<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div dir="ltr"><b style="font-family: Calibri, sans-serif; font-size: 10pt; -webkit-text-size-adjust: auto;"><span style="font-size: 14pt; font-family: Helvetica;"> Youming Qiao</span></b><meta http-equiv="content-type" content="text/html; charset=utf-8"><div dir="ltr"></div></div><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 14pt; font-family: Helvetica;">University of Technology, Sydney</span></b><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"> <o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><img width="288" height="288" id="Picture_x0020_1" src="cid:1ACC8656-168C-4EA8-A047-C702D91FD59C" alt="image001.jpg" style="width: 3in; height: 3in;"><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span> <o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt;"><span dir="ltr">Tuesday, </span></span></b><b><span style="font-size: 11pt;"><span dir="ltr">May 13</span><span dir="ltr">, 202</span><span dir="ltr">5,</span><span dir="ltr"> at 3:30pm</span></span></b><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; background: yellow;">Location: Kent 102</span></b><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><i><span style="font-size: 14pt; font-family: Aptos, sans-serif; color: rgb(33, 33, 33);">Title:</span></i></b><span style="font-size: 12pt; font-family: Aptos, sans-serif; color: rgb(33, 33, 33);"> </span><span style="font-size: 14pt; font-family: "Times New Roman", serif; color: rgb(33, 33, 33);">Tensor Isomorphism: complexity, algorithms, and cryptography</span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in 0in 12pt; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 12pt; font-family: Aptos, sans-serif; color: rgb(33, 33, 33);"><br></span><b><i><span style="font-size: 14pt; font-family: Aptos, sans-serif; color: rgb(33, 33, 33);">Abstract:</span></i></b><span style="font-size: 12pt; font-family: Aptos, sans-serif; color: rgb(33, 33, 33);"> </span><span style="font-size: 14pt; font-family: "Times New Roman", serif; color: rgb(33, 33, 33);">Two matrices are called equivalent if one can be transformed into the other by multiplying with invertible matrices on the left and right. Extending this idea to 3-tensors, it is natural to define two 3-tensors as isomorphic if they can be transformed into one another by multiplication with three invertible matrices along the three directions.<br> <br>In this talk, we explore tensor isomorphism through the lenses of complexity, algorithms, and cryptography. Starting from complexity, we will examine how tensor isomorphism relates to well-known problems such as graph isomorphism, code equivalence, and group isomorphism. Compared to graph isomorphism, tensor isomorphism seems a much harder algorithmic problem, despite some recent advances. These support the use of tensor isomorphism in cryptography, such as the security basis of some digital signature schemes. </span><o:p></o:p></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 14pt; font-family: "Times New Roman", serif; color: rgb(33, 33, 33);">Finally, we shall indicate how Tensor Isomorphism over Z naturally leads to connections with Calabi--Yau threefolds and Bhargava's approach to Gauss composition laws.<br><br>Based on joint work with many collaborators, including Josh Grochow, Gábor Ivanyos, Xiaorui Sun, Kate Stange, and more. </span></p></body></html>