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X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9aa23d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180118T133000
CATEGORIES:Combinatorics Seminar
SUMMARY:Sam Hopkins: Chip-Firing for Root Systems
DESCRIPTION:Jim Propp recently introduced a variant of chip-firing
on the infinite path where the chips are given distinct integer
labels and conjecture that this process sorts certain (but not all)
initial configurations of chips. In earlier work with Thomas
McConville and Jim Propp\, we proved Propp's sorting conjecture.
With Pavel Galashin\, Thomas McConville\, and Alex Postnikov\, we
recast this result in terms of root systems: the labeled chip-firing
game can be seen as a “vector-firing” process which allows the
moves $\\lambda \\to \\lambda + \\alpha$ for $\\alpha \\in \\Phi^+$
whenever $\\langle \\lambda\, \\alpha^\\vee \\rangle = 0$\, where
$\\Phi^+$ is the set of positive roots of a root system of type
$A_{2n-1}$. We give conjectures about confluence for this process in
the general setting of an arbitrary root system. We show that the
process is always confluent from any initial point after modding out
by the action of the Weyl group (an analog of unlabeled chip-firing
in arbitrary type). We also show that if we instead allow firing
when $\\langle \\lambda\, \\alpha^\\vee \\rangle \\in [-k-1\,k-1]$
or $[-k\,k-1]$\, we always get confluence from any initial point.
Moreover\, in these two settings\, the set of weights with given
stabilization has a remarkable geometric structure related to
permutohedra. This geometric structure leads us to define certain
“Ehrhart-like” polynomials that conjecturally have nonnegative
integer coefficients. In very recent joint work with Alex
Postnikov\, which I will discuss if time permits\, we prove the part
of this Ehrhart positivity conjecture corresponding to the
$[-k-1\,k-1]$ intervals.
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9aa5f6@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180118T143000
DTEND;TZID=America/New_York:20180118T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:John Voight: Strong approximation III
DESCRIPTION:Theorems over global fields are often first investigated
locally\, and then a global result is recovered using some form of
approximation. Approximation provides a way to transfer analytic
properties (encoded in congruences or bounds) into global elements.
We will explain robust approximation theorems and investigate their
arithmetic applications.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9aa93d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180118T153000
CATEGORIES:Topology Seminar
SUMMARY:Inanc Baykur: Symplectic and exotic 4-manifolds via positive
factorizations
DESCRIPTION:We will discuss new ideas and techniques for producing
positive\nDehn twist factorizations of surface mapping classes which
yield novel\nconstructions of interesting symplectic and smooth
4-manifolds\, such as\nsmall symplectic Calabi-Yau surfaces and
exotic rational surfaces\, via\nLefschetz fibrations and pencils.
LOCATION:Kemeny 201
URL:https://www.math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9aab65@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:008 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9aadba@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180119T160000
CATEGORIES:Math Colloquium
SUMMARY:Larry Gonick: From Math Department to Art Department
DESCRIPTION:Gonick will talk about\nhow he left graduate\nschool for
a cartooning\ncareer and describe his\ntechniques for\nrendering
history\,\nscience\, and\nmathematics into\ncomics.
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9aafe9@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180125T143000
DTEND;TZID=America/New_York:20180125T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:John Cullinan: On local-global torsion for abelian surfaces
DESCRIPTION:Let E be an elliptic curve defined over the rational
numbers Q. It is well known that Tors(E(Q)) injects into E(F_p) for
all but finitely many primes p. Thus\, if |Tors(E(Q))| is divisible
by m\, then so are the numbers |E(F_p)|. On the other hand\, what
if the |E(F_p)| are divisible by some fixed integer m? Is it true
that |Tors(E(Q))| is also divisible by m? (Not necessarily.) \n\nIn
this talk we will consider the same divisibility question in the
context of abelian varieties over general number fields and
reinterpret it in terms of representation theory and the Bruhat-Tits
building of certain symplectic groups. After a brief survey of known
results we will present work in progress on abelian surfaces.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ab22f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180125T153000
CATEGORIES:Topology Seminar
SUMMARY:Yu Pan: Wrapped Floer Homology for exact Lagrangian fillings
and cobordisms
DESCRIPTION: I will give a brief introduction of the Legendrian
contact homology\, which is an invariant of Legendrian knots Λ
defined in the spirit of Symplectic Field Theory. With the similar
idea\, the wrapped Floer homology for exact Lagrangian fillings
gives an isomorphism between the linearized contact homology of Λ
and the singular homology of the Lagrangian filling. The wrapped
Floer homology for exact Lagrangian cobordisms also gives relations
between linearized contact homology of boundary Legendrian knots and
the singular homology of the Lagrangian cobordism. At the end\, I
would like to mention an on-going project with Dan Rutherford about
the wrapped Floer theory for immersed exact Lagrangian fillings.
