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$B%H%k!'(B Newton-Okounkov bodies, Bott-Samelson varieties, and Schubert</span>
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
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!important; float: none; background-color: rgb(255, 255, 255);">calculus</span><br
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<br style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
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$B%9%H%i%/%H!'(B</span><br style="color: rgb(0, 0, 0); font-family: 'MS
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
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!important; float: none; background-color: rgb(255, 255, 255);">The
theory of Newton-Okounkov bodies is a far-reaching generalization</span><br
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
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!important; float: none; background-color: rgb(255, 255, 255);">of
the theory of toric varieties. Given a complex variety X and some</span><br
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
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word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">extra
data (e.g. a very ample line bundle L on X and a valuation v on</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">its
homogeneous coordinate ring), the Newton-Okounkov body of (X, L,</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
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word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">v)
is a convex body of "maximal dimension", i.e., the (complex)</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">dimension
of X. In many interesting cases, it is in fact a rational</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">polytope.
In the case when X is a toric variety and the accompanying</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">data
(L,v) is chosen to be torus-invariant, the Newton-Okounkov body</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">is
the usual Newton polytope from toric geometry. In the case when X
=</span><br style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
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font-weight: normal; letter-spacing: normal; line-height: normal;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">G/B
is a (full) flag variety G/B of a complex semisimple algebraic</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">group
G, Kaveh recently showed that an appropriate choice of (L,v)</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">yields
the so-called "string polytopes" of Berenstein-Littelmann,</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">which
are fundamental objects of study in representation theory. In</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">particular,
the Gel'fand-Zetlin polytopes associated to</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">representations
of GL(n,\C) are Newton-Okounkov bodies of the standard</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">flag
variety Flags(\C^n) of nested subspaces in \C^n. It is widely</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">believed
that the theory of Newton-Okounkov bodies will provide a</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">fruitful
new approach to the study of Schubert calculus, through a</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">careful
study of the Newton-Okounkov bodies of flag varieties and of</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">associated
Bott-Samelson varieties. In particular, it can be _hoped_</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">that
a "Schubert calculus" can be developed where "intersecting</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">Schubert
varieties" translates to "intersecting (unions of) faces of a</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">single
polytope", in the same spirit as the work of</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">Kiritchenko-Smirnov-Timorin
for the GL(n,\C) (i.e. Gelfand-Zetlin)</span><br style="color:
rgb(0, 0, 0); font-family: 'MS PGothic'; font-size: medium;
font-style: normal; font-variant: normal; font-weight: normal;
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text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">case
and the recent work of Kiritchenko on divided-difference</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">operators
on polytopes and a "geometric mitosis" on polytopes.</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<br style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
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font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">This
lecture series will be aimed at a broad audience and will attempt</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">to
explain the basic background behind the "hope" mentioned above. In</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">particular,
the lectures are not intended to explain a particular</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
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!important; float: none; background-color: rgb(255, 255, 255);">significant
theorem. Instead, I hope to, first, explain the necessary</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
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auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
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word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">context
and, second, convey some feeling for the reasons why I believe</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
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!important; float: none; background-color: rgb(255, 255, 255);">this
subject is so interesting and promising. In particular, the</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
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<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">lectures
will be full of questions to which I do not know the answer.</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">The
audience is encouraged to actively participate in the discussion.</span><br
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medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
-webkit-text-stroke-width: 0px;">
<span style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline
!important; float: none; background-color: rgb(255, 255, 255);">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</span><br
style="color: rgb(0, 0, 0); font-family: 'MS PGothic'; font-size:
medium; font-style: normal; font-variant: normal; font-weight:
normal; letter-spacing: normal; line-height: normal; orphans:
auto; text-align: start; text-indent: 0px; text-transform: none;
white-space: normal; widows: auto; word-spacing: 0px;
-webkit-text-stroke-width: 0px;">
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font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-stroke-width: 0px;">
<br style="color: rgb(0, 0, 0); font-family: 'MS PGothic';
font-size: medium; font-style: normal; font-variant: normal;
font-weight: normal; letter-spacing: normal; line-height: normal;
orphans: auto; text-align: start; text-indent: 0px;
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