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X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d96863@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170425T143000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Donghwan Kim: Optimized gradient method for smooth convex
minimization
DESCRIPTION:First-order algorithms are widely used to solve
large-scale optimization problems in various fields such as signal
and image processing\, machine learning\, communications and many
other areas\, since their computational cost per iteration is mildly
dependent on the problem dimension. Among first-order methods\,
Nesterov's fast gradient method (FGM) has been celebrated in various
applications as it is computationally efficient and achieves the
optimal rate O(1/N^2) for decreasing the cost function\, where N
denotes the number of iterations. In search of the best-performing
first-order methods\, this talk presents a new first-order method\,
named optimized gradient method (OGM)\, that is computationally as
efficient as FGM\, and has a worst-case cost function convergence
bound that is twice smaller than that of FGM and that is recently
found to be optimal for large-dimensional smooth convex problems. In
addition\, this talk presents another new algorithm called OGM-OG
(optimized over gradient) by optimizing the step coefficients with
respect to the rate of gradient norm decrease\, whereas we optimized
the original OGM with respect to the cost function decrease.
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d969ab@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170425T160000
CATEGORIES:Geometry and Topology Seminar
SUMMARY:Martin Bridgeman: Simple Length Rigidity for Hitchin
Representations
DESCRIPTION:Abstract: We show that a Hitchin representation is
determined by the spectral radii of the images of simple\,
non-separating closed curves. As a consequence\, we classify
isometries of the intersection function on Hitchin components of
dimension 3 and on the self-dual Hitchin components in all
dimensions.\nThis is joint work with Richard Canary\, François
Labourie\n
LOCATION:307 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d96aac@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170427T163000
CATEGORIES:Math Colloquium
SUMMARY:Theodore Slaman: Three Theorems Between Computability and
Diophantine Approximation
DESCRIPTION:We will describe joint work with Veronica Becher\, Yann
Bugeaud and Jan Reimann in which we construct real numbers so as to
control the properties of their expansions in different integer
bases.
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d96ba6@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170502T133000
DTEND;TZID=America/New_York:20170502T143000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Kuga-Satake varieties and the Hodge conjecture
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d96c97@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170502T144500
DTEND;TZID=America/New_York:20170502T153500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Dianbin Bao: Polynomial Identities between Hecke Eigenforms
DESCRIPTION:Polynomial identities between Hecke Eigenforms can give
relations between their Fourier coefficients\, which often contain
important arithmetic information. Polynomial identities of specific
type have been studied by various authors. In this talk\, we will
show that\, assuming Maeda's conjecture\, solutions to the equation
of the type $X^2=\\sum_{i}a_iY_i$ in terms of Hecke eigenforms for
the full modular group $SL_2(\\mathbb{Z})$ are all forced by
dimension considerations. Our proof uses Galois theory for the
eigenvalues of the Hecke operators acting the space of cusp forms
for $SL_2(\\mathbb{Z})$. We will also talk about the congruence
subgroup case.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d96d97@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170503T190000
CATEGORIES:Kemeny Lecture
SUMMARY:Toshiyuki Kobayashi: "Universal sounds" of anti-de Sitter
manifolds
DESCRIPTION: In musical instruments\, shorter strings produce a
higher pitch than \nlonger strings. The question\, ``Can one hear
the shape of a drum?” (M. \nKac\, 1966)\, shows a typical aspect
of spectral geometry\, which asks the \nrelationship between
analysis (spectrum of Laplacian) and the Riemannian
\ngeometry.\n\nWhat will happen about ``music instrument" beyond
Riemannian geometry? A \nbasic case is Lorentz geometry familiar to
us as the spacetime of \nrelativity theory.\n\nRecently\, a new
phenomenon has been discovered in anti-de Sitter \nmanifolds\,
analog of spheres in Lorentz geometry\, asserting that ``\nuniversal
sounds exist"\, namely\, some eigenvalues of the Laplacian do \nnot
vary under the deformation of geometric structure. \n\nI plan to
explain this strange phenomenon and the methods.
LOCATION:Arvo J Oopik '78 Auditorium
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d96e9a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170504T163000
CATEGORIES:Kemeny Lecture
SUMMARY:Toshiyuki Kobayashi: Local to global — geometry of
symmetric spaces with indefinite-metric.
