BEGIN:VCALENDAR
VERSION:2.0
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PRODID:-//Mathematics Department//NONSGML mathical.php//EN
X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed173186@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171027T153000
CATEGORIES:Math Colloquium
SUMMARY:Liliana Borcea: Untangling the nonlinearity in inverse
scattering using data-driven reduced order models
DESCRIPTION:We discuss an inverse problem for the wave equation\,
where an array of sensors probes an unknown\, heterogeneous medium
\nwith pulses and measures the scattered waves. The goal in
inversion is to determine from these measurements scattering
structures \nin the medium\, modeled mathematically by a
reflectivity function. Most imaging methods assume a linear mapping
between the \nunknown reflectivity and the array data. The
linearization\, known as the Born (single scattering) approximation
is not accurate in \nstrongly scattering media\, so the
reconstruction of the reflectivity may be poor. We show that it is
possible to remove the multiple \nscattering (nonlinear) effects
from the data using a reduced order model (ROM). The ROM is defined
by an orthogonal projection\nof the wave propagator operator on the
subspace spanned by the time snapshots of the solution of the wave
equation. The snapshots are \nknown only at the sensor locations\,
which is enough information to construct the ROM. The main result
discussed in the talk is a \nnovel\, linear-algebraic algorithm that
uses the ROM to map the data to its Born approximation.
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed17353c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171031T143000
DTEND;TZID=America/New_York:20171031T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Doug Cochran: Maximum-Likelihood Registration in Networks
DESCRIPTION:A key aspect of integrating and ultimately exploiting
information collected across a distributed network of assets is
establishing and maintaining synchronization across the nodes of the
network. In this presentation\, a statistical framework to allow
foundational issues in this type of problem to be addressed a
rigorous fashion. While the work is applicable to a broad class of
problems involving synchronization or registration of data across a
sensor network in the presence of noise\, it is not a panacea\;
rather important and difficult challenges involving disparate data
types\, occlusion\, model mismatch\, and other characteristics of
real-world applications remain. Nevertheless\, this framework
enables an estimation-theoretic approach to the design and
characterization of synchronization algorithms that can play a role
in larger fusion problems. The Fisher information is expressed in
terms of the distribution of the measurement noise and standard
algebraic descriptors of the networkâ€™s graph structure for
several important cases. This leads to maximum-likelihood and
approximate maximum- likelihood registration algorithms and also to
distributed iterative algorithms that\, when they converge\, attain
statistically optimal solutions. The relationship between ML
estimation in this setting and Kirchhoffâ€™s laws is also
elucidated. This is joint work with Steve Howard and Bill Moran.
LOCATION:Kemeny 201
URL:https://math.dartmouth.edu/~acms/Doug.html
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed1738e9@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171031T160000
CATEGORIES:Geometry Seminar
SUMMARY:Samuel Lin: Rank Rigidity in Dimension Three\, Part II
DESCRIPTION:Abstract: Fixing K=-1\, 0\, 1\, a complete Riemannian
manifold is said to have higher hyperbolic\, Euclidean\, or
spherical rank if every geodesic admits a normal parallel field
making curvature K with the geodesic. Examples for manifolds of
higher rank includes locally symmetric spaces. The main goal of the
study of rank rigidity is to show that with suitable assumptions\,
locally symmetric spaces are the only manifolds of higher rank.
LOCATION:307 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed173bff@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171102T132000
CATEGORIES:Combinatorics Seminar
SUMMARY:Tamar Friedmann: The action of the symmetric group on a
generalization of the free Lie algebra: a CataLAnKe Theorem
DESCRIPTION:The free Lie algebra is a natural mathematical
construction that is central in algebraic combinatorics and has
applications in other fields. I will discuss a generalization of
the free Lie algebra based on an n-ary commutator. The action of the
symmetric group on its multilinear component generalizes the
well-known representation Lie(k). I will discuss results and
conjectures about this generalization of Lie(k)\, including a
representation whose dimension is the Catalan number
LOCATION:Geometry Lab (Kemeny 307)
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed173f30@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171103T153000
CATEGORIES:Math Colloquium
SUMMARY:Henry Segerman: Design of 3D printed mathematical art
DESCRIPTION:When visualising topological objects via 3D printing\,
we need a three-dimensional geometric representation of the object.
There are approximately three broad strategies for doing this:
"Manual" - using whatever design software is available to build the
object by hand\; "Parametric/Implicit" - generating the desired
geometry using a parametrisation or implicit description of the
object\; and "Iterative" - numerically solving an optimisation
problem.\n\nThe manual strategy is unlikely to produce good results
unless the subject is very simple. In general\, if there is a
reasonably canonical geometric structure on the topological object\,
then we hope to be able to produce a parametrisation of it.
