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X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193ab3c@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
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193aba3@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:343 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193abf4@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
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193ac4b@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:343 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193ac9b@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/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193ace4@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
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193ad23@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191001T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:Martin Tassy: Delocalization of uniform graph homomorphisms
from Z^2 to Z
DESCRIPTION:Graph homomorphisms from the Z^2 lattice to Z are
functions on Z^2 whose gradients equal 1 in absolute value. Using
percolation arguments\, we will show that this model delocalizes in
two dimensions that is: the fluctuations of the height at the origin
become unbounded as the size of the region considered grows. This
answer a fundamental question when studying the convergence of the
model towards the Gaussian free field.
LOCATION:Kemeny 120
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193ad64@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191001T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:James Ronan: Parameter Estimation using Optimal Transport
DESCRIPTION:By using the Wasserstein distance\, a concept from
Optimal transport\, we are able to compare images to outputs of a
model of the scene. This provides a consistent way of estimating the
error from the model that is more physically meaningful than an
$L_2$ distance. This talk will look at the Wasserstein Distance\, a
reformulation of it more suitable for use in calculations and
provide details on how to use this in estimating the parameters for
a physical law governing the evolution of the scene.
LOCATION:Haldeman 252 (The Neukom Conference Room)
URL:https://math.dartmouth.edu/~acms/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193adaf@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191001T143000
DTEND;TZID=America/New_York:20191001T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Eran Assaf: Diagrams mod $p$ and Integral Structures in
Representations of Reductive Groups of Semisimple Rank One
DESCRIPTION:Let $p$ be a prime\, and let $F$ be a finite extension
of $\\mathbb{Q}_{p}$. The local Langlands correspondence associates
packets of representations of (the $F$-points of) a reductive group
$G$ with conjugacy classes of homomorphisms
$\\text{Gal}(\\overline{\\mathbb{Q}}_{p}/F)\\rightarrow ^{\\textrm
L}G$. When $G=GL_{2}(\\mathbb{Q}_{p})$\, such a correspondence has
been built between representations on $p$-adic Banach spaces and
2-dimensional Galois representations. For other groups (e.g.
$GL_{2}(F)$ where $F\\ne\\mathbb{Q}_{p}$\, or $GL_{n}(F)$ for $n>2$)
such a correspondence has not yet been found. One of the main tools
in establishing the correspondence for $GL_{2}(\\mathbb{Q}_{p})$ was
the existence of integral structures in locally algebraic
representations of $GL_{2}(\\mathbb{Q}_{p})$. In this talk\, we
prove criteria for the existence of such norms in certain locally
algebraic representations of groups of semisimple rank one\, defined
over $F$. This both gives simpler proofs of previous results and
generalizes them. We build on the work of Hu for $GL_{2}(F)$\, using
the classification of mod $p$ diagrams and generalize it. We will
also present some computational aspects involved in this research.
LOCATION:343 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193adfb@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191003T140000
CATEGORIES:Topology Seminar
SUMMARY:Bulent Tosun: Stein domains in complex 2-plane with
prescribed boundary
DESCRIPTION:In this talk\, I would like to discuss the question of
"which integral homology spheres can be embedded into complex
2-plane as the boundaries of Stein submanifolds". This question was
first considered and explored in detail by Gompf. At that time\, he
made a fascinating conjecture that: a Brieskorn homology sphere\,
with either orientation\, cannot be embedded into complex 2-plane as
the boundary of a Stein submanifold. In this talk\, I will provide
partial progress (some completed work as well as report on some
recent work in progress) towards resolving this conjecture.
LOCATION:201 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193ae3e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191008T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Victor Churchill: Title: Identifying damage in sea ice from
sparse laser strain measurements
DESCRIPTION:Abstract:\n\nWe discuss several methods for identifying
damage in sea ice when given laser strain or displacement
measurements at only a few sparse locations in the domain of
interest. We begin by modifying the equations of linear elasticity
in order to account for damage in the displacement field. We then
present a standard method for solving an inverse problem of this
type which minimizes a data misfit cost function that is constrained
by the aforementioned partial differential equations. We consider
several regularization schemes for this method. Finally\, we propose
a method which minimizes an unconstrained cost function with respect
to two variables via alternating minimization. Our results using
both simulated and real data suggest that this method\, which allows
for variation away from both the given data as well as the model\,
is promising.\n\n*** Please note the special location ***
LOCATION:Kemeny 200
URL:https://math.dartmouth.edu/~acms/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193ae88@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191008T143000
DTEND;TZID=America/New_York:20191008T153000
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:343 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193aecd@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191008T160000
CATEGORIES:Geometry Seminar
SUMMARY:Dragomir Saric: Integrable holomorphic quadratic
differentials on infinite surfaces
DESCRIPTION:Abstract: The Heights Theorem of Marden and Strebel
states that an integrable holomorphic quadratic differential on a
Riemann surface of parabolic type is uniquely determined by its
heights with respect to all homotopy classes of simple closed
curves. We extend this theorem to all Riemann surfaces whose
fundamental group is of the first kind. In fact\, we consider a map
which assigns a measured lamination to each quadratic differential
by straightening the horizontal foliation of the differential. We
show that this map is injective which extends the Heights Theorem.
