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PRODID:-//Mathematics Department//NONSGML mathical.php//EN
X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c944219134f0@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190219T130000
CATEGORIES:Combinatorics Seminar
SUMMARY:Mike Zabrocki: Multiset tableaux as a model for the
multivariate polynomial ring as an $S_n$ module
DESCRIPTION:Let the symmetric group $S_n$ act on a set of n
variables $x_1\, x_2\, ...\, x_n$ by permutation of the indices and
then create the polynomial ring in k different copies of of those n
variables. This is again a space acted on by the symmetric group
and we can ask how it decomposes into irreducible submodules. The
answer is that for each partition $\\lambda$\, the multiplicity of
the irreducible of that shape is equal to the number of multiset
tableaux of shape $\\lambda$.\n\nI'll explain how the mutlivariate
polynomial ring arises in a number different algebraic and
representation theoretic constructions: from diagonal harmonics to
(multiset) partition algebras and how they relate to this
combinatorial model.
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913569@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190221T143000
CATEGORIES:Topology Seminar
SUMMARY:C.-M. Michael Wong: Some developments in the Legendrian GRID
invariants
DESCRIPTION:For Legendrian and transverse links in the 3-sphere\,
Ozsvath\, Szabo\, and Thurston defined combinatorial invariants that
reside in grid homology. Known as the GRID invariants\, they are
effective in distinguishing some transverse knots that have the same
classical invariants. In this talk\, we describe some recent
developments: First\, we show that the GRID invariants obstruct
decomposable Lagrangian cobordisms\; second\, we outline a
computable generalization via cyclic branched covers. The first
result is joint with John Baldwin and Tye Lidman\, and the second
with Shea Vela-Vick.
LOCATION:201 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c944219135bc@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190226T130000
CATEGORIES:Combinatorics Seminar
SUMMARY:Laura Colmenarejo: Signatures of paths transformed by
polynomial maps
DESCRIPTION:In this talk\, I would like to characterize the
signature of piecewise continuously differentiable paths transformed
by a polynomial map in terms of the signature of the original path.
For this aim\, I will define recursively an algebra homomorphism
between two shuffle algebras on words. This homomorphism does not
depend on the path and behaves well with respect to composition and
homogeneous maps. It will allow us to describe the relation between
the coefficients of the signature of a piecewise continuously
differentiable path transformed by a polynomial map and the
coefficients of the signature of the initial path.\nThis is joint
work with Rosa Preiß.
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c9442191360c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190227T160000
CATEGORIES:Math Colloquium
SUMMARY:Sam Stechmann: Clouds\, climate\, and extreme precipitation
events: Asymptotics and stochastic models
DESCRIPTION:Clouds and precipitation are among the most challenging
aspects of weather and climate prediction. Moreover\, our
mathematical and physical understanding of clouds is far behind our
understanding of a "dry" atmosphere where water vapor is neglected.
In this talk\, in working toward overcoming these challenges\, we
present new results on clouds and precipitation from two
perspectives: first\, in terms of the partial differential equations
(PDEs) for atmospheric fluid dynamics\, and second\, in terms of
stochastic models. A new asymptotic limit will be described\, and it
leads to new PDEs for a precipitating version of the
quasi-geostrophic equations\, now including phase changes of water.
Also\, a new energy will be presented for an atmosphere with phase
changes\, and it provides a generalization of the quadratic energy
of a "dry" atmosphere. Finally\, it will be shown that the
statistics of clouds and precipitation can be described by
stochastic differential equations and stochastic PDEs. As one
application\, it will be shown that\, under global warming\, the
most significant change in precipitation statistics is seen in the
largest events -- which become even larger and more probable -- and
the distribution of event sizes conforms to the stochastic models.
Such changes have substantial societal consequences\, and they can
also be quantified in terms of risk ratio.
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913666@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190228T130000
CATEGORIES:Topology Seminar
SUMMARY:Joshua Sussan: p-DG braid group actions
DESCRIPTION:p-DG theory is a useful framework for categorifying
quantum groups and their representations at prime roots of unity.
We review this structure and then apply this machinery in the
context of a specific categorical braid group action.
