<div dir="ltr"><div dir="ltr"><div><div class="gmail_default" style="font-size:small"><font style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b> </font></font><font style="font-family:arial,sans-serif;color:rgb(80,0,80);vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(0,0,0)"> Mon</font><span class="gmail_default" style="color:rgb(0,0,0)">day, December 16,<span class="gmail_default"> </span>2024</span><font style="color:rgb(0,0,0)"> at</font><b style="color:rgb(0,0,0)"> <span style="background-color:rgb(255,255,0)"><u>11:30</u></span></b><span style="background-color:rgb(255,255,0)"><b><u><font color="#000000"> am</font></u></b><b><u><font color="#000000"> CT</font></u><font color="#000000"> </font></b></span></font></font></div><div class="gmail_default"><div class="gmail_default"><div class="gmail_default"><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b><font color="#500050" face="arial, sans-serif"><br></font></b></p><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><font face="arial, sans-serif"><b><font color="#500050">Where: </font></b><font color="#000000">Talk will be given </font><font color="#000000" style="font-weight:bold"><u>live, in-person</u></font><font style="font-weight:bold"> </font>at<br></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font color="#500050"> </font><font color="#000000"> TTIC, 6045 S. Kenwood Avenue</font></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif" color="#000000"> 5th Floor, Room 530<b> </b></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><b><span style="color:black"><br></span></b></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><b style="color:rgb(60,64,67);letter-spacing:0.2px">Virtually:</b><span style="color:rgb(60,64,67);letter-spacing:0.2px"> <i>via panopto: </i><a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=99c36a24-7e58-430d-aeef-b242001316be" target="_blank"><b>livestream</b></a></span></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b style="color:rgb(60,64,67);letter-spacing:0.2px"><font size="1"><font face="georgia, serif"> </font></font></b><font face="arial, sans-serif"><br></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="color:rgb(60,64,67);letter-spacing:0.2px"><b><font face="arial, sans-serif"> </font></b></span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="color:rgb(80,0,80);vertical-align:inherit"><font style="vertical-align:inherit"><b>Who: </b> <font color="#500050"> </font><font color="#000000"><font color="#500050"> </font></font></font></font></font>Nikhil Bansal, University of Michigan</p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><br></p><div style="border-top:none;border-right:none;border-left:none;border-bottom:2.25pt solid rgb(11,118,159);padding:0in 0in 1pt"></div><div><br></div></div></div><div class="gmail_default"><div dir="ltr"><div><div><font face="arial, sans-serif"><b>Title:</b> Quasi-Monte Carlo Integration and Discrepancy<br><br><b>Abstract: </b>A classical approach to numerically integrating a function f is using Monte Carlo (MC) methods. Here, one evaluates f at random points and the estimation error scales as \sigma(f)/n^{1/2} with n samples, where \sigma(f) is the standard deviation of f. A different approach, widely used in practice, is using quasi-Monte Carlo (QMC) methods, where f is evaluated at carefully chosen deterministic points and the error scales roughly as 1/n. Both methods have distinctive advantages and shortcomings, and a key question has been to find a method that combines the advantages of both. </font></div><div><font face="arial, sans-serif"><br></font></div><div><font face="arial, sans-serif">In this talk, I will introduce the fascinating area of QMC methods and their connections to various areas of mathematics and to geometric discrepancy. I will then show how recent developments in algorithmic discrepancy theory can be used to give a method that combines the benefits of MC and QMC methods, and even improves upon previous QMC approaches in various ways.<br><br></font></div><div><font face="arial, sans-serif">The talk will be completely self-contained and elementary, and no prior knowledge of either discrepancy or integration is required. Based on joint work with Haotian Jiang (U. Chicago).