enlighten the deep connection between determinacy, which is a game related concept, and the theory of definable sets of reals.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]</p></div>
Mon, 06 Mar 2017 09:51:36 +0000pjmendes@fc.ul.pt46 at http://cmafcio.ciencias.ulisboa.ptDo we need new academic skills in healthcare innovation, and how should we teach them? [Statistics]
http://cmafcio.ciencias.ulisboa.pt/node/45
<span>Do we need new academic skills in healthcare innovation, and how should we teach them? [Statistics]</span>
<div><time datetime="2017-03-07T14:30:00Z">Tue, 03/07/2017 - 14:30</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Thu, 03/02/2017 - 14:46</span>
<div><p><strong>Finn Valentin</strong> (Professor at Copenhagen Business School (CBS) - Director of the EIT-labelled MSc Innovation in Health Care)</p>
<p>In preparation of launching the new MSc in Innovation in Health Care we surveyed what new skills and approaches to innovation are requested by key stakeholder (companies, hospitals etc). The IHC program was designed largely as an answer to these needs. My talk reports on the needs identified in this survey and how we translated them into the skills we should teach in an MSc degree, and the way we should teach them.</p>
<p>This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.4.31</a> [⤴]</p></div>
Thu, 02 Mar 2017 14:46:49 +0000pjmendes@fc.ul.pt45 at http://cmafcio.ciencias.ulisboa.ptNormal complex spaces with near to quotient singularities [Geometry]
http://cmafcio.ciencias.ulisboa.pt/node/44
<span>Normal complex spaces with near to quotient singularities [Geometry]</span>
<div><time datetime="2017-03-24T14:00:00Z">Fri, 03/24/2017 - 14:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Wed, 03/01/2017 - 16:24</span>
<div><p><strong>Daniel Barlet</strong> (Univ. Nancy)</p>
<p>This is a joint work with J. Magnusson. We introduce an interesting class of normal complex spaces having only mild singularities (near to quotient singularities) in which we can generalize the notion of (analytic) fundamental class for complex cycles and also the notion of relative fundamental class for an analytic family of cycles. We also generalize to these spaces the intersection theory for cycles with rational positive coefficients. This also extends to the intersection of analytic families of cycles. We show that almost all the properties of these notions generalize to this context with the exception of the fact that the fundamental classes of the intersection of two cycles whose intersection has the expected co-dimension is not always given by the cup-product of their fundamental classes.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]</p></div>
Wed, 01 Mar 2017 16:24:10 +0000pjmendes@fc.ul.pt44 at http://cmafcio.ciencias.ulisboa.ptRate-independent systems and anisotropic dry friction [Analysis & Diff. Eqs.]
http://cmafcio.ciencias.ulisboa.pt/node/43
<span>Rate-independent systems and anisotropic dry friction [Analysis & Diff. Eqs.]</span>
<div><time datetime="2017-03-16T13:30:00Z">Thu, 03/16/2017 - 13:30</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Wed, 03/01/2017 - 16:17</span>
<div><p><strong>Paolo Gidoni</strong> (CMAF-CIO, Universidade de Lisboa)</p>
<p>In this talk we discuss how the framework and techniques of rate-independent systems can be applied to models involving dry friction. After a quick overview on the motility of bio-inspired crawlers, we will focus on the genesis of an anisotropy in friction when the interaction is mediated by bristle-like elements. We illustrate a convergence result, showing the rate-independent nature of the limit of a family of systems characterized by a vanishing viscosity and a wiggly perturbation in the energy, scaling to zero. We then apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations, and discuss the effect of the geometry and elasticity of the bristle on the friction coefficients.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]</p></div>
Wed, 01 Mar 2017 16:17:21 +0000pjmendes@fc.ul.pt43 at http://cmafcio.ciencias.ulisboa.pt