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X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20210613T150201Z
UID:20210613T11020160c61de930e8d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20210518T100000
CATEGORIES:Combinatorics Seminar
SUMMARY:Stoyan Dimitrov: Sorting by shuffling methods and a queue
DESCRIPTION:We consider sorting by a queue that can apply a
permutation from a given set over its content. This gives us a
sorting device $\\mathbb{Q}_{\\Sigma}$ corresponding to any
shuffling method $\\Sigma$ since every such method is associated
with a set of permutations. Two variations of these devices are
considered - $\\mathbb{Q}_{\\Sigma}^{\\prime}$ and
$\\mathbb{Q}_{\\Sigma}^{\\text{pop}}$. These require the entire
content of the device to be unloaded after a permutation is applied
or unloaded by each pop operation\, respectively.\n\nFirst\, we show
that sorting by a deque is equivalent to sorting by a queue that can
reverse its content. Next\, we focus on sorting by cuts\, which has
significance in computational biology and a natural interpretation.
We prove that the set of permutations that can be sorted by using
$\\mathbb{Q}_{\\text{cuts}}^{\\prime}$ is the set of the
321-avoiding separable permutations. We also give lower and upper
bounds to the maximum number of times the device must be used to
sort a permutation. These are analogues of the bounds previously
obtained by Eriksson et al.\n\nFurthermore\, we give a formula for
the number of n-permutations that one can sort by using
$\\mathbb{Q}_{\\Sigma}^{\\prime}$\, for any shuffling method
$\\Sigma$\, such that the permutations associated with it are
irreducible. The rest of the work is dedicated to a surprising
conjecture inspired by Diaconis and Graham which states that one can
sort the same number of permutations of any given size by using the
devices $\\mathbb{Q}_{\\text{In-sh}}^{\\text{pop}}$ and
$\\mathbb{Q}_{\\text{Monge}}^{\\text{pop}}$\, corresponding to the
popular In-shuffle and Monge shuffling methods. \n\nThe talk will
happen over Zoom\, and will be followed by a tea with the
speaker.\n\nMeeting ID: 954 4736 6763\n\nPasscode: Catalan#
LOCATION:Zoom
URL:https://math.dartmouth.edu/~comb/
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DTSTAMP:20210613T150201Z
UID:20210613T11020160c61de930fbb@math.dartmouth.edu
DTSTART;TZID=America/New_York:20210518T145000
DTEND;TZID=America/New_York:20210518T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Juanita Duque Rosero: First Homology of Quotients of Fermat
Curves
DESCRIPTION:Suppose that C is a curve that is a cyclic Galois cover
of the projective line branched at three points. In this talk we
determine the structure of the graded Lie algebra of the lower
central series of the fundamental group of C. To do this\, we
construct such curves as quotients of Fermat curves x^n+y^n=z^n.
Using modular symbols\, we find an explicit basis for the first
étale homology of C\, which is essential when describing the
structure of the desired Lie algebra. This is joint work with Rachel
Pries.
LOCATION:Meeting ID: 939 1193 8570\, Passcode: 876807
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DTSTAMP:20210613T150201Z
UID:20210613T11020160c61de93108f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20210519T180000
CATEGORIES:&ac\; Prosser Lecture &ac\;
SUMMARY:Colm Mulcahy: Given Any Five Cards
DESCRIPTION:Zoom ID 922 7125 3913 and the Zoom Link is
\n\n\nhttps://dartmouth.zoom.us/j/92271253913?pwd=V28zVVA4S2xiSVVCMFRzckxjNVg3Zz09.
\n\nPlease contact Vladimir Chernov vladimir.chernov@dartmouth.edu
for the password.\n\nOne of the most astonishing mathematical card
tricks ever invented dates back over 70 years: given any five cards
from a regular deck\, it is possible to show just four of them to a
friend and magically convey the identity of the fifth.\n\nIt
is also possible to switch one of the five cards for a different
card in such a way that the friend knows which card is new.\n\nIt's
even possible to show the friend fewer than four cards and have her
ID the missing ones\, if you play your cards right.\n\nWe will
survey a variety of "Given Any Five Cards" scenarios\, explaining
the diverse mathematical principles involved\, as well as "Given Any
Four Cards" and even "Given Any Three Cards" counterparts.
LOCATION:Zoom ID 922 7125 3913
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DTSTAMP:20210613T150201Z
UID:20210613T11020160c61de931173@math.dartmouth.edu
DTSTART;TZID=America/New_York:20210520T153000
CATEGORIES:Math Colloquium
SUMMARY:Colm Mulcahy: One\, Two\, Many (or a dozen reasons why
mathematics isn't as easy as 1\,2\,3)
DESCRIPTION:Zoom ID 922 7125 3913 Zoom Web
Link\n\nhttps://dartmouth.zoom.us/j/92271253913?pwd=V28zVVA4S2xiSVVCMFRzckxjNVg3Zz09\nPlease
contact Vladimir Chernov vladimir.chernov@dartmouth.edu for the
password. \n\nAre there really primitive tribes whose system of
counting goes: One\, Two\, Many\, ... indicating that from three on
it's more or less a blur? Maybe we modern humans are such a tribe.