</font></div></div><div><font face="arial, sans-serif"><br></font></div><div><font face="arial, sans-serif"><br></font></div></div><div><div id="m_-1728083531740743797m_-2577816196403041565m_-6888902794661989909m_-8269051215838676082m_-4857504361292392405m_-7894017567204943m_-4885984857739340928m_-7774452752044639306m_4484082192933670602m_-1727381471164456222m_-748841883188655251m_611962526655464537m_-2291386001826280818m_8446205837173851621m_8555462040290332708m_6451956535360448322m_-6976229087647104413m_7917979885129397482m_-5423657134431402203m_-1337599008586739890m_8237382617653311322m_-1231130334284673048m_-1282025577005441955m_-1973358356214118865m_-5815637555669013367m_1779572315514282115m_-4485402625451270420m_1520697528942856564m_5948359943660736735m_-4789039193346764527m_3599676094611771654m_8264976978369198918m_7474850050874458051m_5107577024390010371m_253820422674989860m_3983419646637522536m_-7220900540036838011gmail-:qg" role="button" aria-label="Show trimmed content" aria-expanded="false"><font face="arial, sans-serif"><b>Host: </b><a href="mailto:avrim@ttic.edu" target="_blank"><b>Avrim Blum</b></a></font></div></div><div id="m_-1728083531740743797m_-2577816196403041565m_-6888902794661989909m_-8269051215838676082m_-4857504361292392405m_-7894017567204943m_-4885984857739340928m_-7774452752044639306m_4484082192933670602m_-1727381471164456222m_-748841883188655251m_611962526655464537m_-2291386001826280818m_8446205837173851621m_8555462040290332708m_6451956535360448322m_-6976229087647104413m_7917979885129397482m_-5423657134431402203m_-1337599008586739890m_8237382617653311322m_-1231130334284673048m_-1282025577005441955m_-1973358356214118865m_-5815637555669013367m_1779572315514282115m_-4485402625451270420m_1520697528942856564m_5948359943660736735m_-4789039193346764527m_3599676094611771654m_8264976978369198918m_7474850050874458051m_5107577024390010371m_253820422674989860m_3983419646637522536m_-7220900540036838011gmail-:qg" role="button" aria-label="Show trimmed content" aria-expanded="false"><br></div><div id="m_-1728083531740743797m_-2577816196403041565m_-6888902794661989909m_-8269051215838676082m_-4857504361292392405m_-7894017567204943m_-4885984857739340928m_-7774452752044639306m_4484082192933670602m_-1727381471164456222m_-748841883188655251m_611962526655464537m_-2291386001826280818m_8446205837173851621m_8555462040290332708m_6451956535360448322m_-6976229087647104413m_7917979885129397482m_-5423657134431402203m_-1337599008586739890m_8237382617653311322m_-1231130334284673048m_-1282025577005441955m_-1973358356214118865m_-5815637555669013367m_1779572315514282115m_-4485402625451270420m_1520697528942856564m_5948359943660736735m_-4789039193346764527m_3599676094611771654m_8264976978369198918m_7474850050874458051m_5107577024390010371m_253820422674989860m_3983419646637522536m_-7220900540036838011gmail-:qg" role="button" aria-label="Show trimmed content" aria-expanded="false"><br></div><div id="m_-1728083531740743797m_-2577816196403041565m_-6888902794661989909m_-8269051215838676082m_-4857504361292392405m_-7894017567204943m_-4885984857739340928m_-7774452752044639306m_4484082192933670602m_-1727381471164456222m_-748841883188655251m_611962526655464537m_-2291386001826280818m_8446205837173851621m_8555462040290332708m_6451956535360448322m_-6976229087647104413m_7917979885129397482m_-5423657134431402203m_-1337599008586739890m_8237382617653311322m_-1231130334284673048m_-1282025577005441955m_-1973358356214118865m_-5815637555669013367m_1779572315514282115m_-4485402625451270420m_1520697528942856564m_5948359943660736735m_-4789039193346764527m_3599676094611771654m_8264976978369198918m_7474850050874458051m_5107577024390010371m_253820422674989860m_3983419646637522536m_-7220900540036838011gmail-:qg" role="button" aria-label="Show trimmed content" aria-expanded="false"><br></div></div></div><br clear="all"></div><div><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><span style="font-family:arial,helvetica,sans-serif;font-size:x-small">Mary C. Marre</span><br></div><div><div><font face="arial, helvetica, sans-serif" size="1">Faculty Administrative Support</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1">6045 S. Kenwood Avenue, Rm 517</font></i></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL 60637</font></i><br></font></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">773-834-1757</font></i></font></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif" size="1">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div><br></div><br><div class="gmail_quote gmail_quote_container"><div dir="ltr" class="gmail_attr">On Mon, Dec 9, 2024 at 7:23 PM Mary Marre <<a href="mailto:mmarre@ttic.edu">mmarre@ttic.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr"><div><div style="font-size:small"><font style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b> </font></font><font style="font-family:arial,sans-serif;color:rgb(80,0,80);vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(0,0,0)"> Mon</font><span class="gmail_default" style="color:rgb(0,0,0)">day, December 16,<span class="gmail_default"> </span>2024</span><font style="color:rgb(0,0,0)"> at</font><b style="color:rgb(0,0,0)"> <span style="background-color:rgb(255,255,0)"><u>11:30</u></span></b><span style="background-color:rgb(255,255,0)"><b><u><font color="#000000"> am</font></u></b><b><u><font color="#000000"> CT</font></u><font color="#000000"> </font></b></span></font></font></div><div><div><div><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b><font color="#500050" face="arial, sans-serif"><br></font></b></p><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><font face="arial, sans-serif"><b><font color="#500050">Where: </font></b><font color="#000000">Talk will be given </font><font