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BEGIN:VEVENT
DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531acc@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190917T110000
DTEND;TZID=America/New_York:20190917T120000
CATEGORIES:Combinatorics Seminar
SUMMARY:Erik Slivken: The Fixed-Point Forest
DESCRIPTION:Consider the following partial “sorting algorithm”
on permutations: take the first entry of the permutation in one-line
notation and insert it into the position of its own value. Continue
until the first entry is 1. This process imposes a forest structure
on the set of all permutations of size n\, where the roots are the
permutations starting with 1 and the leaves are derangements.
Viewing the process in the opposite direction towards the leaves\,
one picks a fixed point and moves it to the beginning. Despite its
simplicity\, this “fixed-point forest” exhibits a rich
structure. We consider the fixed point forest in the limit
n\\to\\infty and show that at a random permutation the local
structure weakly converges to a tree that can be described in terms
of independent Poisson point processes. We study various statistics
on this tree like the shortest or longest distance to a leaf\, or
the total number of vertices. We also consider similar types of
algorithms on permutation which give rise to some type of forest
structure. This talk will summarize the main results and spend much
time discussing open problems. \n\nThis is based on joint work with
Tobias Johnson\, Anne Schilling\, and Sam Regan.\n
LOCATION:Kemeny 120
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DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531b3b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190917T143000
DTEND;TZID=America/New_York:20190917T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Kuan-Wen Lai: Biregular Cremona transformations of the plane
DESCRIPTION:Over a field k\, we say a birational automorphism on a
projective space is biregular if it acts bijectively on the set of
k-rational points. If k is a finite field\, then the rational points
form a finite set\, so such maps induce permutations. --- Can we
realize any permutation on the k-rational points via birational
maps? Based on a strategy provided by S. Cantat in 2009\, we give
positive answers for the plane in odd characteristics and the field
of two elements. For the other cases\, it is conjectured that only
even permutations can be recovered\, and we provide evidences
supporting it. This is a work in progress joint with S. Asgarli\, M.
Nakahara\, and S. Zimmermann.
LOCATION:307 Kemeny Hall
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DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531b84@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190919T153000
CATEGORIES:Math Colloquium
SUMMARY:John Voight: Identities for 1/pi^2 and special
hypergeometric motives
DESCRIPTION:More than a century ago\, Ramanujan discovered
remarkable formulas for 1/pi. Inspired by these discoveries\,
similar Ramanujan-like expressions for 1/pi^2 have been uncovered
recently by Guillera. We explain the provenance of these formulas:
we recognize certain special hypergeometric motives as arising from
Hilbert modular forms in an explicit way. This is joint work with
Lassina Dembele\, Alexei Panchishkin\, and Wadim Zudilin.
LOCATION:004 Kemeny
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DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531bc8@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190924T143000
DTEND;TZID=America/New_York:20190924T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:V. Suresh: Symbol length in Galois cohomology group
DESCRIPTION:The Bloch-Kato conjecture (a theorem of Voevodsky)
implies that every element in the degree n mod l Galois cohomology
group of a field F (containing the primitive lth roots of unity) is
a sum of symbols. Symbols\, or cup products of degree 1 Kummer
classes\, are the simplest kind of Galois cohomology classes. If
there exists an integer N such that every element in this group is a
sum of at most N symbols\, then we say that the $n$-symbol length of
$F$ is bounded by $N$. In the talk\, I'll discuss the relationship
between bounded symbol length and the $u$-invariant of a field.
I'll show that if $F$ is a function fields of a curve over a totally
imaginary number field\, then every element in degree 3 Galois
cohomology is a symbol.
LOCATION:307 Kemeny Hall
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DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531c19@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190926T140000
CATEGORIES:Topology Seminar
SUMMARY:Andrei Malyutin: Decomposition of prime knots
DESCRIPTION:In mathematics\, various objects admit canonical
decompositions into prime components: we have the fundamental
theorem of arithmetic for integers\, the fundamental theorem of
algebra for polynomials\, the Jordan normal form\, the ergodic
decomposition\, etc.\, etc. For 3-manifolds we have a two-level
decomposition: the prime decomposition (the Kneser-Milnor theorem)
and the JSJ decomposition. A similar two-level decomposition is
known for knots: Schubert's theorem on decomposition into primes and
the JSJ decomposition for knot complements. It turns out that the
knots (but not the links) have also a third-level decomposition:
each prime knot has a canonical decomposition into two-strand Conway
irreducible tangles. We will discuss this decomposition into
tangles. An interesting application of this decomposition is a
complete classification of mutant knots.
LOCATION:201 Kemeny
URL:https://math.dartmouth.edu/~topology/
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BEGIN:VEVENT
DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531c60@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190926T153000
CATEGORIES:Math Colloquium
SUMMARY:Andrei Malyutin: Hyperbolic knots are not generic
DESCRIPTION:A well-known conjecture in knot theory says that the
proportion of hyperbolic knots among all of the prime knots of n or
fewer crossings approaches 1 as n approaches infinity. We disprove
this conjecture. This is joint work with Yury Belousov.
LOCATION:004 Kemeny Hall
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BEGIN:VEVENT
DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531c9e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191008T143000
DTEND;TZID=America/New_York:20191008T133000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Gabriel Dorfsman-Hopkins: Projective Geometry for Perfectoid
Spaces
DESCRIPTION:To understand the structure of an algebraic variety we
often embed it in various projective spaces. This develops the
notion of projective geometry which has been an invaluable tool in
algebraic geometry. We develop a perfectoid analog of projective
geometry\, and explore how equipping a perfectoid space with a map
to a certain analog of projective space can be a powerful tool to
understand its geometric and arithmetic structure. In particular\,
we show that maps from a perfectoid space X to the perfectoid analog
of projective space correspond to line bundles on X together with
some extra data\, reflecting the classical theory. Along the way we
give a complete classification of vector bundles on the perfectoid
unit disk\, and compute the Picard group of the perfectoid analog of
projective space.
LOCATION:307 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531ce3@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191015T143000
DTEND;TZID=America/New_York:20191015T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:David Treumann: TBA
LOCATION:343 Kemeny Hall
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BEGIN:VEVENT
DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531d23@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191022T143000
DTEND;TZID=America/New_York:20191022T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Ben Antieau: TBA
LOCATION:343 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190922T064701Z
UID:20190922T0247015d8718e531d5b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20200227T153000
CATEGORIES:Math Colloquium
SUMMARY:Ben Adcock: TBA
LOCATION:004 Kemeny
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