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SUMMARY:Yuji Tachikawa (Kavli IPMU)
DTSTART;VALUE=DATE-TIME:20210528T063000Z
DTEND;VALUE=DATE-TIME:20210528T073000Z
DTSTAMP;VALUE=DATE-TIME:20230208T074942Z
UID:UTokyoMathColloquium/1
DESCRIPTION:Title: Physics and algebraic topology\nby Yuji Tachikawa (Kavli
IPMU) as part of UTokyo Math Colloquium\n\n\nAbstract\nAlthough we often t
alk about the "unreasonable effectiveness of mathematics in the natural sc
iences"\, there are great disparities in the relevance of various subbranc
hes of mathematics to individual fields of natural sciences. Algebraic top
ology was a subject whose influence to physics remained relatively minor f
or a long time\, but in the last several years\, theoretical physicists st
arted to appreciate the effectiveness of algebraic topology more seriously
. For example\, there is now a general consensus that the classification o
f the symmetry-protected topological phases\, which form a class of phases
of matter with a certain particularly simple property\, is done in terms
of generalized cohomology theories.\n\nIn this talk\, I would like to prov
ide a historical overview of the use of algebraic topology in physics\, em
phasizing a few highlights along the way. If the time allows\, I would als
o like to report my struggle to understand the anomaly of heterotic string
s\, using the theory of topological modular forms.\n
LOCATION:https://researchseminars.org/talk/UTokyoMathColloquium/1/
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SUMMARY:Gang Tian (BICMR\, Peking University)
DTSTART;VALUE=DATE-TIME:20211126T063000Z
DTEND;VALUE=DATE-TIME:20211126T073000Z
DTSTAMP;VALUE=DATE-TIME:20230208T074942Z
UID:UTokyoMathColloquium/2
DESCRIPTION:Title: Ricci flow on Fano manifolds\nby Gang Tian (BICMR\, Pekin
g University) as part of UTokyo Math Colloquium\n\n\nAbstract\nRicci flow
was introduced by Hamilton in early 80s. It preserves the Kahlerian struct
ure and has found many applications in Kahler geometry. In this expository
talk\, I will focus on Ricci flow on Fano manifolds. I will first survey
some results in recent years\, then I will discuss my joint work with Li a
nd Zhu. I will also discuss the connection between the long time behavior
of Ricci flow and some algebraic geometric problems for Fano manifolds.\n
LOCATION:https://researchseminars.org/talk/UTokyoMathColloquium/2/
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SUMMARY:Jun-Muk Hwang (Center for Complex Geometry\, IBS\, Korea)
DTSTART;VALUE=DATE-TIME:20211217T063000Z
DTEND;VALUE=DATE-TIME:20211217T073000Z
DTSTAMP;VALUE=DATE-TIME:20230208T074942Z
UID:UTokyoMathColloquium/3
DESCRIPTION:Title: Growth vectors of distributions and lines on projective hyper
surfaces\nby Jun-Muk Hwang (Center for Complex Geometry\, IBS\, Korea)
as part of UTokyo Math Colloquium\n\n\nAbstract\nFor a distribution on a
manifold\, its growth vector is a finite sequence of integers measuring th
e dimensions of the directions spanned by successive Lie brackets of local
vector fields belonging to the distribution. The growth vector is the mos
t basic invariant of a distribution\, but it is sometimes hard to compute.
As an example\, we discuss natural distributions on the spaces of lines c
overing hypersurfaces of low degrees in the complex projective space. We e
xplain the ideas in a joint work with Qifeng Li where the growth vector is
determined for lines on a general hypersurface of degree 4 and dimension
5.\n
LOCATION:https://researchseminars.org/talk/UTokyoMathColloquium/3/
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