<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div dir="ltr"><b style="font-family: Helvetica; font-size: 14pt; -webkit-text-size-adjust: auto;">Shivam Nadimpalli</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-family: Calibri, sans-serif; font-size: 10pt;"><span style="font-family: Helvetica; font-size: 14pt;"><b>Massachusetts Institute of Technology</b></span></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-family: Calibri, sans-serif; font-size: 10pt;"> </p><img src="cid:D1A2763F-F35A-4330-A309-F4FB8D76936E" id="C89CF669-CF1C-481F-9251-CFE537E54F97" aria-label="Mail.messageViewer.inlineAttachment.NadimpalliPhoto.png" class="x-apple-edge-to-edge" style="-webkit-text-size-adjust: auto; width: calc(100% + 0px); margin-left: 0px; padding: 1px 0px;" alt="cid:C89CF669-CF1C-481F-9251-CFE537E54F97"><span style="-webkit-text-size-adjust: auto; background-color: rgb(255, 255, 255);"></span><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-family: Calibri, sans-serif; font-size: 10pt;"><span style="font-size: 11pt;"> </span> </p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-family: Calibri, sans-serif; font-size: 10pt;"><span style="font-size: 11pt;"><b><span dir="ltr">Tuesday, October 14, 202</span></b></span><span style="font-size: 11pt;"><b><span dir="ltr">5,</span></b></span><span style="font-size: 11pt;"><b><span dir="ltr"> at 3:30pm</span></b></span></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-family: Calibri, sans-serif; font-size: 10pt;"><span style="font-size: 11pt; background-color: yellow;"><b>Kent Chemical Laboratory, Room 102</b></span></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-family: Calibri, sans-serif; font-size: 10pt;"><span style="font-size: 11pt;"> </span></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-family: Calibri, sans-serif; font-size: 10pt;"><span style="font-size: 11pt;"> </span></p><p class="MsoNormal" style="-webkit-text-size-adjust: auto; margin: 0in; font-family: Calibri, sans-serif; font-size: 10pt;"><span style="font-size: 12pt;"> </span></p><div style="font-size: 12pt; -webkit-text-size-adjust: auto; font-family: Aptos, Arial, Helvetica, sans-serif;"><span style="background-color: rgb(255, 255, 255);"><b><i>Title: </i></b>Polyhedral Approximation and Sparsification</span></div><ul data-editing-info="{"applyListStyleFromLevel":false,"unorderedStyleType":1}" style="-webkit-text-size-adjust: auto; margin-top: 0px; margin-bottom: 0px;"><li style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; display: block;"><div dir="ltr" class="elementToProof" role="presentation" style="background-color: rgb(255, 255, 255); margin: 0px; font-family: Aptos, Arial, Helvetica, sans-serif;"><b><i><br></i></b></div></li></ul><div dir="ltr" style="font-size: 12pt; -webkit-text-size-adjust: auto; background-color: rgb(255, 255, 255); margin: 0px;"><span style="font-family: Aptos, Arial, Helvetica, sans-serif;"><b><i>Abstract: </i></b></span><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif;">Given an intersection of (possibly infinitely many) halfspaces at bounded distance from the origin, we show that it can be <i>sparsified, </i>i.e. approximated (under the Gaussian distribution) by an intersection of a halfspaces where the number of halfspaces depends only on the desired accuracy. This yields efficient algorithms for learning, tolerant testing, and volume estimation of convex sets of bounded width. Our result follows from a more general sparsification lemma for Gaussian processes, which relies on Talagrand's majorizing measures theorem. As another consequence, we obtain a "junta theorem" for norms over Gaussian space: Every norm over R^n can be multiplicatively approximated (under the Gaussian measure) by a norm that depends on only a constant number of coordinates.<br><br>The talk will be self-contained and will require no prior background on Gaussian processes.<br><br>(Based on joint works with Anindya De, Ryan O'Donnell, and Rocco Servedio: </span><span style="font-family: Aptos, Arial, Helvetica, sans-serif; color: rgb(31, 167, 116);"><a href="https://urldefense.com/v3/__https://arxiv.org/abs/2311.08575__;!!BpyFHLRN4TMTrA!7H-FX0Klfc_UA5K8hDM3Xn7teXBkEoUpWEUhR195h_DeL1ljEzqpOydCyUhOJ2WzFTzUKaWzboc2bhKSU46u$" id="OWA0f0d6b62-5e36-2964-f205-ba1d01eda1db" class="OWAAutoLink" title="https://urldefense.com/v3/__https://arxiv.org/abs/2311.08575__;!!BpyFHLRN4TMTrA!7H-FX0Klfc_UA5K8hDM3Xn7teXBkEoUpWEUhR195h_DeL1ljEzqpOydCyUhOJ2WzFTzUKaWzboc2bhKSU46u$" data-outlook-id="cad8edc0-8e3b-47fd-8ed0-c881c260329f" style="color: rgb(31, 167, 116);">https://arxiv.org/abs/2311.08575</a></span><span style="font-family: Aptos, Arial, Helvetica, sans-serif;">, </span><span style="font-family: Aptos, Arial, Helvetica, sans-serif; color: rgb(31, 167, 116);"><a href="https://urldefense.com/v3/__https://arxiv.org/abs/2411.14664__;!!BpyFHLRN4TMTrA!7H-FX0Klfc_UA5K8hDM3Xn7teXBkEoUpWEUhR195h_DeL1ljEzqpOydCyUhOJ2WzFTzUKaWzboc2bs5_UjHQ$" id="OWA0b352f00-ca84-edfa-6e38-b4f6bb297c48" class="OWAAutoLink" title="https://urldefense.com/v3/__https://arxiv.org/abs/2411.14664__;!!BpyFHLRN4TMTrA!7H-FX0Klfc_UA5K8hDM3Xn7teXBkEoUpWEUhR195h_DeL1ljEzqpOydCyUhOJ2WzFTzUKaWzboc2bs5_UjHQ$" data-outlook-id="671ede54-1fae-4922-af9c-af795f8c0822" style="color: rgb(31, 167, 116);">https://arxiv.org/abs/2411.14664</a></span><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif;">.)</span></div></body></html>