LOCATION:Kemeny 201
URL:https://math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ab476@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180126T160000
CATEGORIES:Math Colloquium
SUMMARY:Larry Gonick: From Math Department to Art Department
DESCRIPTION:Gonick will talk about\nhow he left graduate\nschool for
a cartooning\ncareer and describe his\ntechniques for\nrendering
history\,\nscience\, and\nmathematics into\ncomics.
LOCATION:008 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ab6e5@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180129T160000
DTEND;TZID=America/New_York:20180129T170000
CATEGORIES:Math Colloquium
SUMMARY:Maria Riolo: Finding communities in networks without knowing
how many to look for.
DESCRIPTION:One way to make sense of network data is to summarize
the broad patterns of connection between groups of nodes. Killer
whales tend to socialize within their family groups. Nouns in
English text often appear next to adjectives\, but rarely next to
other nouns. \n\nHowever\, picking an informative set of groups
isn't always easy. Many methods for community detection require us
to specify the number of groups\, and we often don't know in advance
how many there are\, or whether they'll be assortative like the
whales or disassortative like the adjectives and nouns. \n\nI will
present a method for exploring the space of possible partitions
using some Bayesian inference and a Monte Carlo sampling scheme.
Beyond just finding one good partition of nodes into group\, I'll
also introduce some other applications of the method such as
estimating a probability distribution for the number of communities
in the network\, estimating how likely any particular pair of nodes
are to be in the same group\, and generating nice layouts for
visualization.\n
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ab939@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180201T153000
CATEGORIES:Topology Seminar
SUMMARY:David Freund: Multistring Based Matrices
DESCRIPTION:Flat virtual links can be interpreted as combinatorial
models for curves on surfaces. Using a canonical surface
representation of a chord diagram\, Turaev associated a matrix to a
flat virtual knot that captures invariants of the knot. Our first
talk will focus on the development of this based matrix and its
computation\, justifying that the construction does not naturally
generalize to flat virtual links. In the second talk\, we construct
a generalization of Turaev's based matrix to flat virtual links that
successfully generates analogous invariants.
LOCATION:Kemeny 201
URL:https://www.math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9abb6e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180202T160000
DTEND;TZID=America/New_York:20180202T170000
CATEGORIES:Math Colloquium
SUMMARY:Boris Kramer: Reduced-order models for data-driven modeling
and uncertainty quantification
DESCRIPTION:Reduced-order models (ROMs) exploit low-dimensional
structures in complex systems. They provide powerful surrogates for
expensive\, many-query applications\, such as control\, uncertainty
quantification\, and design. In this talk\, I present a new
data-driven reduced-order modeling technique and then show how
reduced-order models can enable uncertainty quantification with
significant computational savings.\n\nFirst\, I present a CUR-based
eigensystem realization algorithm for building a data-driven ROM.
The method targets applications with large-scale data by combining a
mathematically sound\, system-theoretic reduced-order modeling
algorithm with modern numerical linear algebra. It works on the
basis of using a state-of-the-art low-rank matrix compression
algorithm to obtain a CUR decomposition of an associated Hankel
matrix. The method only requires loading a small amount of data into
fast memory\, comes with a worst-case error bound\, and enjoys a
number of other computational advantages.\n\nNext\, I demonstrate
the benefits of reduced-order models for an uncertainty
quantification problem\, namely failure probability estimation. I
employ a suite of reduced-order models within a multifidelity
modeling framework to estimate failure probabilities for
expensive-to-evaluate systems. Computing failure probabilities
amounts to evaluating the expectation of low-probability events. I
use importance sampling combined with a suite of surrogates to
design a biasing distribution that can evaluate the original failure
probability with much fewer samples - and hence much fewer
evaluations of the expensive model - while achieving high accuracy.