However\, in many cases this seems to be impossible and some form of
iterative method is the best we can do. Within the parametric
setting\, there are still better and worse ways to proceed. For
example\, a geometric representation should demonstrate as many of
the symmetries of the object as possible. There are similar issues
in making three-dimensional representations of higher dimensional
objects. I will discuss these matters with many examples\, including
visualisation of four-dimensional polytopes (using orthogonal versus
stereographic projection) and Seifert surfaces (comparing my work
with Saul Schleimer with Jack van Wijk's iterative techniques).\n\nI
will also describe some computational problems that have come up in
my 3D printed work\, including the design of 3D printed mobiles
(joint work with Marco Mahler)\, "Triple gear" and a visualisation
of the Klein Quartic (joint work with Saul Schleimer)\, and hinged
surfaces with negative curvature (joint work with Geoffrey Irving).
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed1742bd@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171106T101000
DTEND;TZID=America/New_York:20171106T111500
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Daniele Venturi: Data-driven closures for kinetic equations
DESCRIPTION:In this talk I will address the problem of constructing
data-driven closures for reduced-order kinetic equations. Such
equations arise\, e.g.\, when we coarse-grain high-dimensional
systems of stochastic ODEs and PDEs. I will first review the basic
theory that allows us to transform such systems into conservation
laws for probability density functions (PDFs). Subsequently\, I will
introduce coarse-grained PDF models\, and describe how we can use
data\, e.g.\, sample trajectories of the ODE/PDE system\, to
estimate the unclosed terms in the reduced-order PDF equation. I
will also discuss a new paradigm to measure the information content
of data which\, in particular\, allows us to infer whether a certain
data set is sufficient to compute accurate closure approximations or
not. Throughout the lecture I will provide numerical examples and
applications to prototype stochastic systems such as Lorenz-96\,
Kraichnan-Orszag and Kuramoto-Sivashinsky equations.
LOCATION:Kemeny 108
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed174620@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171107T143000
DTEND;TZID=America/New_York:20171107T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Robyn Barbato: TBA
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed17488f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171109T132000
CATEGORIES:Combinatorics Seminar
SUMMARY:Justin Troyka: Combinatorial proofs of power-series
identities
DESCRIPTION:In this talk\, I will show how several important
identities on polynomials or power series can be given a
combinatorial interpretation in terms of lattice paths\,
permutations\, and other objects. One such identity is the Lagrange
Inversion Formula\, a useful tool for enumerating trees and other
similar structures\; classical proofs of this were analytic in
nature\, but an elegant combinatorial proof dates back to a 1960
paper of George N. Raney. I will also present a new (as far as I am
aware) combinatorial proof of Newton's binomial expansion (for
(1+x)^u with u not necessarily an integer)\, in which the Stirling
Numbers will arise.
LOCATION:Geometry Lab (Kemeny 307)
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed174a53@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171109T143000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Jonathan Huang: Zeta functions\, Witt rings\, and a
classical formula of MacDonald
DESCRIPTION:A remarkable formula of MacDonald provides a closed
expression for the generating series of the Poincare polynomial of
the symmetric powers $Sym^n X$ of a space $X$. We show that this
formula takes a very nice form when rewritten in the big ring of
Witt vectors $W(\\mathbb{Z}[z])$ of the polynomial ring
$\\mathbb{Z}[z]$. We then provide some motivation for similarly
viewing the Hasse-Weil zeta function of varieties over finite fields
as elements in the big Witt ring $W(\\mathbb{Z})$. In this
setting\, the zeta function $Z(X\,t)$ takes the form of an
Euler-Poincare characteristic\; specifically\, it is a motivic
measure on the Grothendieck ring of varieties. \n
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed174c1c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171109T153000
CATEGORIES:Topology Seminar
SUMMARY:Nathan Dowlin: Khovanov Homology\, Unknotting Number\, and
the Knight Move Conjecture
DESCRIPTION:I will discuss a version of Khovanov homology which has
interesting torsion under the basepoint action. It turns out that
this torsion gives a lower bound for the unknotting number\, and is
