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SUMMARY:Professor Larry Guth (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20210707T180000Z
DTEND;VALUE=DATE-TIME:20210707T190000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225243Z
UID:MIT_Mathematics/1
DESCRIPTION:Title: Focusing waves and combinatorics of lines\nby Professor Larry
Guth (MIT Mathematics) as part of SPUR / RSI Lectures\n\n\nAbstract\nSolut
ions of the wave equation model sound waves\, light waves\, etc. Focusing
refers to the amplitude getting very large in a small region of space. E
stimating how much waves can focus is a problem in real analysis. Over th
e last 25 years\, mathematicians have approached this problem using ideas
from combinatorics about the intersection patterns of lines. The story in
volves parts of math that sound rather far from PDE\, such as some topolog
y and some finite fields. In this talk\, we will begin with a gentle intr
oduction to waves and the wave equation\, and then describe how ideas from
some of these other fields come into play.\n\nzoom link: https://mit.zoo
m.us/j/93882149522\n
LOCATION:https://researchseminars.org/talk/MIT_Mathematics/1/
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SUMMARY:Alexei Borodin (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20210721T180000Z
DTEND;VALUE=DATE-TIME:20210721T190000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225243Z
UID:MIT_Mathematics/2
DESCRIPTION:Title: Domino tilings of the Aztec diamond\nby Alexei Borodin (MIT Ma
thematics) as part of SPUR / RSI Lectures\n\n\nAbstract\nThe talk is a sur
vey of one of the most beautiful solvable probabilistic models and its rel
ations with other fields - interacting particle systems\, random interface
s in 3d\, and random matrices.\n
LOCATION:https://researchseminars.org/talk/MIT_Mathematics/2/
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SUMMARY:Lisa Sauermann (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20210804T180000Z
DTEND;VALUE=DATE-TIME:20210804T190000Z
DTSTAMP;VALUE=DATE-TIME:20230925T225243Z
UID:MIT_Mathematics/3
DESCRIPTION:Title: On the cap-set problem and the slice rank polynomial method\nb
y Lisa Sauermann (MIT Mathematics) as part of SPUR / RSI Lectures\n\n\nAbs
tract\nIn 2016\, Ellenberg and Gijswijt made a breakthrough on the famous
cap-set problem\, which asks about the maximum size of a subset of \\mathb
b{F}_3^n not containing a three-term arithmetic progression. They proved t
hat any such set has size at most 2.756^n. Their proof was later reformula
ted by Tao\, introducing what is now called the slice rank polynomial meth
od. This talk will explain Tao's proof of the Ellenberg-Gijswijt bound for
the cap-set problem\, and discuss some related problems.\n\nzoom link: h
ttps://mit.zoom.us/j/93882149522\n\nAlso\, our big wrap-up SPUR Conference
will be held next Friday\, August 6\, where our SPUR/SPUR+ students will
report on their summer's work. More details on that to follow next week..
.\n
LOCATION:https://researchseminars.org/talk/MIT_Mathematics/3/
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