Despite the sophistication we see in ourselves compared with our
less advanced ancestors from times long past\, it's surprising how
little progress we've made in addressing some basic problems in 3D
or beyond\, or when solving seemingly simple equations in ≥3
variables.We'll survey a dozen fun topics in shapes and numbers
and patterns whose basics and generalisations can be explored with
little mathematical background\, and which speedily lead to ``what
if?'' questions ranging from easy to tricky to ``we just don't
know.''Fruit\, cakes\, doughnuts\, bagels\, coins\, boxes\,
cubes\, primes\, squares\, and sums involving powers will all
make appearances. Once or twice we will stray into deeper waters and
touch on more sophisticated topics.
LOCATION:004 Kemeny Hall
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DTSTAMP:20210613T150201Z
UID:20210613T11020160c61de93124a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20210525T145000
DTEND;TZID=America/New_York:20210525T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Carl Pomerance: Denominators of Bernoulli numbers
DESCRIPTION:The Bernoulli numbers are certain rational numbers\nthat
appear as coefficients of a particular Taylor series.\nAlready over
3 centuries old\, they were introduced to give us\nformulas for
adding the sum of consecutive k-th powers.\nThey later appeared in
the formula for the Riemann zeta-function\nat positive even
integers. And still later\, they were once thought\nto be the
gateway to Fermat's Last Theorem.\nThis talk will briefly review
some of this history\, and then focus\non some interesting problems
connected with the denominators.\nFor example\, how frequently does
a given denominator appear?\,\nand which numbers occur as
denominators? This is joint work with\nSam Wagstaff.
LOCATION:Meeting ID: 939 1193 8570\, Passcode: 876807
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DTSTAMP:20210613T150201Z
UID:20210613T11020160c61de931312@math.dartmouth.edu
DTSTART;TZID=America/New_York:20210527T153000
CATEGORIES:Math Colloquium
SUMMARY:Anne Schilling: New ideas about Markov chain
DESCRIPTION:The Zoom ID is 870 912 2782 and the direct link is
https://dartmouth.zoom.us/j/8709122782?pwd=NHhGcTNPU3BXVkZOTW9FYVR6OWpZQT09\n\n\nPlease
ask Vladimir Chernov vladimir.chernov@dartmouth.edu for the
password\n\nWe will discuss some new ideas from semigroup theory to
analyze the stationary distribution and mixing time of finite Markov
chains. An example for a Markov chain is card shuffling and a
natural question is: how often do you have to shuffle the deck
before it is mixed or random? It turns out that semigroup theory can
help answer these questions.\n
LOCATION:Zoom
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DTSTAMP:20210613T150201Z
UID:20210613T11020160c61de9313e8@math.dartmouth.edu
DTSTART;TZID=America/New_York:20210601T100000
CATEGORIES:Combinatorics Seminar
SUMMARY:Shraddha Srivastava: Jucys-Murphy elements for rook monoid
algebras
DESCRIPTION:Abstract: Representation theories of rook monoids and
symmetric groups are closely related. The direct sum of Grothendieck
groups of the categories of finite dimensional representations of
all symmetric groups can be identified with the basic representation
of affine special linear Lie algebras. The actions of Chevalley
generators of the aforementioned Lie algebra can be interpreted in
terms of Jucys-Murphy (JM) elements for symmetric group algebras. In
this talk\, we will define JM elements for rook monoid algebras
which share many fundamental properties of JM elements for the
classical case of symmetric groups. Utilizing JM elements we will
also define operators\, corresponding to Chevalley generators and
generators of the bicyclic monoid\, on the direct sum of
Grothendieck groups of the categories of finite dimensional
representations of all rook monoids. This is joint work with
Volodymyr Mazorchuk.\n\nThe talk will happen over Zoom\, and will be
followed by a tea with the speaker.\n\nMeeting ID: 954 4736
6763\n\nPasscode: Catalan#
LOCATION:Zoom
URL:http://www.math.dartmouth.edu/~comb/
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BEGIN:VEVENT
DTSTAMP:20210613T150201Z
UID:20210613T11020160c61de9314c9@math.dartmouth.edu
DTSTART;TZID=America/New_York:20210602T100000
CATEGORIES:Thesis Defence
SUMMARY:Andreas Louskos '21: Physics-Informed Neural Networks and
Options Pricing
LOCATION:https://dartmouth.zoom.us/j/94859256386?pwd=WVVxeEVDcHVpMkErNW5oeUtHNDlIQT09
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BEGIN:VEVENT
DTSTAMP:20210613T150201Z
UID:20210613T11020160c61de93157b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20210602T150000
CATEGORIES:Thesis Defence
SUMMARY:Jacob Swenberg '21: Fields of Moduli for QM Abelian Surfaces
with CM
DESCRIPTION:"Motivated by class number 1 problems\, we provide a
complete description of the Galois action on the set of principally
polarized abelian surfaces with QM by a maximal quaternion order $O$
and CM by an imaginary quadratic order $S$. The set $\\mathcal{A}$
of such abelian surfaces is in bijection with a set of classes of
optimal embeddings of $S$ into $O$. We describe an action of the
absolute Galois group on these optimal embeddings and show that the
action agrees with the action on abelian surfaces. By completely
describing the action on optimal embeddings\, we describe the action
on abelian surfaces. As a consequence\, we determine various fields
of moduli of abelian surfaces. The results are applied to give a new
solution to the Gauss class number 1 problem."
LOCATION:https://dartmouth.zoom.us/j/7776492973
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