DESCRIPTION:How local geometric structure affects the global nature
of manifolds?\n\nThe local to global study of geometries was a major
trend of 20th \ncentury geometry\, with remarkable developments
achieved particularly in \nRiemannian geometry. \n\nIn contrast\, in
areas such as Lorentz geometry\, familiar to us as the \nspace-time
of relativity theory\, and more generally in pseudo-Riemannian
\ngeometry of general signature\, surprising little has been known
about \nglobal properties of the geometry until recently even if we
impose a \nlocally homogeneous structure.\n\nI plan to survey this
young topic in geometry such as the existence \nproblem of compact
locally homogeneous manifolds and their deformation \ntheory.
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d96f9a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170505T160000
CATEGORIES:Kemeny Lecture
SUMMARY:Toshiyuki Kobayashi: Analysis on locally pseudo-Riemannian
symmetric spaces
DESCRIPTION:Analysis on Riemann surface\, or more generally\,
locally Riemannian \nsymmetric spaces\, has been developed
extensively in connection with \nautomorphic form theory and
representation theory of reductive groups. \n\nIn the more general
setting where the metric is not positive definite\, \nnew
difficulties arise from analysis\, geometry\, and representation
\ntheory.\n\nI will discuss some new developments and methods in my
lecture.\n
LOCATION:Kemeny 007
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97093@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170509T093000
CATEGORIES:Thesis Defence
SUMMARY:Tim Dwyer: c-Wilf Equivalences of Permutations
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97182@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170509T143000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Toby Sanders: Multiscale Higher Order TV for l1
Regularization and Applications to Particular Inverse Problems
DESCRIPTION:L1 regularization techniques have generated a great deal
of attention with many variants to solve a wide variety of inverse
problems. A key component for their success is that under certain
assumptions\, the solution of minimum L1 norm (a reasonably solvable
problem) is a good approximation to the solution of minimum L0 norm
(an NP hard problem). In this talk\, we demonstrate for L1
regularization approaches\, known as higher order total variation
(HOTV)\, this approximation may yield suboptimal results in some
instances. To overcome this drawback\, we have developed a
multiscale higher order total variation (MHOTV) approach\, which we
argue is closely related to the use of multiscale Daubechies
wavelets. In the talk we will outline all of the necessary
ingredients for efficient and effective implementation of the
design\, and show a number of promising numerical examples with both
real and simulated data.
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97269@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170509T163000
CATEGORIES:Math Colloquium
SUMMARY:Bruce Sagan: The protean chromatic polynomial
DESCRIPTION:Let t be a positive integer and let G be a combinatorial
graph with vertices V and edges E. A proper coloring of G from a
set with t colors is a function c from V to {1\,2\,...\,t} such
that if uv is an edge then c(u) is different from c(v)\, that is\,
the endpoints of an edge must be colored differently. These are the
colorings considered in the famous Four Color Theorem. The
chromatic polynomial of G\, P(G\;t)\, is the number of proper
colorings of G from a set with t colors. It turns out that this is
a polynomial in t with many amazing properties. One can
characterize the degree and coefficients of P(G\;t). There are also
connections with acyclic orientations\, increasing spanning
forests\, hyperplane arrangements\, symmetric functions\, and Chern
classes in algebraic geometry. This talk will survey some of these
results.\n
LOCATION:105 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97375@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170511T130000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Ilker Kocyigit: l1-based optimization methods in array
imaging and Synthetic Aperture Radar (SAR)
DESCRIPTION:In this talk\, we discuss l1 based optimization methods
and their applications to some inverse problems such as the ones
arising from array imaging and SAR. These inverse problems can be
formulated as a sparsity promoting l1 optimization problem. We
discuss the conditions where the solution of these optimization
problems are close to the exact solution and therefore useful. We
present estimates that quantify the resolution of the images
reconstructed by these methods. We then consider the case where data
from "multiple measurements" are available and discuss the
resolution improvements brought by it. We present numerical
simulations of the discussed results.