Numerical examples on a convection-diffusion-reaction equation
illustrate the approach.\n\n
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9abde0@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180205T160000
DTEND;TZID=America/New_York:20180205T170000
CATEGORIES:Math Colloquium
SUMMARY:Li Wang: Front capturing schemes for nonlinear PDEs with a
free boundary limit
DESCRIPTION:Evolution in physical or biological systems often
involves interplay\nbetween nonlinear interaction among the
constituent “particles”\, and\nconvective or diffusive
transport\, which is driven by density\ndependent pressure. When
pressure-density relationship becomes highly\nnonlinear\, the
evolution equation converges to a free boundary\nproblem as a stiff
limit. In terms of numerics\, the nonlinearity and\ndegeneracy bring
great challenges\, and there is lack of standard\nmechanism to
capture the propagation of the front in the limit. In\nthis talk\, I
will introduce a numerical scheme for tumor growth models\nbased on
a prediction-correction reformulation\, which naturally\nconnects to
the free boundary problem in the discrete sense. As
an\nalternative\, I will present a variational method for a class
of\ncontinuity equations (such as Keller-Segel model) using the
gradient\nflow structure\, which has built-in stability\, positivity
preservation\nand energy decreasing property\, and serves as a good
candidate in\ncapturing the stiff pressure limit.
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ac02d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180207T150000
DTEND;TZID=America/New_York:20180207T160000
CATEGORIES:Math Colloquium
SUMMARY:Yoonsang Lee: Multiscale Data Assimilation for
Physcis-constraind Problems
DESCRIPTION:Abstract: Data assimilation quantifies the uncertainties
of a physical system and provides the best statistical estimate by
combining a forecast model and observational data. Ensemble-based
data assimilation methods have proved to be indispensable filtering
tools in atmosphere and ocean systems that are typically high
dimensional nonlinear systems. In operational applications\, due to
the limited computing power in solving the high dimensional
systems\, it is desirable to use a cheap and robust reduced-order
forecast model to increase the number of ensemble for accuracy and
reliability. This talk describes a multiscale data assimilation
framework to incorporate a reduced-order multiscale forecast model
for data assimilation of high dimensional complex systems. A
reduced-order model for two-layer quasi-geostrophic equations\,
which uses stochastic modeling for unresolved scales\, will be
discussed and applied for filtering to capture important features of
geophysical flows such as zonal jets. If time permits\, a
generalization of the ensemble-based methods\, multiscale clustered
particle filters\, will be discussed\, which can capture strongly
non-Gaussian statistics using relatively few particles.
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ac27f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180208T153000
CATEGORIES:Topology Seminar
SUMMARY:David Freund: Multistring Based Matrices (part II)
DESCRIPTION:Flat virtual links can be interpreted as combinatorial
models for curves on surfaces. Using a canonical surface
representation of a chord diagram\, Turaev associated a matrix to a
flat virtual knot that captures invariants of the knot. Our first
talk will focus on the development of this based matrix and its
computation\, justifying that the construction does not naturally
generalize to flat virtual links. In the second talk\, we construct
a generalization of Turaev's based matrix to flat virtual links that
successfully generates analogous invariants.
LOCATION:Kemeny 201
URL:https://www.math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ac4b4@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180209T160000
DTEND;TZID=America/New_York:20180209T170000
CATEGORIES:Math Colloquium
SUMMARY:Daniele Venturi: Dimensionality reduction in stochastic
dynamical systems: from functional differential equations to
data-driven approximations
DESCRIPTION:Infinite-dimensional stochastic dynamical systems arise
naturally in many areas of engineering\, physical sciences and
mathematics. Whether it is a physical system being studied in a
lab\, or an equation being solved on a computer\, the full state of
the system as a point evolving in some phase space is often
intractable to handle in all its complexity. Instead\, it is often
desirable to attempt to reduce such complexity by passing from a
model of the full dynamics to a reduced-order model that involves
only the observables of interest. The dynamics of such observables
may be simpler than that of the entire system\, although the
underlying law by which they evolve in space and time is often quite
complex. In this talk\, I will first review the mathematical theory
that allows us to transform finite- and infinite-dimensional
stochastic dynamical systems into linear transport equations for
suitable functionals of the phase space such as the Hopf
characteristic functional. Subsequently\, I will discuss
state-of-the-art numerical techniques\, in particular numerical
tensor methods\, to approximate the solution to such transport
equations. In the second part of the talk\, I will address the
dimensionality reduction problem\, i.e.\, the problem of deriving
exact evolution equations governing the dynamics of low-dimensional
observables of interest. In particular\, I will present recent
developments on the Mori-Zwanzig approach\, and discuss effective
approximations based on data-driven models\, perturbation series and
operator cumulant expansions.
