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X-WR-CALNAME:IAS Special Year
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DTSTAMP:20220928T091323Z
CREATED:20210105T144556Z
DESCRIPTION:During the 2022-2023 academic year\, the School will have a spe
cial\nprogram on Applications of Dynamics in Number Theory and Algebraic\n
Geometry. Tamar Ziegler of the Hebrew University in Jerusalem will be\nthe
Distinguished Visiting Professor. Confirmed participants include\nK. Adip
rasito\, V.Bergelson\, J.Draisma\, J.Maynard\, S.Peluse\, T.Tao.\n\nThe sp
ecial year will focus on (still-evolving) interfaces between\nergodic theo
ry\, additive combinatorics\, multiplicative number theory\,\nand algebrai
c geometry. In the past 20 years there have been\nspectacular interlacing
advancements in ergodic theory\, analytic\nnumber theory and additive comb
inatorics\, leading to the resolution of\nlong standing conjectures. A wel
l known example is the Green-Tao\ntheorem on arithmetic progressions in pr
imes. A more recent example is\nthe proof of the logarithmic Sarnak conjec
ture for uniquely ergodic\nsystems\; this proof combines structure theorem
s from dynamics and\nadditive combinatorics with the recent understanding
of the behavior\nof multiplicative functions in short intervals. One focus
of the\nspecial year will be to further advance the interaction between t
hese\nfields. Another goal of the program will be to advance the interplay
\nbetween additive combinatorics\, theoretical computer science and\nalgeb
raic geometry over rings with many variables. In recent years\nthere is gr
owing interest in stability phenomena in algebraic\ngeometry\, specificall
y in properties of polynomial rings that are\nstable in the number of vari
ables (e.g. Stillman conjecture). Problems\nof a similar nature were indep
endently studied by researchers in\nadditive combinatorics in relation to
Ramsey questions in finite field\ngeometry. The two contexts are linked vi
a model theory. The program\nwill bring together researchers on both sides
to explore this\nconnection further.
DTSTART:20220901T040000Z
DTEND:20230430T040000Z
LAST-MODIFIED:20220927T172049Z
LOCATION:
SUMMARY:Special Year on Dynamics\, Additive Number Theory and Algebraic Geo
metry
URL:https://www.ias.edu/math/events/sp/dynamics-additive-number-theory-and-
algebraic-geometry
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