BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Claremont Center for the Mathematical Sciences - ECPv6.15.17.1//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-ORIGINAL-URL:https://colleges.claremont.edu/ccms X-WR-CALDESC:Events for Claremont Center for the Mathematical Sciences REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:America/Los_Angeles BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20200308T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20201101T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20210314T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20211107T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20220313T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20221106T090000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210412T150000 DTEND;TZID=America/Los_Angeles:20210412T160000 DTSTAMP:20260519T205054 CREATED:20210112T180713Z LAST-MODIFIED:20210406T193121Z UID:2110-1618239600-1618243200@colleges.claremont.edu SUMMARY:Applied math. talk: Large Eddy Simulation Reduced Order Models by Traian Iliescu\, Virginia Tech DESCRIPTION:In this talk\, we present reduced order models (ROMs) for turbulent flows\,\nwhich are constructed by using ideas from large eddy simulation (LES) and\nvariational multiscale (VMS) methods.  First\, we give a\ngeneral introduction to reduced order modeling and emphasize the\nconnection to classical Galerkin methods (e.g.\, the finite element method)\nand the central role played by data.  Then\, we describe the closure\nproblem\, which represents one of the main obstacles in the development of\nROMs for realistic\, turbulent flows.  To tackle the ROM closure problem\,\nwe use ROM spatial filters (e.g.\, the ROM projection and the ROM\ndifferential filter) and build new LES-ROMs that capture the large scale\nROM features and model the interaction between these large scales and the\nsmall scale ROM features. Finally\, we present results for these LES-ROMs\nin the numerical simulation of\nunder-resolved engineering flows (e.g.\, flow past a cylinder and\nturbulent channel flow) and the quasi-geostrophic equations (which model\nthe large scale ocean circulation). URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-traian-iliescu-virginia-tech/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210419T150000 DTEND;TZID=America/Los_Angeles:20210419T160000 DTSTAMP:20260519T205054 CREATED:20210112T180844Z LAST-MODIFIED:20210417T022158Z UID:2112-1618844400-1618848000@colleges.claremont.edu SUMMARY:Applied math. talk: Adversarially robust classification via geometric flows\, by Ryan Murray\, North Caroline State University DESCRIPTION:Abstract: Classification is a fundamental task in data science and machine learning\, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). However\, recently there have been a number of works demonstrating that these improved algorithms can be “fooled” using specially constructed adversarial examples. In turn\, there has been increased attention given to creating machine learning algorithms which are more robust against adversarial attacks. In this talk I will describe a recently proposed framework for optimal adversarial robustness which is related to optimal transportation. I will then discuss some recent work\, with Nicolas Garcia Trillos\, which characterizes solutions of the optimal adversarial robust classification problem by using a geometric evolution equation. Surprisingly\, this geometric evolution equation asymptotically takes the form of a weighted mean curvature flow\, which suggests new analytical and computational approaches to the problem. I will also discuss a number of related open questions. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-ryan-murray-north-caroline-state-university/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210426T150000 DTEND;TZID=America/Los_Angeles:20210426T160000 DTSTAMP:20260519T205054 CREATED:20210128T180721Z LAST-MODIFIED:20210426T165641Z UID:2155-1619449200-1619452800@colleges.claremont.edu SUMMARY:Applied Math. Talk: Balancing Geometry and Density: Path Distances on High-Dimensional Data by Anna Little\, University of Utah DESCRIPTION: Abstract: This talk discusses multiple methods for clustering\nhigh-dimensional data\, and explores the delicate balance between utilizing\ndata density and data geometry. I will first present path-based spectral\nclustering\, a novel approach which combines a density-based metric with\ngraph-based clustering. This density-based path metric allows for fast\nalgorithms and strong theoretical guarantees when clusters concentrate\naround low-dimensional sets. However\, the method suffers from a loss of\ngeometric information\, information which is preserved by simple linear\ndimension reduction methods such as classic multidimensional scaling\n(CMDS). The second part of the talk will explore when CMDS followed by a\nsimple clustering algorithm can exactly recover all cluster labels with\nhigh probability. However\, scaling conditions become increasingly\nrestrictive as the ambient dimension increases\, and the method will fail\nfor irregularly shaped clusters. Finally\, I will discuss how a more\ngeneral family of path metrics\, when combined with CMDS\, give\nlow-dimensional embeddings which respect both data density and data\ngeometry. This new method exhibits promising performance on single cell\nRNA sequence data and can be computed efficiently by restriction to a\nsparse graph. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-anna-little-university-of-utah/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT END:VCALENDAR