LOCATION:Kemeny 120
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c944219136af@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190228T143000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Daniel Smertnig: On noncommutative rational Pólya series
DESCRIPTION:A univariate rational series over a field K is a
(formal) power series\nrepresenting a rational function at 0.\nIt is
called a Pólya series if its coefficients are contained in
a\nfinitely generated multiplicative subgroup of K^\\times.\nPólya
(in 1921) and Bézivin (in 1987\, positive characteristic)
showed\nthat every Pólya series can be written as a polynomial plus
a finite\nnumber of "merges" of geometric series.\n\nRational series
can more generally be defined for multivariate formal\npower series
in noncommuting variables. We discuss an extension of
the\ncharacterization of Pólya series to this setting\, confirming
a 1979\nconjecture of Reutenauer. The proof uses S-unit
equations.\n\nThis is joint work with Jason Bell.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c944219136ff@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190305T130000
CATEGORIES:Combinatorics Seminar
SUMMARY:John Wilmes: Automorphisms of primitive coherent
configurations
DESCRIPTION:Coherent configurations are fundamental objects of study
in algebraic combinatorics\, closely\nconnected to the theory of
permutation groups\, block designs\, and the Graph Isomorphism
problem.\nIn joint work with Xiaorui Sun\, we study the asymptotic
properties of primitive coherent\nconfigurations (PCCs) as the
number of vertices grows. Among other structural discoveries\, we
find\n``asymptotically uniform clique geometries'' in PCCs\, along
with bounds on diameter and vertex\nexpansion. These new tools allow
us to classify those PCCs with the largest automorphism groups.
We\nshow that only the Johnson and Hamming schemes have more than
exp(\\tilde{O}(n^{1/3})) automorphisms\n(where n is the number of
vertices and the tilde hides polylogarithmic factors). As a
corollary\, we\ngive an elementary proof of a classification of
primitive permutation groups of degree n and order\ngreater than
exp(\\tilde{O}(n^{1/3}))\; this corollary was previously known only
through the\nclassification of finite simple groups.
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913755@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190305T153000
DTEND;TZID=America/New_York:20190305T163000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Arnold Song: High resolution sea ice modeling with the
discrete element method
DESCRIPTION:As the seasonal ice conditions trend to smaller minimum
extents and thinner ice\, maritime activity in the Arctic has and
will continue to increase. Accurate ice forecasts will be crucial
for supporting operations and planning in ice-laden waters. Our long
range goal is to develop a high resolution sea ice forecast model to
improve maritime domain awareness and support operations in the
Arctic basin. I will give an overview of sea ice modeling
approaches and challenges\, then present our sea ice model that is
based upon the discrete element method (DEM). The DEM is a particle
method that enables us to explicitly model the fracture and ridging
processes\, thus provides some advantages over the continuum based
models. I will present details of our modeling framework\, several
application examples\, and areas for future work.
LOCATION:Haldeman 252
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c944219137a7@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190307T143000
CATEGORIES:Topology Seminar
SUMMARY:Akram Alishahi: Braid invariant related to knot Floer
homology and Khovanov homology
DESCRIPTION:Khovanov homology and knot Floer homology are two knot
invariants that were defined around the same time\, and despite
their different constructions\, share many formal similarities.
After reviewing the construction of Khovanov homology and some of
these similarities\, I will sketch the definition of an algebraic
braid invariant which is closely related to both Khovanov homology
and the refinement of knot Floer homology into tangle invariants.
This is a joint work with Nathan Dowlin.
LOCATION:201 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c944219137f3@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190308T153000
CATEGORIES:Math Colloquium
SUMMARY:Penny Haxell: Algorithms for independent transversals vs.
small dominating sets
DESCRIPTION:An independent transversal (IT) in a vertex-partitioned
graph\nG is an independent set in G consisting of one vertex in
each\npartition class. There are\nseveral known criteria that
guarantee the\nexistence of an IT\, of the following general form:
the graph\nG has an IT unless the subgraph G_S of G\, induced by the
union of some\nsubset S of vertex classes\, has a small dominating
set. These\ncriteria have been used over the years to solve many
combinatorial problems. \n\nThe known proofs of these IT theorems do
not give efficient\nalgorithms\nfor actually finding an IT or a
subset S of classes such that G_S\nhas a small dominating set. Here
we present appropriate weakenings of\nsuch results that do have
effective proofs. These result in\nalgorithmic versions of many of
the original applications of IT\ntheorems. We will discuss a few of
these here\, including hitting sets\nfor maximum cliques\, circular
edge colouring of bridgeless cubic\ngraphs\, and hypergraph matching
problems. \n
LOCATION:Haldmean 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913845@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190326T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Michael Nicholson: Competing evolutionary paths in growing
populations with applications to multidrug resistance
DESCRIPTION:Investigating the emergence of a particular cell type is
a recurring theme in models of growing cellular populations. The
evolution of resistance to therapy is a classic example. Common
questions are: when does the cell type first occur\, and via which
sequence of steps is it most likely to emerge? For growing
populations\, these questions can be formulated in a general
framework of branching processes spreading through a graph from a
root to a target vertex. Cells have a particular fitness value on
each vertex and can transition along edges at specific rates.
