<div dir="ltr"><div dir="auto"><div dir="auto">Dear all,<div dir="auto"><br></div><div dir="auto">We remind you the upcoming talk of "Insalate di Matematica".</div><div dir="auto">Here the details:</div><div dir="auto"><br></div><div dir="auto"><u>Speaker</u>: Elia Bubani (Universität Bern, Mathematisches Institut)</div><div dir="auto"><br></div><div dir="auto"><u>Date and time</u>: <b>25th of January 2023, 4:00 pm (CET)</b></div><div dir="auto"><br></div><div dir="auto"><u>Information to attend</u></div><div dir="auto"><u>In presence</u>: The seminar will take place in room 3014, at the building U5-Ratio, Università degli Studi di Milano Bicocca.</div><div dir="auto"><u>Online</u>: The seminar will be streamed via Webex platform at the following link: <a href="https://unimib.webex.com/unimib/j.php?MTID=mf6e65bdc68ff6e42f66f375532a90f05" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">https://unimib.webex.com/unimib/j.php?MTID=mf6e65bdc68ff6e42f66f375532a90f05</a> (Password: Insalate (46725283 from phones))</div><div dir="auto"><br></div><div dir="auto"><u>Title</u>: "The Modulus of a curve family"</div><div dir="auto"><br></div><div dir="auto"><u>Abstract</u>: <span style="font-size:12.8px">Let's try to set up a geometric problem in the Euclidean plane: consider a square </span><img alt="Q = (0, 1) \times (0, 1)" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=Q%09=%09(0,%091)%09%5Ctimes%09(0,%091)" height="16" width="125" style="font-size:12.8px;display:inline;vertical-align:-4.333px"><span style="font-size:12.8px"> and a rectangle </span><img alt="R_{a,b} = (0, a) \times (0, b)" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=R%5F%7Ba,b%7D%09=%09(0,%09a)%09%5Ctimes%09(0,%09b)" height="17" width="139" style="font-size:12.8px;display:inline;vertical-align:-5px"><span style="font-size:12.8px">. The Riemann mapping theorem guarantees that </span><img alt="Q" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=Q" height="14" width="11" style="font-size:12.8px;display:inline;vertical-align:-3.333px"><span style="font-size:12.8px"> and </span><img alt="R_{a,b}" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=R%5F%7Ba,b%7D" height="16" width="26" style="font-size:12.8px;display:inline;vertical-align:-5px"><span style="font-size:12.8px"> are conformally equivalent. Any conformal homeomorphism between the square and the rectangle extends homeomorphically to the boundary. One might ask whether it is possible to do this in </span><span style="font-size:12.8px">such a way that the horizontal edges of </span><img alt="Q" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=Q" height="14" width="11" style="font-size: 12.8px; display: inline; vertical-align: -3.333px;"><span style="font-size:12.8px"> are mapped to the corresponding horizontal edges of </span><img alt="R_{a,b}" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=R%5F%7Ba,b%7D" height="16" width="26" style="font-size: 12.8px; display: inline; vertical-align: -5px;"><span style="font-size:12.8px"> ,and analogously for the vertical edges of the rectangles. </span><span style="font-size:12.8px">In order to answer such questions we shall introduce the Modulus of a curve family. </span><span style="font-size:12.8px">This tool has been relevant for the notion of Quasiconformal maps and related theory.</span></div><div dir="auto"><br></div><div dir="auto"><u>Keywords</u>: Conformal geometry, Modulus of a curve family, Quasiconformal maps</div><div dir="auto"><br></div><div dir="auto"><b>** We inform you that the talk will be recorded and uploaded on our website. If you join the talk after the starting time, we kindly ask you to ensure that your microphone and webcam are turned off **</b></div><div dir="auto"><br></div><div dir="auto">You can find the poster of the event in the attachment.</div><div dir="auto">We are looking forward to seeing you! </div><div dir="auto"><br></div><div dir="auto">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">insalate.matematica@unimib.it</a>. Find us also on our Instagram page: <a href="https://www.instagram.com/insalate_di_matematica22/" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://www.instagram.com/insalate_di_matematica22/</a>.</div><div dir="auto"><br></div><div dir="auto">The organizers: Andrea Bisterzo, Alberto Cassella, Bianca Marchionna, Andrea Rivezzi, Giovanni Siclari, Marta Tameni, Matteo Tarocchi, Marco Zullino.</div></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto">Il Gio 19 Gen 2023, 08:00 Mbs Insalate Di Matematica <<a href="mailto:insalate.matematica@unimib.it" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">insalate.matematica@unimib.it</a>> ha scritto:<br></div><div dir="auto"><div class="gmail_quote" dir="auto"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Dear all,<div dir="auto"><br></div><div dir="auto">As part of the series of seminars "Insalate di Matematica", <b>Elia Bubani</b> (Universität Bern, Mathematisches Institut) will give a talk. </div><div dir="auto">The speaker will deliver the talk <u>in presence</u> and the meeting will also be broadcasted <u>online</u> (see below for more information).