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97485@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170511T133000
CATEGORIES:Combinatorics Seminar
SUMMARY:Torin Greenwood: RNA Folding and Analytic Combinatorics
DESCRIPTION:The combinatorial arrangement of RNA base pairings
encodes functional information\, but is hard to verify
experimentally. Instead\, discrete optimization methods are
commonly used to predict foldings. One popular approach is to use
stochastic context free grammars (SCFGs) to assign probabilities to
potential structures. In this talk\, we will analyze the
distribution produced by stochastic context free grammars by using
multivariate generating functions and analytic combinatorics. We
will spend half the time discussing results on SCFGs and RNA
folding\, and the other half on developing tools in analytic
combinatorics.
LOCATION:Kemeny 120
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97588@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170511T140000
CATEGORIES:Thesis Defence
SUMMARY:Seth Harris: On-Line Algorithms and Reverse Mathematics
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d9767a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170516T133000
DTEND;TZID=America/New_York:20170516T143000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Kuga-Satake varieties and the Hodge conjecture
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d9776a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170516T143000
DTEND;TZID=America/New_York:20170516T152000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Will Chen: Moduli Interpretations for Noncongruence Modular
Curves
DESCRIPTION:For a finite 2-generated group G\, we define the notion
of a "G-structure" on an elliptic curve. When G is abelian\, we
recover classical congruence level structures. When G is
sufficiently nonabelian\, the resulting moduli spaces are
noncongruence modular curves - that is\, quotients of the upper half
plane by noncongruence subgroups of SL(2\,Z). By a theorem of
Asada\, all noncongruence modular curves can be obtained in this way
as moduli spaces of nonabelian G-structures. As time permits\, we
will discuss connections to the Inverse Galois Problem and the
Unbounded Denominators Conjecture for noncongruence modular forms.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97868@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170516T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Hermann J Eberl: Spatially implicit and spatially explicit
models of bacterial cellulose degradation
DESCRIPTION:Cellulosic ethanol is a biofuel that is produced from
non-edible plants\nand plant materials\, such switchgrass and corn
stover. It can have a\npositive net energy output with a reduction
in green house gas emissions\nthat is drastically lower than that of
corn based ethanol and fossil\nfuels. Clostridium thermocellum is a
bacteria that is able to directly\nconvert cellulose into ethanol
(and other by products). These bacteria\ncolonize cellulose material
and degrade cellulose by "chewing" their way\nthrough their
substrate. In this talk we first present a very simple\,\nspatially
implicit reactor scale model for cellulose degradation
by\nC.thermocellum biofilms. This ODE can be studied with
elementary\ntechniques and quantitatively compared against
experimental data. However\,\nit does not allow for a detailed
description of the spatial effects as the\nbacteria break down their
substratum. To address this\, we formulate then a\nspatially
explicit model\, which consists of a highly
degenerate\ndiffusion-reaction equation for bacterial biomass that
is coupled with an\nordinary differential equation for the growth
limiting substrate. We study\nthis model numerically and
qualitatively compare simulation results\nagainst experimental
observations. The simulations suggest the existence\nof a traveling
wave\; time permitting we investigate those in a simplified\nsetting
in more detail.\nThis is joint work with Gideon Wolfaardt
(Stellenbosch) and Alex\nDumitrache (Oar Ridge National Labs)
LOCATION:Kemeny 004
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97978@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170516T160000
CATEGORIES:Geometry and Topology Seminar
SUMMARY:Patricia Cahn: Linking numbers and Dihedral branched covers
of $S^3$ and $S^4$
DESCRIPTION:We describe an algorithm for computing the linking
numbers between any two rationally null-homologous curves in a
3-fold dihedral cover of $S^3$. This algorithm generalizes an
algorithm of Perko\, who computed the linking numbers between the
two branch curves in the cover. Since every closed oriented
3-manifold is a 3-fold dihedral cover of $S^3$\, our algorithm
computes the linking number between any two rationally
null-homologous curves in any closed oriented 3-manifold. As an
application\, we explain how this algorithm can be used to compute
signatures of dihedral covers of $S^4$ with singular branching
sets\, using a formula of Kjuchukova. (Joint with Alexandra
Kjuchukova).
