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X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119dff36@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211108T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Grant Molnar: Counting 7-isogenies
DESCRIPTION:In this talk\, we discuss asymptotics for the number of
elliptic curves of height up to X which are equipped with a
7-isogeny. Even solving this problem for curves with rational
coefficients up to Q^ alg-isomorphism requires some delicacy\,
because they are parameterized by polynomials that share a common
factor. This problem is magnified when working with elliptic curves
up to Q-isomorphism\, which requires summing over quadratic twists.
We report partial progress and avenues for future investigation.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen/
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119dffa4@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211109T101500
DTEND;TZID=America/New_York:20211109T111500
CATEGORIES:Combinatorics Seminar
SUMMARY:Sumit Mukherjee: Generalized birthday problem for November 9
DESCRIPTION:Abstract: Suppose there are $n$ students in a class. But
assume that not everybody is friends with everyone else\, and there
is a graph which determines the friendship structure. What is the
chance that there are two friends in this class\, both with
birthdays on November 9? More generally\, given a simple labelled
graph $G_n$ on $n$ vertices\, color each vertex with one of $c=c_n$
colors chosen uniformly at random\, independent from other vertices.
We study the question: what is the number of monochromatic edges of
color 1?\n\nAs it turns out\, the limiting distribution has three
parts\, the first and second of which are quadratic and linear
functions of a homogeneous Poisson point process\, and the third
component is an independent Poisson. In fact\, we show that any
distribution limit must belong to the closure of this class of
random variables. As an application\, we characterize exactly when
the limiting distribution is a Poisson random variable.\n\nThis talk
is based on joint work with Bhaswar Bhattacharya and Somabha
Mukherjee.\n\nThe talk will be given in a hybrid Zoom/in-person
format. The room on campus will be Kemeny 307\, with a broadcast on
Zoom. \n\nMeeting ID: 954 4736 6763\nPasscode: Catalan#
LOCATION:Zoom + Kemeny 307
URL:https://math.dartmouth.edu/~comb/
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119dffff@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211109T140000
DTEND;TZID=America/New_York:20211109T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Philipp Öffner: Entropy stable residual distribution
schemes
DESCRIPTION:Hyperbolic conservation/balance laws laws play a
fundamental role within mathematical models for various physical
processes\, including fluid mechan- ics\, electromagnetism and wave
phenomena. Depending on the considered sys- tem\, they contain
several structural properties like entropy\, angular momentum\,
preservation of kinetic energy\, and more. The numerical schemes
should be con- structed in a way to mimic these behaviors discretely
and avoid to violate them. Recently\, a lot of work has been done in
the development and construction of such structure preserving
schemes where one has to pay attention to several components.\nIn
this talk\, we consider this topic in the context of residual
distribution (RD) schemes focussing on entropy stability. RD is a
unifying framework for sev- eral high order methods including
continuous/discontinuous Galerkin\, and Flux Reconstruction. I
repeat the main idea of RD\, describe a general approach to
construct entropy conservative/dissipative schemes using entropy
correction terms and the relaxation approach. By the application of
limiter strategies we further can ensure the positivity of several
physical quantities. At the end\, I give an outlook to convergence
investigations of the proposed RD scheme for the Euler equations.
LOCATION:Zoom. Meeting ID: 98173120301. Passcode: 314159265
URL:https://math.dartmouth.edu/~acms/
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e005a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211111T151500
CATEGORIES:Math Colloquium
SUMMARY:Jacopo Borga: Local limits for permutations and generating
trees
DESCRIPTION:For large combinatorial structures\, two main notions of
convergence can be defined: scaling limits and local limits. In
particular\, for graphs both notions are well-studied and
well-understood. For permutations only a notion of scaling limits\,
called permutons\, has been investigated in the last decade. In the
first part of the talk\, we introduce a new notion of local
convergence for permutations and we prove some characterizations in
terms of proportions of consecutive pattern occurrences. In the
second part of the talk\, we investigate a new method to establish
local limits for pattern-avoiding permutations using generating
trees. The theory of generating trees has been widely used to
enumerate families of combinatorial objects\, in particular
permutations. The goal of this talk is to introduce a new facet of
generating trees encoding families of permutations\, in order to
establish probabilistic results instead of enumerative ones.