An interesting question is to characterize the image of the
horizontal straightening map. The answer seems to depend on the
hyperbolic geometry properties of an infinite surface.
LOCATION:307 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193af12@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191015T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Colin Meyer: Title: A continuum model for meltwater flow
through compacting snow
DESCRIPTION:Abstract: Water flowing through snow and refreezing
leads to changes in snowpack characteristics such as the structure\,
temperature\, and strength. In this way\, refreezing is critical to
snowpack hydrology\, avalanche initiation\, and melting on the
surface of glaciers. To understand the temperature evolution and
density structure of snow for a variety of applications\, we
construct and analyze a continuum model consisting of a series of
coupled partial differential equations for water percolation\, heat
conduction\, refreezing\, and mechanical compaction. The model is
forced by surface mass and energy balances\, and the percolation
process is described using Darcy's law\, allowing for both partially
and fully saturated pore space. The model outputs include the
temperature\, density\, and water-content profiles as well as the
surface runoff and water storage. Using this model\, we also examine
the stability of two-dimensional refreezing fronts to the 'piping'
instability and discuss the implications for snowpack evolution.
LOCATION:Haldeman 252 (The Neukom Conference Room)
URL:https://math.dartmouth.edu/~acms/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193af5d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191015T143000
DTEND;TZID=America/New_York:20191015T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:David Treumann: Symplectic\, or mirrorical\, look at the
Fargues-Fontaine curve
DESCRIPTION:Homological mirror symmetry describes Lagrangian Floer
theory on a torus in terms of vector bundles on the Tate elliptic
curve. A version of Lekili and Perutz's works "over Z[[t]]"\, where
t is the Novikov parameter. I will review this story and describe a
modified form of it\, which is joint work with Lekili\, where the
Floer theory is altered by a locally constant sheaf of rings on the
torus. When the fiber of this sheaf of rings is perfectoid of
characteristic p\, and the holonomy around one of the circles in the
torus is the pth power map\, it is possible to specialize to t = 1\,
and the resulting theory there is described in terms of vector
bundles on the equal-characteristic-version of the Fargues-Fontaine
curve.
LOCATION:343 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193afa2@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191016T170000
CATEGORIES:Undergraduate Math Society Talk
SUMMARY:Arunas Rudvalis: Solving 2×2 Linear\, Constant Coeﬃcient
Systems Without Using Eigenvalues and Eigenvectors
LOCATION:Haldeman 028
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193afdb@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191017T180000
DTEND;TZID=America/New_York:20191017T190000
CATEGORIES:Prosser Lecture
SUMMARY:Bjorn Engquist: Mathematics and science: the Abel and Nobel
Prizes
DESCRIPTION:We will answer the questions: “why is there no Nobel
Prize in mathematics” and “how did the Abel Prize get started”
as a beginning to a discussion on mathematics and science. This is
related to scientific computing\, which is often referred to as the
third pillar of science\, complementing experiments and theory. It
has also enabled large parts of sophisticated mathematics that
previously was not regarded as having applied value to impact
science and engineering. We will give some elementary classical
examples and see how modern versions of these examples engage deeper
mathematics and enhance science. Finally\, we will remark on the
future of mathematics and scientific theory in the world of big data
and machine learning.\n
LOCATION:Life Sciences Center 100\, Arvo J. Oopik '78 Auditorium
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b022@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191018T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Bjorn Engquist: Title: Seismic imaging and optimal
transport.
DESCRIPTION:Abstract: The purpose of exploration seismology is to
find geophysical properties\, such as wave velocity and location of
reflecting sub layers in the earth from measurements of seismic
waves at the surface. A recently popular computational technique for
seismic imaging is Full Waveform Inversion\, which is formulated as
PDE constrained minimization where the miss-match between measured
and computed signals plays an important role. The geophysical
properties are given by unknown variable coefficients in the PDE. We
propose using optimal transport and the Wasserstein metric for this
miss-match in order to reduce the risk of only finding local minima
in the PDE constrained minimization. The optimal transport can be
given by the gradient of the solution to a Monge–Ampère equation.
