BEGIN:VCALENDAR
VERSION:2.0
METHOD:PUBLISH
PRODID:-//Mathematics Department//NONSGML mathical.php//EN
X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf22517237@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:20180317T104701Z
UID:20180317T0647015aacf2251752f@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:20180317T104701Z
UID:20180317T0647015aacf22517804@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180223T153000
CATEGORIES:Math Colloquium
SUMMARY:Anthony Varilly-Alvarado: Elliptic curves\, torsion
subgroups\, and uniform bounds for Brauer groups of K3 surfaces
DESCRIPTION:Elliptic curves are smooth plane curves defined by a
homogeneous equation of degree three that come with a marked point.
Results on elliptic integrals going back to Euler show that one can
endow such a curve with an abelian group structure\, making the
marked point the origin of this group. Mordell showed in 1922 that
if E is an elliptic curve defined by an equation over the rational
numbers Q\, then the group of points E(Q) is finitely generated.
Surprisingly\, there are only 15 possibilities for the torsion
subgroup of E(Q). This is a spectacular theorem of Mazur from 1977.
I will explore this circle of ideas for a higher dimensional
analogue of elliptic curves: K3 surfaces. Unlike "abelian
surfaces"\, K3 surfaces have no group structure\, so even
understanding what the analogue of E(Q) should be is tricky. I will
explain how the Brauer group of K3 surface comes to the rescue\,
argue for a conjecture along the lines of Mazur's theorem\, and
explain the impact this would have in our understanding of K3
surfaces.
LOCATION:008 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf22517acb@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180301T143000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Jared Lichtman: The reciprocal sum of primitive nondeficient
numbers
DESCRIPTION:We investigate the reciprocal sum of primitive
nondeficient numbers\, or pnds. In 1934\, Erdos showed that the
reciprocal sum of pnds converges\, which he used to prove that
abundant numbers have a natural density. However no one has
investigated the value of this series. We show the reciprocal sum of
pnds is between 0.348 and 0.380.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf22517d87@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:20180317T104701Z
UID:20180317T0647015aacf22518046@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:20180317T104701Z
UID:20180317T0647015aacf225182b1@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180306T160000
CATEGORIES:Geometry Seminar
SUMMARY:Thomas Brooks: Riemannian 3-Manifolds with Ricci Eigenvalues
(-1\,-1\,0)
DESCRIPTION:3-Manifolds have their curvature tensor determined (up
to an isometry of the tangent plane) by the eigenvalues of the Ricci
tensor. The project to classify manifolds with "constant curvature"
(in the sense of curvature homogeneity) becomes\, in 3 dimensions\,
the study of manifolds with prescribed Ricci eigenvalues (lambda_1\,
lambda_2\, lambda_3). This breaks down into various cases depending
on the signs of the eigenvalues. All of these cases are well-studied
locally. The (-1\,-1\,0) case is particularly interesting in the
global case\, which is what we will consider. In particular\, we
will show that such manifolds have interesting geometric structure
and must have a free fundamental group\, which classifies their
topology since their universal cover is diffeomorphic to R^3.
LOCATION:307 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf2251855b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180313T160000
CATEGORIES:Geometry Seminar
SUMMARY:Joe Hoisington: The Complex Projective Chern-Lashof Theorems
DESCRIPTION:Abstract: We will show that the sum of the Betti numbers
of a complex projective manifold can be bounded above in terms of
its total curvature\, and characterize those manifolds whose total
curvature is small\, and is minimal. These results extend the
classic theorems of Chern and Lashof to the setting of complex
projective space.
LOCATION:307 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf225187e0@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180327T160000
CATEGORIES:Geometry Seminar
SUMMARY:Regular trees in random regular graphs
DESCRIPTION:We investigate the size of the embedded regular tree
rooted at a vertex in a $d$ regular random graph. We show that
almost always\, the size of this tree will be $\\frac{1}{2}\\log
n$\, where $n$ is the number of vertices in the graph. We use this
to give an asymptotic estimate for Gauss' Hypergeometric Function.
LOCATION:307 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf22518a63@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:20180317T104701Z
UID:20180317T0647015aacf22518d00@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:20180317T104701Z
UID:20180317T0647015aacf22518e1e@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:20180317T104701Z
UID:20180317T0647015aacf22518f3c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180406T153000
CATEGORIES:Math Colloquium
SUMMARY:Adrianna Gillman: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf22519047@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:20180317T104701Z
UID:20180317T0647015aacf22519152@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180418T180000
CATEGORIES:Kemeny Lecture
SUMMARY:Martin Nowak: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf2251925c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180419T153000
CATEGORIES:Kemeny Lecture
SUMMARY:Martin Nowak: TBA
LOCATION:Kemeny 008
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf22519366@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180420T153000
CATEGORIES:Kemeny Lecture
SUMMARY:Martin Nowak: TBA
LOCATION:Carson L01
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf22519471@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180427T153000
CATEGORIES:Math Colloquium
SUMMARY: Yun Kang: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf2251957c@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:20180317T104701Z
UID:20180317T0647015aacf225196a2@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180511T153000
CATEGORIES:Math Colloquium
SUMMARY:Asher Auel: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf225197ad@math.dartmouth.edu
DTSTART;TZID=America/New_York:20180518T153000
CATEGORIES:Math Colloquium
SUMMARY:David Roberts: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20180317T104701Z
UID:20180317T0647015aacf225198b8@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