BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Lewis & Clark//NONSGML v1.0//EN BEGIN:VTIMEZONE TZID:America/Los_Angeles BEGIN:DAYLIGHT TZNAME:PDT DTSTART:20150308T100000 RDATE:20150308T100000 TZOFFSETFROM:-0800 TZOFFSETTO:-0700 END:DAYLIGHT END:VTIMEZONE BEGIN:VTIMEZONE TZID:America/Los_Angeles BEGIN:STANDARD TZNAME:PST DTSTART:20151101T090000 RDATE:20151101T090000 TZOFFSETFROM:-0700 TZOFFSETTO:-0800 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20150429T153000 DTEND;TZID=America/Los_Angeles:20150429T170000 LOCATION:John Howard 254 GEO:45.451619;-122.669391 SUMMARY:Mathematics Senior Thesis Presentations DESCRIPTION:Things Fall Apart: The Spontaneous Blowup of Water Sam Stewa rt '15 Major in Mathematics If you throw a rock into a calm pond\, you will see a splash\, some ripples\, and then the surface of the pond will slowly become smooth again. Regardless of how hard you throw the rock\, t he pond will eventually become smooth (perhaps after a few hours). The wa ve equation is a mathematical model that describes such behavior. However \, minor changes to the equation produces models with intriguing behavior . Under these models\, the pond water can spontaneously \;explode\, e ven after a gentle toss. How forcefully can we throw the rock without the water exploding? What is the correct way to we measure "force"? Can we p redict if the water will explode from the size of the splash? How can we simulate such explosions computationally? How can we understand such expl osions mathematically? \; \; In this presentation\, I examine suc h a "pathological" version of the wave equation and present numerical ans wers to some of these questions. \;Mean Curvature Flow of Tori of Rev olution Colin Gavin '15 Major in Mathematics and Physics Mean curvatur e flow is the gradient flow of the volume functional on embedded surfaces . As a nonlinear system of parabolic equations\, its behavior is quite co mplicated\, but generally solutions become more spherical over time as th eir volume decreases. The evolution of tori under this flow is of interes t because their non-trivial topology prevents them from becoming round. T his leads to the formation of a variety of singularities. In this talk\, I will focus on tori of revolution\, which reduces the problem to a versi on of planar curve shortening flow. From this viewpoint\, the possible si ngularities can be classified and\, in some cases\, their asymptotic beha vior can be determined. I will give a brief overview of my results\, and discuss some of the methods in differential geometry and partial differen tial equations that I used.An Introduction to Alexandrov Spaces Isaac Go ldstein '16 pre-thesis report for Honors in Mathematics Alexandrov Spac es are a special kind of metric space invented and defined by some of the most influential geometers of the twentieth century. This talk will focu s on mathematically defining Alexandrov Spaces and Gromov-Hausdorff dista nce\, one of the main tools used in generating Alexandrov Spaces. X-ALT-DESC;FMTTYPE=text/html:
Things Fall Apart:
The Spontaneous Blowup of Water
Sam Stewart '15
Major in Mathematics
If you throw a rock into a calm pond\, you will see a splash\, some ripples\, and then the surface of the pond will slowly become smooth again. Regardless of ho w hard you throw the rock\, the pond will eventually become smooth (perha ps after a few hours). The wave equation is a mathematical model that des cribes such behavior. However\, minor changes to the equation produces mo dels with intriguing behavior. Under these models\, the pond water can sp ontaneously \;explode\, even after a gentle toss. H ow forcefully can we throw the rock without the water exploding? What is the correct way to we measure "force"? Can we predict if the water will e xplode from the size of the splash? How can we simulate such explosions c omputationally? How can we understand such explosions mathematically? 0\; \; In this presentation\, I examine such a "pathological" version of the wave equation and present numerical answers to some of these ques tions. \;
Mean Curvature Flow of Tori of Revolution
Colin Gavin '15
Major in Mathematics and Physics
Mean curvature flow is the gradient flow of the volume functional on embedded surfaces. As a no nlinear system of parabolic equations\, its behavior is quite complicated \, but generally solutions become more spherical over time as their volum e decreases. The evolution of tori under this flow is of interest because their non-trivial topology prevents them from becoming round. This leads to the formation of a variety of singularities. In this talk\, I will fo cus on tori of revolution\, which reduces the problem to a version of pla nar curve shortening flow. From this viewpoint\, the possible singulariti es can be classified and\, in some cases\, their asymptotic behavior can be determined. I will give a brief overview of my results\, and discuss s ome of the methods in differential geometry and partial differential equa tions that I used.
An Introduction to Alexan drov Spaces
Isaac Goldstein '16
pre-thesis report for Honors in Mathematics
Alexand rov Spaces are a special kind of metric space invented and defined by som e of the most influential geometers of the twentieth century. This talk w ill focus on mathematically defining Alexandrov Spaces and Gromov-Hausdor ff distance\, one of the main tools used in generating Alexandrov Spaces.
UID:20150429T223000Z-40835@college.lclark.edu DTSTAMP:20150427T100815Z URL:https://college.lclark.edu/live/events/40835-mathematics-senior-thesi s-presentations LAST-MODIFIED:20150427T180135Z X-LIVEWHALE-TYPE:events X-LIVEWHALE-ID:40835 X-LIVEWHALE-TIMEZONE:America/Los_Angeles X-LIVEWHALE-SUMMARY:Math Thesis presentations: Things Fall Apart: The Spo ntaneous Blowup of Water\, Mean Curvature Flow of Tori of Revolution and An Introduction to Alexandrov Spaces X-LIVEWHALE-TAGS:Mathematical Sciences Colloquium END:VEVENT END:VCALENDAR