Analysis of convexity properties and numerical examples comparing
these new techniques with the classical L2 miss-match will be
presented.
LOCATION:Haldeman 252 (Neukom Conference Room)
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b069@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191022T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Jihun Han: Title: Spontaneous oscillation and
fluid-structure interaction of cilia
DESCRIPTION:Abstract: The exact mechanism to orchestrate the action
of hundreds of dynein motor proteins to generate wave-like ciliary
beating remains puzzling and has fascinated many scientists. We
present a three-dimensional model of a cilium and the simulation of
its beating in a fluid environment. The model cilium obeys a simple
geometric constraint that arises naturally from the microscopic
structure of a real cilium. This constraint allows us to determine
the whole three dimensional structure at any instant in terms of the
configuration of a single space curve. The tensions of active links
which model the dynein\nmotor proteins follow a dynamical law we
contrived\, and\, together with the passive elasticity of
microtubules\, this dynamical law is responsible for the ciliary
motions. In particular\, our postulated tension dynamics lead to
the dynamical instability of a symmetrical steady state in which the
cilium is straight and active links are under equal tensions. The
result of this instability is a stable\, wave-like\, limit-cycle
oscillation. We have also investigated the fluid-structure
interaction of cilia using the immersed boundary (IB) method. In
this setting we see not only coordination within a single cilium\,
but also well-coordinated wave motion in which multiple cilia in an
array organize their beating to pump fluid\, in particular\, by
breaking phase synchronization.
LOCATION:Haldeman 252 (The Neukom Conference Room)
URL:https://math.dartmouth.edu/~acms/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b0c3@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191022T143000
DTEND;TZID=America/New_York:20191022T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Ben Antieau: Rational points and derived equivalence
DESCRIPTION:Suppose that X and Y are smooth projective varieties
over a field k and suppose that X and Y have equivalent derived
categories of sheaves. If X has a rational point\, does Y have a
rational point? This question was asked 10 years ago by Esnault. I
will report on joint work with Addington\, Frei\, and Honigs which
shows that\, in general\, the answer is ‘no’\, in contrast to
what happens for curves (Antieau—Krashen—Ward) or in dimension
at most 3 over finite fields (Honigs).
LOCATION:343 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b105@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191029T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Olivia Chu: Title: TBA
LOCATION:Haldeman 252 (The Neukom Conference Room)
URL:https://math.dartmouth.edu/~acms/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b13f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191029T153000
DTEND;TZID=America/New_York:20191029T163000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Ben Breen: Cyclic cubic fields with a totally positive
systems of fundamental units
DESCRIPTION:How often do number fields have a totally positive
systems of fundamental units? In the case of a real quadratic fields
$\\mathbb{Q}(\\sqrt{D})$ this is linked to solvability of the
negative pell equation $x^2-Dy^2 = -1$. Using techniques from
arithmetic geometry\, we analyze the equation $x^3-ax^2+bx -1$ to
prove that there are infinitely many cyclic cubic fields with a
totally positive system of fundamental units. Joint work with Noam
Elkies\, Ila Varma\, and John Voight.