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ac73d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180212T160000
DTEND;TZID=America/New_York:20180212T170000
CATEGORIES:Math Colloquium
SUMMARY:Naoki Masuda: Collective dynamics on time-varying graphs
DESCRIPTION:An increasing amount of empirical data suggests that
social networks (i.e.\, graphs) on which individuals interact are
more often than not dynamic. While the research in the last two
decades has clarified various aspects of how collective dynamical
processes on graphs behave and how the behavior depends on the
graph\, the time-varying nature of graphs may change the behavior of
such dynamical processes as compared to the same processes on static
graphs. Focusing on diffusive/synchronization processes driven by
the Laplacian matrix and a standard epidemic process model\, I
present my recent work on dynamics on time-varying graphs. We show
that time-varying graphs slow down diffusion and enhance (suppress)
epidemic spreading if the "concurrency" (i.e.\, simultaneity of
edges) is high (low). Mathematical open problems originating from
the present work and future research plans will also be discussed.
LOCATION:008 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ac97b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180214T160000
DTEND;TZID=America/New_York:20180214T170000
CATEGORIES:Math Colloquium
SUMMARY:Yilun Wu: Steady States of Rotating Stars and Galaxies
DESCRIPTION:The equilibrium shape and density distribution of
rotating fluids under self-gravitation is a classical problem in
mathematical physics. Early efforts before the twentieth century
revealed ellipsoidal solutions with constant density. In the
twentieth century\, major progress was made by studying steady
rotating solutions to the compressible Euler-Poisson equations.
Assuming a polytropic equation of state $p=\\rho^\\gamma$\, a
variational method\, pioneered by the work of Auchmuty and Beals\,
proves existence of solutions if $\\gamma>\\frac43$. On the other
hand\, we present in this talk a perturbative method that
establishes a continuous set of solutions for $\\gamma>\\frac65$.
This method opens up new ways to prove existence results for the
Vlasov-Poisson equations and for magnetic stars\, together with
global continuation to large rotation speed.
LOCATION:Carpenter 13
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9acbc1@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180216T160000
DTEND;TZID=America/New_York:20180216T170000
CATEGORIES:Math Colloquium
SUMMARY:Vera Mikyoung Hur: Water waves: breaking\, peaking and
disintegration
DESCRIPTION:Water waves describe the situation where water lies
below a body of air and is acted upon by gravity. Describing what we
may see or feel at the beach or in a boat\, water waves are a
perfect specimen of applied mathematics. They encompass wide-ranging
wave phenomena\, from ripples driven by surface tension to tsunamis
and to rogue waves. The interface between the water and the air is
free and poses profound and subtle difficulties for rigorous
analysis and numerical computation. \n\nI will discuss some recent
developments in the mathematical aspects of water wave phenomena.
Particularly\, \n\n(1) is the solution to the Cauchy problem
regular\, or do singularities form after some time?\n(2) are there
solutions spatially periodic? \n(3) are they dynamically stable?
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9acdff@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180222T153000
CATEGORIES:Topology Seminar
SUMMARY:Vladimir Chernov: Causality and Linking in globally
hyperbolic and causally simple spacetimes. (parts 1 and 2)
DESCRIPTION:In the first part of the talk we recall the notions of a
globally hyperbolic spacetime X and of the associated contact
manifold of light rays N_X. Conjectures on relations of causality in
such spacetimes and of linking in N_X of spheres of light rays
through the two points were first formulated by Low (for topological
linking) and later by Natario and Tod (for Legendrian linking).
These conjectures were solved by Nemirovski and the author. \n\nIn
the second talk we formulate the generalization of the Legendrian
Low conjecture of Natario and Tod (proved by Nemirovski and myself
before) to the case of causally simple spacetimes. We prove a
weakened version of the corresponding statement. \nIn all known
examples\, a causally simple spacetime X can be conformally embedded
into some globally hyperbolic \\tilde X and the space of light rays
N_X is an open submanifold of the space of light rays in N_{\\tilde
X}. If this is always the case\, this provides an approach to
solving the conjectures relating causality and linking in causally
simples spacetimes.