</div><div dir="auto"><br></div><div dir="auto">Here the details:</div><div dir="auto"><br></div><div dir="auto"><u>Date and time</u>: 25th of January 2023, 4:00 pm (CET)</div><div dir="auto"><br></div><div dir="auto"><u>Title</u>: "The Modulus of a curve family"</div><div dir="auto"><br></div><div dir="auto"><u>Abstract</u>: Let's try to set up a geometric problem in the Euclidean plane: consider a square <img alt="Q = (0, 1) \times (0, 1)" title="Q = (0, 1) \times (0, 1)" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=Q%09=%09(0,%091)%09%5Ctimes%09(0,%091)" id="m_-1630625441884155417m_4987539709559204003m_-2820915040475545318m_2840651351333992155m_2317894252064516837m_-4116235816642768638m_7222650772971176376m_-3936592748596884061m_-1492797053028058444m_-5403980044539766774m_-6514202956528603003l0.654297222624326" height="16" width="125" style="display:inline;vertical-align:-4.333px"> and a rectangle <img alt="R_{a,b} = (0, a) \times (0, b)" title="R_{a,b} = (0, a) \times (0, b)" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=R%5F%7Ba,b%7D%09=%09(0,%09a)%09%5Ctimes%09(0,%09b)" id="m_-1630625441884155417m_4987539709559204003m_-2820915040475545318m_2840651351333992155m_2317894252064516837m_-4116235816642768638m_7222650772971176376m_-3936592748596884061m_-1492797053028058444m_-5403980044539766774m_-6514202956528603003l0.5351911391889741" height="17" width="139" style="display:inline;vertical-align:-5px">. The Riemann mapping theorem guarantees that <img alt="Q" title="Q" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=Q" id="m_-1630625441884155417m_4987539709559204003m_-2820915040475545318m_2840651351333992155m_2317894252064516837m_-4116235816642768638m_7222650772971176376m_-3936592748596884061m_-1492797053028058444m_-5403980044539766774m_-6514202956528603003l0.8187093389063083" height="14" width="11" style="display:inline;vertical-align:-3.333px"> and <img alt="R_{a,b}" title="R_{a,b}" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=R%5F%7Ba,b%7D" id="m_-1630625441884155417m_4987539709559204003m_-2820915040475545318m_2840651351333992155m_2317894252064516837m_-4116235816642768638m_7222650772971176376m_-3936592748596884061m_-1492797053028058444m_-5403980044539766774m_-6514202956528603003l0.9270124996999485" height="16" width="26" style="display:inline;vertical-align:-5px"> are conformally equivalent. Any conformal homeomorphism between the square and the rectangle extends homeomorphically to the boundary. One might ask whether it is possible to do this in</div>such a way that the horizontal edges of <img alt="Q" title="Q" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=Q" id="m_-1630625441884155417m_4987539709559204003m_-2820915040475545318m_2840651351333992155m_2317894252064516837m_-4116235816642768638m_7222650772971176376m_-3936592748596884061m_-1492797053028058444m_-5403980044539766774m_-6514202956528603003l0.6495223096113683" style="display:inline;vertical-align:-3.333px" height="14" width="11"> are mapped to the corresponding horizontal edges of <img alt="R_{a,b}" title="R_{a,b}" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=R%5F%7Ba,b%7D" id="m_-1630625441884155417m_4987539709559204003m_-2820915040475545318m_2840651351333992155m_2317894252064516837m_-4116235816642768638m_7222650772971176376m_-3936592748596884061m_-1492797053028058444m_-5403980044539766774m_-6514202956528603003l0.48912707061605887" style="display:inline;vertical-align:-5px" height="16" width="26"> ,and analogously for the vertical edges of the rectangles.<br>In order to answer such questions we shall introduce the Modulus of a curve family.<br>This tool has been relevant for the notion of Quasiconformal maps and related theory.<div><br><div dir="auto"><u>Keywords</u>: Conformal geometry, Modulus of a curve family, Quasiconformal maps</div><div dir="auto"><br></div><div dir="auto"><u><b>Information to attend in room 3014</b></u></div><div dir="auto">The seminar will take place in room 3014, at the building U5-Ratio, Università degli Studi di Milano Bicocca.</div><div dir="auto"><br></div><div dir="auto"><u><b>Information to attend online</b></u></div><div dir="auto"><font color="#0000ff"><u><a href="https://unimib.webex.com/unimib/j.php?MTID=mf6e65bdc68ff6e42f66f375532a90f05" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://unimib.webex.com/unimib/j.php?MTID=mf6e65bdc68ff6e42f66f375532a90f05</a></u></font> (Password: Insalate (46725283 from phones))<br></div><div dir="auto"><br></div><div dir="auto"><b>** We inform you that the talk will be recorded and uploaded on our website. If you join the talk after the starting time, we kindly ask you to ensure that your microphone and webcam are turned off **</b></div><div dir="auto"><br></div><div dir="auto">You can find the poster of the event in the attachment. </div><div dir="auto">We are looking forward to seeing you! </div><div dir="auto"><br></div><div dir="auto">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">insalate.matematica@unimib.it</a>. Find us also on our Instagram page: <a href="https://www.instagram.com/insalate_di_matematica22/" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://www.instagram.com/insalate_di_matematica22/</a></div><div dir="auto"><br></div><div dir="auto">The organizers: Andrea Bisterzo, Alberto Cassella, Bianca Marchionna, Andrea Rivezzi, Giovanni Siclari, Marta Tameni, Matteo Tarocchi, Marco Zullino.</div></div></div>
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