LOCATION:343 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b181@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191029T160000
CATEGORIES:Geometry Seminar
SUMMARY:Ivan Contreras: Genus integration of Lie algebroids and the
Hurewicz theorem
DESCRIPTION:Abstract: Lie algebroids are natural objects in
differential geometry and\nthey serve as a 'vector-bundle' version
of Lie algebras. In this work we\nstudy the existence of an abelian
integration of the abelianization of Lie\nalgebroids and how this
extends the classical Hurewicz theorem. We prove\nthat the
obstructions of such integration are given by the
so-called\nextended monodromy groups. We also show that the
abelianization can be\nconstructed geometrically\, in terms of
homology equivalence. This is joint\nwork with Rui Fernandes
(University of Illinois\, Urbana-Champaign)
LOCATION:307 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b1d4@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191031T140000
CATEGORIES:Topology Seminar
SUMMARY:Ivan Dynnikov: Distinsguishing Legendrian and transverse
knots
DESCRIPTION:The talk is based on joint works (recent and in
progress) with Maxim\nPrasolov and Vladimir Shastin.\n\nA smooth
knot (or link) $K$ in the three-space $\\mathbb R^3$ is
called\nLegendrian if the restriction of the
$1$-form~$\\alpha=x\\\,dy+dz$\non $K$ vanishes\, where $x\,y\,z$ are
the standard coordinates in~$\\mathbb\nR^3$. If $\\alpha|_K$ is
everywhere non-vanishing on $K$\, then $K$ is\ncalled
transverse.\n\nClassification of Legendrian and transverse knots up
to respectively\nLegendrian and transverse isotopy is an important
unsolved problem of\ncontact topology. A number of useful invariants
have been constructed in\nthe literature\, but there are still small
complexity examples in which the\nexisting methods do not suffice to
decide whether or not the given\nLegendrain (or transverse) knots
are equivalent.\n\nWe propose a totally new approach to the
equivalence problem for\nLegendrian and transverse knots\, which
allows one to practically\ndistinguish between non-equivalent
Legendrian (or transverse) knots in\nsmall complexity cases\, and
gives rise to a complete algorithmic solution\nin the general
case.\n
LOCATION:201 Kemeny
URL:https://math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b220@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191105T160000
CATEGORIES:Geometry Seminar
SUMMARY:Ian Biringer: TBA
LOCATION:307 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b259@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191112T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Sean Carney: Title: TBA
LOCATION:Haldeman 252 (The Neukom Conference Room)
URL:https://math.dartmouth.edu/~acms/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b293@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191114T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Paul Constantine: Title: TBA
LOCATION:Haldeman 252 (Neukom Conference Room)
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b2cb@math.dartmouth.edu
DTSTART;TZID=America/New_York:20191119T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Chris Rackauckas: Title: Neural Differential Equations as a
Basis for Scientific Machine Learning
DESCRIPTION:Abstract: Scientific Machine Learning (SciML) is an
emerging discipline which merges the mechanistic models of science
and engineering with non-mechanistic machine learning models to
solve problems which were previously intractable. Recent results
have showcased how methods like Physics Informed Neural Networks
(PINNs) can be utilized as a data-efficient learning method\,
embedding the structure of physical laws as a prior into a learnable
structures so that small data and neural networks can sufficiently
predict phenomena. Additionally\, deep learning embedded within
backwards stochastic differential equations has been shown to be an
effective tool for solving high-dimensional partial differential
equations\, like the Hamilton-Jacobian-Bellman equation with 1000
dimensions. In this talk we will introduce the audience to these
methods and show how these diverse methods are all instantiations of
a neural differential equation\, a differential equation where all
or part of the equation is described by a latent neural network.
Once this is realized\, we will show how a computational tool\,
DiffEqFlux.jl\, is being optimized to allow for efficient training
of a wide variety of neural differential equations\, explaining how
the performance properties of these equation differ from more
traditional uses of differential equations and some of the early
results of optimizing for this domain. The audience will leave
knowing how neural differential equations and DiffEqFlux.jl may be a
vital part of next-generation scientific tooling.
LOCATION:Haldeman 252 (Neukom Conference Room)
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b31b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20200114T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Akshay K. Mehra: Title: TBA
LOCATION:Haldeman 252 (Neukom Conference Room)
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b355@math.dartmouth.edu
DTSTART;TZID=America/New_York:20200123T153000
CATEGORIES:Math Colloquium
SUMMARY:June Huh: TBA
LOCATION:004 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b38d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20200225T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Jim Lambers: Title: TBA
LOCATION:Haldeman 252 (Neukom Conference Room)
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b3c6@math.dartmouth.edu
DTSTART;TZID=America/New_York:20200227T153000
CATEGORIES:Math Colloquium
SUMMARY:Ben Adcock: TBA
LOCATION:004 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b3ff@math.dartmouth.edu
DTSTART;TZID=America/New_York:20200416T153000
CATEGORIES:Math Colloquium
SUMMARY:Tony Guttmann: Recent developments in self-avoiding walks.
DESCRIPTION:The canonical problem of calculating the properties of
self-avoiding walks (SAWs) has been studied for nearly 80 years.
Remarkably little has been proved. In this talk I will give a brief
introduction to SAWs\, review what is known\, and what is widely
believed to be true\, but has not been proved. Then I will outline
three recent calculations:\n(i) New scaling laws. (ii) The SAW at
the theta point. (iii) Attempts to prove the existence of the
critical exponent for two-dimensional SAWs. Minimal prior knowledge
is assumed.
LOCATION:004 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20191016T020201Z
UID:20191015T2202015da67a193b441@math.dartmouth.edu
DTSTART;TZID=America/New_York:20200424T160000
DTEND;TZID=America/New_York:20200424T170000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Mark de Cataldo: TBA
LOCATION:343 Kemeny Hall
END:VEVENT
END:VCALENDAR