closely related to the page at which the Lee spectral sequence
collapses. In particular\, for knots with $u(K)
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed174dd9@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171110T143000
DTEND;TZID=America/New_York:20171110T150000
CATEGORIES:Thesis Defence
SUMMARY:Jared Duker Lichtman: Numbers free of large prime factors
DESCRIPTION:Abstract\nThis thesis consists of three parts\, each of
which tackles a separate number-theoretic problem and may stand
alone as an individual project. Nevertheless\, these problems are
united by the common thread of numbers free of large prime factors\,
so-called {\\it smooth} numbers. From the vantage point of smooth
numbers\, these three problems (and their methods of proof) build
upon one another in a natural progression of ideas.\n\nThe first
problem concerns primality testing using the Fermat congruence
$a^{n-1}\\equiv 1\\pmod{n}$. The second problem concerns the
reciprocal sum of a certain set of numbers\, so-called primitive
nondeficient numbers. For both these problems\, the proof strategy
relies in large part on smoothness considerations\, that is\, the
relative size of the largest prime factor. Finally\, the third
problem addresses smooth numbers head on\, that is\, to compute the
number of integers up to $x$ whose prime factors are at most $y$.\n
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed174fc1@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171110T153000
CATEGORIES:Math Colloquium
SUMMARY:Nicholas Scoville: $S^1$ and $S^3$ and $S^2$\, oh fi! A
digital Hopf fibration
DESCRIPTION:Digital images surround us. They are found in our
computers\, iPhones\, televisions\, and more. Because they are so
integrated into our lives\, there is a constant need to manipulate
and investigate these images. Anything that one might want to do
with a digital image will inevitably involve some kind of
mathematics\, whether it be linear algebra\, geometry\, or topology.
To that end\, we will introduce topology in the digital setting\,
noting some places where it is similar and different than in the
smooth setting. In particular\, we will work with digital homotopy
between digital images by viewing a digital image as a tolerance
space\, which sits inside of a well-defined category. Although
there is a notion of digital fibration in this context\, there seem
to be very few non-trivial examples of digital fibrations. We will
construct a digital analogue of the Hopf fibration\, the most
important single example in the history of algebraic topology.
Because the $3$-sphere in this setting consists of only $24$
pixels\, this example is robust yet small enough to be written down
and investigated explicitly. This talk will be accessible to
undergraduates.
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed175195@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171116T132000
CATEGORIES:Combinatorics Seminar
SUMMARY:Alejandro Morales: Hook formulas for skew shapes: border
strips and product formulas
DESCRIPTION:The celebrated hook-length formula of Frame\, Robinson
and Thrall from 1954 gives a product formula for the number of
standard Young tableaux of straight shape. No such product formula
exists for general skew shapes but there are determinantal and
positive formulas involving Littlewood-Richardson coefficients. In
2014\, Naruse announced a positive formula without these
coefficients and very close to the formula for the straight shape
case. We give an elementary proof of Naruse's formula based on the
case of border strips using the Hamel-Goulden determinantal
identities of Schur functions. We also give new product formulas for
the number of standard Young tableaux of certain skew shapes using
symmetries for evaluations of factorial Schur functions. This is
joint work with Igor Pak and Greta Panova.\n
LOCATION:Geometry Lab (Kemeny 307)
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed17535f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20171116T153000
CATEGORIES:Topology Seminar
SUMMARY:David Freund: Complexity of Virtual Multistrings
DESCRIPTION:A virtual $n$-string $\\alpha$ is a collection of $n$
closed curves on an oriented surface $M$. Associated to $\\alpha$\,
there are two natural measures of complexity: the genus of $M$ and
the number of intersection points. By considering virtual
$n$-strings up to equivalence by virtual homotopy\, i.e.\,
homotopies of the component curves and
stabilizations/destabilizations of the surface\, a natural question
is whether these quantities can be minimized simultaneously. We show
that this is possible for non-parallel virtual $n$-strings and
that\, moreover\, such a representative can be obtained by
monotonically decreasing genus and the number of intersections from
any initial representative.