LOCATION:007 Kemeny Hall
URL:https://math.dartmouth.edu/calendar/agenda-colloq.php
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e00c3@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211115T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Juanita Duque-Rosero: Enumerating triangular modular curves
of low genus
DESCRIPTION:Triangular modular curves are a generalization of
modular curves that arise from quotients of the upper half-plane by
congruence subgroups of hyperbolic triangle groups. These curves
arise from Belyi maps with monodromy PGL_2(F_q) or PSL_2(F_q). In
this talk\, we will give an idea on the construction of these curves
and we will present a computational approach to enumerate all
triangular modular curves of genus 0\, 1\, and 2. This is joint work
with John Voight.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen/
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e0110@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211116T101500
DTEND;TZID=America/New_York:20211116T111500
CATEGORIES:Combinatorics Seminar
SUMMARY:Yannic Vargas: Monomial bases for combinatorial Hopf
algebras
DESCRIPTION:The algebraic structure of a Hopf algebra can often be
understood in terms of a poset on the underlying family of
combinatorial objects indexing a basis. For example\, the Hopf
algebra of quasisymmetric functions is generated (as a vector space)
by compositions and admits a fundamental (F) basis and a monomial
(M) basis\, related by the refinement poset on compositions. Analogs
bases can be considered for other Hopf algebras\, with similar
properties to the F basis\, e.g. a product described by some notion
of shuffle\, and a coproduct following some notion of
deconcatenation. We give axioms for how these generalised shuffles
and deconcatentations should interact with the underlying poset so
that a monomial-like basis can be analogously constructed\,
generalising the approach of Aguiar and Sottile. We also find
explicit positive formulas for the multiplication of monomial basis
and a cancellation-free and grouping-free formula for the antipode
of monomial elements. We apply these results on classical and new
Hopf algebras\, related by tree-like structures.\nThis is based on
"Hopf algebras of parking functions and decorated planar trees"\, a
joint work with Nantel Bergeron\, Rafael Gonzalez D'Leon\, Amy Pang
and Shu Xiao Li.\n\nThe talk will happen over Zoom. It will be
followed by a 20-minute "tea" break 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:20211207T100201Z
UID:20211207T05020161af3119e0172@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211116T140000
DTEND;TZID=America/New_York:20211116T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Peter J. Baddoo: Integrating physical laws into data-driven
modal decompositions
DESCRIPTION:Incorporating partial knowledge of physical laws into
data-driven architectures can improve the accuracy\,
generalisability\, and robustness of the resulting models. In this
work\, we demonstrate how physical laws – such as symmetries\,
invariances\, and conservation laws – can be integrated into the
dynamic mode decomposition (DMD)\, which is a widely-used data
analysis technique that extracts modal structures from
high-dimensional measurements. Although DMD has been applied
successfully to a broad range of domains\, the algorithm frequently
produces models that are sensitive to noise\, fail to generalize
outside the training regime\, and violate basic physical laws. We
rephrase the DMD optimization by restricting the family of
admissible models to a matrix manifold that respects the physical
structure of the system at hand. Termed 'physics-informed dynamic
mode decomposition’ (piDMD)\, our formulation may be interpreted
as a Procrustes problem\, which allows us to leverage the
substantial existing literature thereof. We focus on five of the
most fundamental physical properties – conservative\,
self-adjoint\, local\, causal\, and shift-invariant – and derive
several closed-form solutions for the corresponding piDMD
optimization problems. We demonstrate piDMD on a range of canonical
problems in the physical sciences\, including energy-preserving
fluid flow\, travelling-wave systems\, the Schrödinger equation\,
solute advection-diffusion and systems with causal dynamics. We
conclude with the challenging example of identifying the spectrum of
the linearized Navier--Stokes equations from transitional channel
flow data. In each case\, piDMD significantly outperforms standard
DMD in metrics such as spectral identification\, state
reconstruction and prediction\, and estimation of optimal forcings
and responses.