LOCATION:Kemeny 201
URL:https://www.math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ad042@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180223T153000
CATEGORIES:Math Colloquium
SUMMARY:Tony Várilly-Alvarado: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ad233@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180301T153000
CATEGORIES:Topology Seminar
SUMMARY:Vladimir Chernov: Causality and Linking in globally
hyperbolic and causally simple spacetimes. (parts 1 and 2)
DESCRIPTION:In the first part of the talk we recall the notions of a
globally hyperbolic spacetime X and of the associated contact
manifold of light rays N_X. Conjectures on relations of causality in
such spacetimes and of linking in N_X of spheres of light rays
through the two points were first formulated by Low (for topological
linking) and later by Natario and Tod (for Legendrian linking).
These conjectures were solved by Nemirovski and the author. \n\nIn
the second talk we formulate the generalization of the Legendrian
Low conjecture of Natario and Tod (proved by Nemirovski and myself
before) to the case of causally simple spacetimes. We prove a
weakened version of the corresponding statement. \nIn all known
examples\, a causally simple spacetime X can be conformally embedded
into some globally hyperbolic \\tilde X and the space of light rays
N_X is an open submanifold of the space of light rays in N_{\\tilde
X}. If this is always the case\, this provides an approach to
solving the conjectures relating causality and linking in causally
simples spacetimes.
LOCATION:Kemeny 201
URL:https://www.math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ad470@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180302T153000
CATEGORIES:Math Colloquium
SUMMARY:Graduate Open House\, Faculty Talks: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ad646@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:20180218T030201Z
UID:20180217T2202015a88eca9ad76e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180329T153000
CATEGORIES:Topology Seminar
SUMMARY:Slava Krushkal: Engel relations in 4-manifold topology.
DESCRIPTION: I will discuss geometric classification techniques in
the theory of topological 4-manifolds\, surgery and the s-cobordism
theorem\, which are known to hold for a certain class of fundamental
groups and are open in general. Starting with an introduction to the
4-dimensional topological surgery conjecture\, this talk will focus
on recent results on the construction of new universal surgery
models. The construction relies on geometric applications of the
group-theoretic 2-Engel relation. (Joint work with Michael
Freedman)\n
LOCATION:Kemeny 201
URL:https://www.math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ad8a3@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180330T153000
CATEGORIES:Math Colloquium
SUMMARY:Slava Krushkal: The combinatorics of planar triangulations
and quantum topology.
DESCRIPTION:I will discuss how quantum topology gives rise to a
conceptual framework for studying combinatorial properties of planar
triangulations. (No prior knowledge of quantum topology will be
assumed.) In the 1960s W.T. Tutte observed that the value of the
chromatic polynomial of planar triangulations at (golden ratio +1)
obeys a number of remarkable properties. I will present several
extensions of Tutte's results and applications to the structure of
the chromatic and flow polynomials of graphs\, and of the Yamada
polynomial of graphs in 3-space. This talk is based on joint works
with Ian Agol and with Paul Fendley.\n
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ad9d7@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180406T153000
CATEGORIES:Math Colloquium
SUMMARY:Tatiana Roque: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9adafd@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180413T153000
CATEGORIES:Math Colloquium
SUMMARY:Norbert A'Campo: TBA
LOCATION:Kemeny 006
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9adc24@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180418T180000
CATEGORIES:Kemeny Lecture
SUMMARY:Martin Nowak: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9add4a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180419T153000
CATEGORIES:Kemeny Lecture
SUMMARY:Martin Nowak: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ade6f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180420T153000
CATEGORIES:Kemeny Lecture
SUMMARY:Martin Nowak: TBA
LOCATION:Carson L01
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9adf93@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180427T153000
CATEGORIES:Math Colloquium
SUMMARY: Yun Kang: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ae0ba@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:20180218T030201Z
UID:20180217T2202015a88eca9ae1f7@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180511T153000
CATEGORIES:Math Colloquium
SUMMARY:Asher Auel: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ae319@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180518T153000
CATEGORIES:Math Colloquium
SUMMARY:David Roberts: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180218T030201Z
UID:20180217T2202015a88eca9ae43f@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