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed17552e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180104T143000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:John Voight: Strong approximation I
DESCRIPTION:Theorems over global fields are often first
investigated\nlocally\, and then a global result is recovered using
some form of\napproximation. Approximation provides a way to
transfer analytic\nproperties (encoded in congruences or bounds)
into global elements.\nWe will explain robust approximation theorems
and investigate their\narithmetic applications.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed1756fe@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180111T143000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:John Voight: Strong approximation II
DESCRIPTION:Theorems over global fields are often first
investigated\nlocally\, and then a global result is recovered using
some form of\napproximation. Approximation provides a way to
transfer analytic\nproperties (encoded in congruences or bounds)
into global elements.\nWe will explain robust approximation theorems
and investigate their\narithmetic applications.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed1758b5@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180112T153000
CATEGORIES:Math Colloquium
SUMMARY:John Baldwin: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed175a52@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180119T153000
CATEGORIES:Math Colloquium
SUMMARY:Miklos Bona: Counting vertices of trees according to their
distance from the closest leaf
DESCRIPTION:Various parameters of many models of random rooted trees
are fairly well understood if they relate to a near-root part of the
tree or to global tree structure. The first group includes\, for
instance\, the numbers of vertices at given distances from the
root\, the immediate progeny sizes for vertices near the top\, and
so on. The second group includes the height or the width of the
tree. \n\nIn recent years there has\nbeen a growing interest in
analysis of the random tree fringe\, i.e. the tree part close to
the leaves. In a network\, these vertices could represent the "most
vulnerable" nodes\, or the "recently added\, and still active"
nodes. \n\nIn this talk\, we will consider three varieties of trees
that appear very frequently in enumerative combinatorics\, and
enumerate their vertices according to their distance from the
closest leaf. Interestingly\, the three examples require three
different methods. Numerous open questions will be presented.
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed175bf3@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180126T160000
CATEGORIES:Math Colloquium
SUMMARY:Reserved for Recruitment talks: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed175d88@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180202T153000
CATEGORIES:Math Colloquium
SUMMARY:Reserved for Recruitment talks: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed175f0a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180209T153000
CATEGORIES:Math Colloquium
SUMMARY:Reserved for Recruitment talks: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed1760a5@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180223T153000
CATEGORIES:Math Colloquium
SUMMARY:Tony Várilly-Alvarado: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed17621a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180302T153000
CATEGORIES:Math Colloquium
SUMMARY:Graduate Open House\, Faculty Talks: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed1763aa@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180327T190000
CATEGORIES:Prosser Lecture
SUMMARY:Po-Shen Loh: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed17651e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180406T153000
CATEGORIES:Math Colloquium
SUMMARY:Tatiana Roque: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed1766b2@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180413T153000
CATEGORIES:Math Colloquium
SUMMARY:Norbert A'Campo: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed176826@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180418T180000
CATEGORIES:Kemeny Lecture
SUMMARY:Martin Nowak: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed17699a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180419T153000
CATEGORIES:Kemeny Lecture
SUMMARY:Martin Nowak: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed176b10@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180420T153000
CATEGORIES:Kemeny Lecture
SUMMARY:Martin Nowak: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed176c84@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180427T153000
CATEGORIES:Math Colloquium
SUMMARY: Yun Kang: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed176df9@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180504T153000
CATEGORIES:Math Colloquium
SUMMARY:Chi-Wang Shu: High order numerical methods for hyperbolic
equations
DESCRIPTION:Hyperbolic equations are used extensively in
applications\nincluding fluid dynamics\, astrophysics\,
electro-magnetism\,\nsemi-conductor devices\, and biological
sciences. High order\naccurate numerical methods are efficient for
solving such\npartial differential equations\, however they are
difficult\nto design because solutions may contain
discontinuities.\nIn this talk we will survey several types of high
order\nnumerical methods for such problems\, including
weighted\nessentially non-oscillatory (WENO) finite difference
and\nfinite volume methods\, discontinuous Galerkin finite
element\nmethods\, and spectral methods. We will discuss
essential\ningredients\, properties and relative advantages of
each\nmethod\, and provide comparisons among these methods.
Recent\ndevelopment and applications of these methods will also
be\ndiscussed.\n
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed176f9a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180511T153000
CATEGORIES:Math Colloquium
SUMMARY:Asher Auel: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed177111@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180518T153000
CATEGORIES:Math Colloquium
SUMMARY:David Roberts: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20171124T053201Z
UID:20171124T0032015a17aed177287@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180525T153000
CATEGORIES:Math Colloquium
SUMMARY:Yuli Rudyak: Title: Maps of Degree 1 and Critical Points.
DESCRIPTION:Given a map of degree 1 of closed oriented manifolds\,
it is known that the domain of the map is more "massive" than the
range. For example\, the map induces epimorphisms in homology and
fundamental groups. So\, it is reasonable to conjecture that minimal
number of critical points of the domain is not less than that of the
range (of the map of degree 1). It is an open question whether the
minimal number of critical points is a homotopy invariant of a
manifold. So\, we pose a homotopy invariant version of the previous
conjecture: the Lusternik-Schnirelmann category of the domain is not
less than that of the range. \n\nIn the talk I want to discuss the
current status of the conjectures.
LOCATION:007 Kemeny Hall
END:VEVENT
END:VCALENDAR