color="#000000" style="font-weight:bold"><u>live, in-person</u></font><font style="font-weight:bold"> </font>at<br></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font color="#500050"> </font><font color="#000000"> TTIC, 6045 S. Kenwood Avenue</font></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif" color="#000000"> 5th Floor, Room 530<b> </b></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><b><span style="color:black"><br></span></b></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><b style="color:rgb(60,64,67);letter-spacing:0.2px">Virtually:</b><span style="color:rgb(60,64,67);letter-spacing:0.2px"> <i>via panopto: </i><a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=99c36a24-7e58-430d-aeef-b242001316be" target="_blank"><b>livestream</b></a></span></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b style="color:rgb(60,64,67);letter-spacing:0.2px"><font size="1"><font face="georgia, serif"> </font></font></b><font face="arial, sans-serif"><br></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="color:rgb(60,64,67);letter-spacing:0.2px"><b><font face="arial, sans-serif"> </font></b></span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="color:rgb(80,0,80);vertical-align:inherit"><font style="vertical-align:inherit"><b>Who: </b> <font color="#500050"> </font><font color="#000000"><font color="#500050"> </font></font></font></font></font>Nikhil Bansal, University of Michigan</p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><br></p><div style="border-top:none;border-right:none;border-left:none;border-bottom:2.25pt solid rgb(11,118,159);padding:0in 0in 1pt"></div><div><br></div></div></div><div><div dir="ltr"><div><div><font face="arial, sans-serif"><b>Title:</b> Quasi-Monte Carlo Integration and Discrepancy<br><br><b>Abstract: </b>A classical approach to numerically integrating a function f is using Monte Carlo (MC) methods. Here, one evaluates f at random points and the estimation error scales as \sigma(f)/n^{1/2} with n samples, where \sigma(f) is the standard deviation of f. A different approach, widely used in practice, is using quasi-Monte Carlo (QMC) methods, where f is evaluated at carefully chosen deterministic points and the error scales roughly as 1/n. Both methods have distinctive advantages and shortcomings, and a key question has been to find a method that combines the advantages of both. </font></div><div><font face="arial, sans-serif"><br></font></div><div><font face="arial, sans-serif">In this talk, I will introduce the fascinating area of QMC methods and their connections to various areas of mathematics and to geometric discrepancy. I will then show how recent developments in algorithmic discrepancy theory can be used to give a method that combines the benefits of MC and QMC methods, and even improves upon previous QMC approaches in various ways.<br><br></font></div><div><font face="arial, sans-serif">The talk will be completely self-contained and elementary, and no prior knowledge of either discrepancy or integration is required. Based on joint work with Haotian Jiang (U. Chicago).</font></div></div><div><font face="arial, sans-serif"><br></font></div></div><div><div id="m_-1728083531740743797m_-2577816196403041565m_-6888902794661989909m_-8269051215838676082m_-4857504361292392405m_-7894017567204943m_-4885984857739340928m_-7774452752044639306m_4484082192933670602m_-1727381471164456222m_-748841883188655251m_611962526655464537m_-2291386001826280818m_8446205837173851621m_8555462040290332708m_6451956535360448322m_-6976229087647104413m_7917979885129397482m_-5423657134431402203m_-1337599008586739890m_8237382617653311322m_-1231130334284673048m_-1282025577005441955m_-1973358356214118865m_-5815637555669013367m_1779572315514282115m_-4485402625451270420m_1520697528942856564m_5948359943660736735m_-4789039193346764527m_3599676094611771654m_8264976978369198918m_7474850050874458051m_5107577024390010371m_253820422674989860m_3983419646637522536m_-7220900540036838011gmail-:qg" role="button" aria-label="Show trimmed content" aria-expanded="false"><font face="arial, sans-serif"><b>Host: </b><a href="mailto:avrim@ttic.edu" target="_blank"><b>Avrim Blum</b></a></font></div></div></div></div><div><font face="arial, sans-serif"><br></font></div><div><div><br></div><div><br></div></div><br clear="all"></div><div><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><span style="font-family:arial,helvetica,sans-serif;font-size:x-small">Mary C. Marre</span><br></div><div><div><font face="arial, helvetica, sans-serif" size="1">Faculty Administrative Support</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1">6045 S. Kenwood Avenue, Rm 517</font></i></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL 60637</font></i><br></font></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">773-834-1757</font></i></font></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif" size="1">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div></div>
</div>
</blockquote></div></div>