<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 1px; margin-left: 58px; text-indent: -58px; font: normal normal normal 12px/normal Helvetica; "><b><span class="Apple-style-span" style="font-weight: normal; font-size: medium; ">Cari colleghi,</span></b></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 1px; margin-left: 58px; text-indent: -58px; font: normal normal normal 12px/normal Helvetica; "><b><span class="Apple-style-span" style="font-weight: normal; font-size: medium; ">vi comunichiamo che domani, mercoledi' </span><span class="Apple-style-span" style="font-weight: normal; font-size: medium; "><b> 26 febbraio</b></span><span class="Apple-style-span" style="font-weight: normal; font-size: medium; "> alle ore </span><span class="Apple-style-span" style="font-weight: normal; font-size: medium; "><b>16.00 </b></span><span class="Apple-style-span" style="font-weight: normal; font-size: medium; ">nell'<u>aula</u> <u>riunioni</u>, presso il Dipartimento di Matematica (Universita'</span></b></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 1px; margin-left: 58px; text-indent: -58px; font: normal normal normal 12px/normal Helvetica; "><b><span class="Apple-style-span" style="font-weight: normal; font-size: medium; ">di Pisa), il Prof. Tohru Ozawa (Waseda University) presentera' un seminario dal titolo: </span></b></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 1px; margin-left: 58px; text-indent: -58px; font: normal normal normal 12px/normal Helvetica; "><span class="Apple-style-span" style="font-size: medium; "><br></span></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 1px; margin-left: 58px; text-indent: -58px; font: normal normal normal 12px/normal Helvetica; "><span class="Apple-style-span" style="font-size: medium; ">"Refinements of Holder's inequality"</span></p><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 1px; margin-left: 58px; text-indent: -58px; font: normal normal normal 12px/normal Helvetica; "><br class="webkit-block-placeholder"></div><div style="font-weight: normal; font-size: medium; "><div><br></div><div>e alle ore <b>17.00</b> il Dott. Matthias Erbar (University of Bonn) presentera' un seminario dal titolo:</div><div><br></div><div><span class="Apple-style-span">"</span>Bochner's inequality and the entropic curvature-dimension condition on metric measure spaces<span class="Apple-style-span">"</span></div><div><br></div><div>Abstract: Bochner's inequality is one of the most fundamental estimates in geometric analysis on Riemannian manifolds.</div>The main result I present in this talk is a Bochner inequality on metric measure spaces with linear heat flow and satisfying the (reduced) </div><div style="font-weight: normal; font-size: medium; ">curvature-dimension condition. Indeed, also the converse is true: if the heat flow on a metric measure space is linear then an appropriate version</div><div style="font-weight: normal; font-size: medium; ">of the Bochner inequality (for the canonical gradient and Laplacian) will imply the reduced curvature-dimension condition. Besides that, I will</div><div style="font-weight: normal; font-size: medium; ">present also new, sharp Wasserstein-contraction results for the heat flow as well as Bakry-Ledoux type gradient estimates each of which is</div><div style="font-weight: normal; font-size: medium; ">equivalent to the curvature-dimension condition.<div><br></div><div>Saluti <br><br></div><div>Agnese & Bozhidar</div></div></body></html>