<div dir="ltr"><div dir="ltr"><div dir="auto"><div dir="auto">Dear all,<div dir="auto"><br></div><div dir="auto"><div dir="auto"><div dir="auto"><div><font face="arial, sans-serif" color="#000000">As a part of </font><span style="font-family:arial,sans-serif">"</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0);font-style:italic;font-variant-ligatures:none;text-align:justify">Geometry & Topology seminars at Unimib</span><span style="font-family:arial,sans-serif">", it is our pleasure to announce t</span><font face="arial, sans-serif">he speaker:</font></div><div><font face="arial, sans-serif"><span style="box-sizing:border-box;color:rgb(0,0,0);font-variant-ligatures:none;vertical-align:baseline"><i>Wei-Chuan Shen</i>, </span><span style="box-sizing:border-box;color:rgb(0,0,0);font-variant-ligatures:none;font-style:italic;vertical-align:baseline">(University of Cologne</span></font><font face="arial, sans-serif"><span style="box-sizing:border-box;color:rgb(0,0,0);font-variant-ligatures:none;font-style:italic;vertical-align:baseline">)</span></font>. </div></div></div><div dir="auto"><div dir="auto">The speaker will deliver the talk <i><u>online</u></i> via Webex platform and the meeting will be <i><u>streamed also in room 3014</u></i>, at the building U5-Ratio, Università degli Studi di Milano Bicocca.</div></div></div></div><div dir="auto"><div dir="auto"><br></div></div></div><div dir="auto"><u>Date and time</u>: 3rd of May 2023, 14.00 pm (CET)</div><div dir="auto"><br></div><div dir="auto"><font face="arial, sans-serif"><u>Title</u>: </font><span style="font-variant-ligatures:none"><font face="arial, sans-serif" style="">Semiclassical spectral asymptotics of Toeplitz operators on CR manifolds</font></span></div><div dir="auto"><br></div><div><font face="arial, sans-serif"><u>Abstract</u>: </font><span class="gmail-C9DxTc" style="box-sizing:border-box;font-variant-ligatures:none;text-align:justify;font-family:Arial;vertical-align:baseline">This talk deals with semiclassical spectral asymptotics of Toeplitz operators on CR manifolds. First, we recall the notions of compact strictly pseudoconvex embeddable CR manifolds and Szeg</span><span style="color:rgb(32,33,34);font-family:sans-serif;font-size:14px">ő</span><span style="color:rgb(32,33,34);font-family:sans-serif;font-size:14px"> </span><span class="gmail-C9DxTc" style="box-sizing:border-box;font-variant-ligatures:none;text-align:justify;font-family:Arial;vertical-align:baseline">kernel expansion. We then review some classical and recent developments for Toeplitz operators and their functional calculus. Finally, we study the spectral operator </span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="gmail-mwe-math-fallback-image-inline" aria-hidden="true" alt="{\displaystyle \chi }" style="color: rgb(32, 33, 34); font-family: sans-serif; font-size: 14px; border: 0px; vertical-align: -0.671ex; margin: 0px; display: inline-block; width: 1.455ex; height: 2.009ex;"><sub style="line-height:1;font-size:11.2px;color:rgb(32,33,34);font-family:sans-serif">k</sub><span style="font-family:Arial;font-variant-ligatures:none;text-align:justify">(</span><span style="font-family:Arial;font-variant-ligatures:none;text-align:justify">T</span><sub style="line-height:1;font-size:11.2px;color:rgb(32,33,34);font-family:sans-serif">P</sub><span class="gmail-C9DxTc" style="box-sizing:border-box;font-variant-ligatures:none;text-align:justify;font-family:Arial;vertical-align:baseline">) constructed by the functional calculus of the first-order Toeplitz operator, which considers a set of eigenvalues in <i>k</i><font size="1"> </font>supp(</span><span class="gmail-mwe-math-element" style="color:rgb(32,33,34);font-family:sans-serif;font-size:14px"><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="gmail-mwe-math-fallback-image-inline" aria-hidden="true" alt="{\displaystyle \chi }" style="border: 0px; vertical-align: -0.671ex; margin: 0px; display: inline-block; width: 1.455ex; height: 2.009ex;">)</span><span style="color:rgb(32,33,34);font-family:sans-serif;font-size:14px"> </span><span class="gmail-C9DxTc" style="box-sizing:border-box;font-variant-ligatures:none;text-align:justify;font-family:Arial;vertical-align:baseline"> and weights them according to the values of a good cutoff function </span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="gmail-mwe-math-fallback-image-inline" aria-hidden="true" alt="{\displaystyle \chi }" style="color: rgb(32, 33, 34); font-family: sans-serif; font-size: 14px; border: 0px; vertical-align: -0.671ex; margin: 0px; display: inline-block; width: 1.455ex; height: 2.009ex;"><sub style="line-height:1;font-size:11.2px;color:rgb(32,33,34);font-family:sans-serif">k</sub><span class="gmail-C9DxTc" style="box-sizing:border-box;font-variant-ligatures:none;text-align:justify;font-family:Arial;vertical-align:baseline"> at each eigenvalue in the set. We will show that the kernel of the spectral operator </span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="gmail-mwe-math-fallback-image-inline" aria-hidden="true" alt="{\displaystyle \chi }" style="color: rgb(32, 33, 34); font-family: sans-serif; font-size: 14px; border: 0px; vertical-align: -0.671ex; margin: 0px; display: inline-block; width: 1.455ex; height: 2.009ex;"><sub style="line-height:1;font-size:11.2px;color:rgb(32,33,34);font-family:sans-serif">k</sub><span style="font-family:Arial;font-variant-ligatures:none;text-align:justify">(</span><span style="font-family:Arial;font-variant-ligatures:none;text-align:justify">T</span><sub style="line-height:1;font-size:11.2px;color:rgb(32,33,34);font-family:sans-serif">P</sub><span class="gmail-C9DxTc" style="box-sizing:border-box;font-variant-ligatures:none;text-align:justify;font-family:Arial;vertical-align:baseline">) </span><span class="gmail-C9DxTc" style="box-sizing:border-box;font-variant-ligatures:none;text-align:justify;font-family:Arial;vertical-align:baseline">is a semi-classical Fourier integral modulo a k-negligible smooth kernel. Time permitting, I will give some applications of such asymptotic expansion, which provides CR analogues (without group action assumption on our CR manifolds) of high power line bundle results in complex geometry.</span><span class="gmail-C9DxTc" style="box-sizing:border-box;font-variant-ligatures:none;text-align:justify;color:rgb(0,0,0);font-family:Arial;vertical-align:baseline"> </span></div><div style="margin:2px 0px 0px"></div></div><div dir="ltr"><div dir="auto"><br></div><div dir="auto"></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"></div><div dir="auto"><u><b>Information to attend online</b></u></div><div dir="auto"><span style="color:rgb(0,0,0);font-family:Arial;font-size:9pt;font-weight:700;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit">Join from the meeting link</span><br></div><div dir="auto"><p dir="ltr" class="gmail-zfr3Q gmail-CDt4Ke" style="box-sizing:border-box;font-variant-ligatures:none;margin:0pt 0px;outline:none;text-decoration-line:inherit;color:rgb(61,61,61);font-size:13pt;font-family:"Open Sans";line-height:2.05714;background-color:transparent;border-width:initial;border-style:none;border-color:initial;padding:0pt"><a class="gmail-XqQF9c" href="https://unimib.webex.com/unimib/j.php?MTID=m64c277795aaa7012a695de98e8a93036" target="_blank" style="box-sizing:border-box;color:inherit;text-decoration-line:none"><span class="gmail-C9DxTc" style="box-sizing:border-box;color:rgb(0,94,125);font-family:Arial;font-size:10.5pt;vertical-align:baseline">https://unimib.webex.com/unimib/j.php?MTID=m64c277795aaa7012a695de98e8a93036</span></a></p><p dir="ltr" class="gmail-zfr3Q gmail-CDt4Ke" style="box-sizing:border-box;font-variant-ligatures:none;margin:0pt 0px 9pt;outline:none;text-decoration-line:inherit;color:rgb(61,61,61);font-size:13pt;font-family:"Open Sans";line-height:1.38;background-color:transparent;border-width:initial;border-style:none;border-color:initial;padding:0pt"><span class="gmail-C9DxTc" style="box-sizing:border-box;color:rgb(0,0,0);font-family:Arial;font-size:9pt;font-weight:700;vertical-align:baseline">Join by meeting number</span></p><p dir="ltr" class="gmail-zfr3Q gmail-CDt4Ke" style="box-sizing:border-box;font-variant-ligatures:none;margin:0pt 0px;outline:none;text-decoration-line:inherit;color:rgb(61,61,61);font-size:13pt;font-family:"Open Sans";line-height:1.88571;background-color:transparent;border-width:initial;border-style:none;border-color:initial;padding:0pt"><span class="gmail-C9DxTc" style="box-sizing:border-box;color:rgb(51,51,51);font-family:Arial;font-size:10.5pt;vertical-align:baseline">Meeting number (access code): 2741 809 0209</span></p><p dir="ltr" class="gmail-zfr3Q gmail-CDt4Ke" style="box-sizing:border-box;font-variant-ligatures:none;margin:0pt 0px;outline:none;text-decoration-line:inherit;color:rgb(61,61,61);font-size:13pt;font-family:"Open Sans";line-height:1.88571;padding:0pt;background-color:transparent;border-width:initial;border-style:none;border-color:initial"><span class="gmail-C9DxTc" style="box-sizing:border-box;color:rgb(51,51,51);font-family:Arial;font-size:10.5pt;vertical-align:baseline">Meeting password: ZVbyAKn59D3 (98292565 from phones)</span></p></div><div dir="auto"><u><b><br></b></u></div><div dir="auto"><u><b><br></b></u></div><div dir="auto"><div dir="auto"><p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline;white-space:pre-wrap"><font face="arial, sans-serif">Please feel free to forward this information to anyone who might be interested.</font></span></p><p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="color:rgb(0,0,0);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline;white-space:pre-wrap">
<span style="color:rgb(34,34,34);white-space:normal">For further information, please visit our website: </span></span><a href="https://sites.google.com/unimib.it/geometryatbicocca" target="_blank">Geometry at Bicocca (google.com)</a></p><p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;vertical-align:baseline"></span></p><br></div><div>The organizers: Gianluca Faraco, Andrea Galasso</div><div class="gmail-yj6qo"></div><div class="gmail-adL"></div><div class="gmail-adL"><br></div></div></div></div>