Vertices represents cell states\, say genotypes or physical
locations\, while possible transitions are acquiring a mutation or
cell migration. In this talk we will focus on the setting where
cells at the root vertex have the highest fitness and transition
rates are small. Simple formulas will be presented for the time to
reach the target vertex and for the probability that it is reached
along a given path in the graph. The applicability our of results to
understanding the emergence of drug resistance will be discussed.\n
LOCATION:Haldeman 252
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c9442191389f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190328T143000
CATEGORIES:Topology Seminar
SUMMARY:Artem Kotelskiy: TBA
LOCATION:201 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c944219138e1@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190402T140000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Kit Newton: Optical tomography in the optically thick regime
in the Bayesian framework
DESCRIPTION:Optical tomographic imaging is a technique for inferring
the properties of \nbiological tissue via measurements of the
incoming and outgoing light intensity\; it may be used as a medical
imaging methodology. Mathematically\, light propagation is modeled
by the radiative transfer equation (RTE)\, and optical tomography
amounts to reconstructing the scattering and the absorption
coefficients in the RTE from boundary measurements. We study this
problem in the Bayesian framework\, focusing on the strong
scattering regime. In this regime the forward RTE is close to the
diffusion equation (DE). We study the RTE in the asymptotic regime
where the forward problem approaches the DE\, and prove convergence
of the inverse RTE to the inverse DE in both nonlinear and linear
settings. Convergence is proved by studying the distance between the
two posterior distributions using the Hellinger metric and
Kullback-Leibler divergence.
LOCATION:Haldeman 252
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913933@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190405T153000
CATEGORIES:Math Colloquium
SUMMARY:Robert Low: Space-time topology: choices and consequences
DESCRIPTION:I will review some of the possible choices of topology
on a Lorentz manifold and their well-known properties. Following
this\, I will take a more detailed look at some of the advantages
and disadvantages of the main choices. Finally (depending on
progress over the next few months) I may spend some time examining
the special case of 2 dimensional Minkowski space.
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c9442191397d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190405T170000
CATEGORIES:Topology Seminar
SUMMARY:Robert Low: Causal structure and spaces of null geodesics
DESCRIPTION:I will review Lorentz manifolds as a model of
space-time\, and how the important notion of causal structure arises
in this context. Then\, observing the fundamental nature of null
geodesics to this structure\, I will describe the space of null
geodesics and the natural topological and geometric structures it
carries. Finally\, I will consider how aspects of the causal
structure of the original space-time is encoded in this space of
null geodesics\, culminating in the notion of Legendrian linking of
those submanifolds in the space of null geodesics representing
points of the space-time.
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c944219139c9@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190412T153000
CATEGORIES:Math Colloquium
SUMMARY:Alexander Dranishnikov: TBA
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913a0b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190418T143000
CATEGORIES:Topology Seminar
SUMMARY:Steven Boyer: TBA
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913a4c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190418T160000
CATEGORIES:Math Colloquium
SUMMARY:Steven Boyer: TBA
LOCATION:Haldeman 41
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913a8e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190502T160000
CATEGORIES:Math Colloquium
SUMMARY:Dick Canary: TBA
LOCATION:Haldeman 41
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913acf@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190516T160000
CATEGORIES:Math Colloquium
SUMMARY:Jean-Francois Lafont: Totally geodesic submanifolds in
hyperbolic manifolds
DESCRIPTION:I will discuss the various constructions of finite
volume hyperbolic manifolds\, with an emphasis on the arithmetic vs.
non-arithmetic dichotomy. I will then explain why certain
non-arithmetic hyperbolic manifolds can only contain finitely many
closed immersed totally geodesic codimension one submanifolds (joint
with D. Fisher\, N. Miller\, and M. Stover). This gives the first
positive answer to a question raised independently by Alan Reid and
by Curt McMullen.
LOCATION:Haldeman 41
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913b1a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190523T160000
CATEGORIES:Math Colloquium
SUMMARY:Peter Woit: TBA
LOCATION:Haldeman 41
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20190322T020201Z
UID:20190321T2202015c94421913b5b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20190524T153000
CATEGORIES:Math Colloquium
SUMMARY:Semyon Dyatlov: TBA
LOCATION:Kemeny 007
END:VEVENT
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