<div dir="ltr"><div dir="ltr"><div><div class="gmail_default"><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><br></div></div></div></div><div class="gmail_default" style="font-size:small"><b>Bio:</b> <span class="gmail-il">Nikhil</span> Bansal is the Patrick C. Fischer professor of Computer Science and Engineering at the University of Michigan. He completed his PhD in 2003 from Carnegie Mellon University, and has previously worked at IBM Research, TU Eindhoven and CWI</div>Amsterdam. He is broadly interested in theoretical computer science with focus on the design and analysis of algorithms, discrete mathematics and combinatorial optimization. His work has been recognized by several best paper awards. He is an ACM fellow and was an invited speaker at ICM 2022.<br clear="all"></div><div><br></div><div><div class="gmail_default" style="font-size:small"><b style="font-family:arial,sans-serif">Host: </b><a href="mailto:avrim@ttic.edu" target="_blank" style="font-family:arial,sans-serif"><b>Avrim Blum</b></a></div><br></div><div><br></div><div><br></div><div><br></div><div><br></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 Sun, Dec 15, 2024 at 3:11 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><font face="arial, sans-serif"><br></font></div></div><div><div id="m_5948607164176753139m_-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_5948607164176753139m_-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_5948607164176753139m_-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_5948607164176753139m_-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"><div dir="ltr" class="gmail_attr">On Mon, Dec 9, 2024 at 7:23 PM Mary Marre <<a href="mailto:mmarre@ttic.edu" target="_blank">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_5948607164176753139m_-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>
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