LOCATION:Neukom Conference Room (Haldeman 252) and also Zoom
(Meeting ID: 98173120301. Passcode: 314159265)
URL:https://math.dartmouth.edu/~acms/
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e01c9@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211116T151500
DTEND;TZID=America/New_York:20211116T161500
CATEGORIES:∿ Lahr Lecture ∿
SUMMARY:Daniel Krashen: Professional Empathy
DESCRIPTION:In this talk I will discuss my own strategies and
difficulties with working towards a more inclusive environment in
various aspects of my professional career: as a member of the
community of mathematics\, as a faculty member\, a teacher\, a
mentor and as a colleague.\n\nI’ll focus on particular examples
that I hope will be easy to relate to\, including hiring\, graduate
admissions\, course scheduling\, high school outreach\, advising and
teaching. I will try to explain how framing these issues through a
lens of empathy\, human relationships and group membership gives
some insight into building processes which support inclusivity\, and
how this relates to diversity and equity. I will also describe some
of the main pitfalls I’ve identified in this process\, and the
strategies I try to use to deal with them.
LOCATION:Kemeny 008
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e0219@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211117T151500
DTEND;TZID=America/New_York:20211117T161500
CATEGORIES:Math Colloquium
SUMMARY:Daniel Krashen: Can you hear the shape of a division
algebra?
DESCRIPTION:The famous question “can you hear the shape of a
drum?” has inspired quite a bit of mathematical activity due to
its rich connections with a wide range of fields\, from number
theory to geometric topology. In this talk\, I will describe how
this problem has a natural extension to the study of division
algebras and describe various recent work in this direction.
LOCATION:Haldeman 041
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e0265@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211207T140000
DTEND;TZID=America/New_York:20211207T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Lifeng Han: Understanding Cancer Invasion Using Mathematics
and Data
DESCRIPTION:Cancer invasion shows perplexing patterns in time and
space. In this talk\, I will show how mathematical modeling and
data-driven methodologies can help understand cancer growth
dynamics. The first part will be focused on the time dimension of
interaction of tumor-immune interactions. By introducing
stochasticity and time delay into a differential equation model\,
simulation and analysis confirms that these two factors contribute
to the tumor escaping immune control. The second part will introduce
a method of estimating vital patient-specific parameters for a
partial differential model of brain tumor growth. The novelty is
that the parameter estimation is made possible from two magnetic
resonance images of each patient. The third part will move on to an
“equation-free” modeling of spatio-temporal processes inspired
by the needs to forecast brain tumor growth with minimal assumptions
and limited data. This approach is based on Gaussian process
regression\, which is adapted to propagate uncertainty of its
prediction in time forward. By a localization assumption\, high data
efficiency can be achieved.
LOCATION:Zoom (Meeting ID: 98173120301. Passcode: 314159265)
URL:https://math.dartmouth.edu/~acms/
END:VEVENT
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e02b5@math.dartmouth.edu
DTSTART;TZID=America/New_York:20211221T140000
DTEND;TZID=America/New_York:20211221T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Amanda Alexander: TBA
LOCATION:Zoom (Meeting ID: 98173120301. Passcode: 314159265)
URL:https://math.dartmouth.edu/~acms/
END:VEVENT
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DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e02fc@math.dartmouth.edu
DTSTART;TZID=America/New_York:20220203T100000
CATEGORIES:Topology Seminar
SUMMARY:Roman Golovko: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e0343@math.dartmouth.edu
DTSTART;TZID=America/New_York:20220203T151500
CATEGORIES:Math Colloquium
SUMMARY:Roman Golovko: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/colloquia/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e038a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20220310T151500
CATEGORIES:Math Colloquium
SUMMARY:Alice Schwarze: Motifs for processes on networks
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/colloquia/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20211207T100201Z
UID:20211207T05020161af3119e03d0@math.dartmouth.edu
DTSTART;TZID=America/New_York:20220512T151500
CATEGORIES:Math Colloquium
SUMMARY:Tye Lidman: TBA
LOCATION:TBA
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