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97a7c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170518T133000
CATEGORIES:Combinatorics Seminar
SUMMARY:Cheyne Homberger: Prolific Permutations and Permuted
Packings
DESCRIPTION:A permutation of $n$ letters is $k$-prolific if each
$(n−k)$-subset of the letters in its one-line notation forms a
unique pattern. We present a complete characterization of
$k$-prolific permutations for each $k$\, proving that $k$-prolific
permutations of $m$ letters exist for every $m \\geq k^2/2+2k+1$\,
and that none exist of smaller size. Key to these results is a
natural bijection between $k$-prolific permutations and certain
"permuted" packings of diamonds.\n
LOCATION:Kemeny 120
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97b77@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170518T144500
DTEND;TZID=America/New_York:20170518T151500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Alex Levin: Fusion subcategories of an equivariantization
DESCRIPTION:Let $G$ be a finite group and let $\\mathcal A$ be a
fusion category over\n $\\mathbb C$. An action of $G$ on $\\mathcal
A$ is a monoidal functor from $G$ \n to the category of
autoequivalences of $\\mathcal A$\, analogous to a\n
$G$-representation. We parameterize subcategories of the
equivariantization\n $\\mathcal A^G$ by invariant triples consisting
of a $G$-stable\n subcategory of $\\mathcal A$\, a normal subgroup
of $G$\, and an isomorphism of\n actions satisfying a $G$-invariance
condition.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97c72@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170518T151500
DTEND;TZID=America/New_York:20170518T154500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Costel Bontea: Brauer groups of finite tensor categories
DESCRIPTION:This talk is an exposition on Brauer groups. I will
recall the classical definition of the Brauer group and show that
the ingredients needed to define such an object are provided by
finite tensor categories. I will give examples of such categories
and a description of their Brauer groups.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97d69@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170518T163000
CATEGORIES:Math Colloquium
SUMMARY:Reinhard Siegmund-Schultze: Richard von Mises (1883-1953)
– an Austrian Engineer\, pioneer of modern applied mathematics and
probability theory\, and Jewish Refugee to the U.S.
DESCRIPTION:The talk will pursue the extraordinary life\, career and
main results of the pioneer of plasticity theory (1913) and
aerodynamics (1917–1920)\, the co-founder of modern probability
theory (1919) and versatile contributor to mathematical statistics\,
Richard von Mises. His life stretched from his birth in Galicia
(Lemberg) under the Hapsburgs\, over Vienna\, Brünn (Brno)\, to
Prussian occupied Straßburg (1909-1914)\, and to service in the
Austrian Airforce (1914-1918)\, from his leadership of a new
Institute for Applied Mathematics in Berlin (1920-1933)\, to
emigration to Turkey (Istanbul)\, and finally to the U.S. (Harvard
from 1939).\nMathematically the talk focusses on von Mises’
controversial foundation of probability theory on his two axioms for
probabilities as limits of relative frequencies of occurrence of
events. This was also controversially discussed between him and
J.L.Doob in a meeting of the American Institute of Mathematical
Statistics at Dartmouth College\, Hanover\, in September 1940.\nVon
Mises’ various other contributions to numerical analysis\,
positivistic philosophy and literary research on Rainer Maria Rilke
cannot go unnoticed but cannot be discussed in detail either.
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97e7b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170523T143000
DTEND;TZID=America/New_York:20170523T153000
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Asher Auel: Applications of point counting to cubic
fourfolds
DESCRIPTION:One of the striking consequences of the Weil conjectures
is that topological information about an algebraic variety in
characteristic zero can be encoded in the number of points the
variety has over a finite field. I will discuss some applications
of counting points over finite fields to smooth four-dimensional
cubic hypersurfaces in projective space. The motivation is to the
rationality problem for these varieties\, which remains one of the
most challenging unsolved problem in algebraic geometry.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d97f7a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170523T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Xiunan Wang: Global Dynamics of Some Vector-Borne Infectious
Disease Models with Seasonality
DESCRIPTION:Vector-borne infectious diseases such as malaria\,
dengue\, West Nile virus disease\, Zika and Lyme disease remain a
threat to public health and economics. Both vector life cycle and
parasite development are greatly influenced by climatic factors.
Understanding the role of seasonal climate in vector-borne
infectious disease transmission is particularly important in light
of global warming. In this talk\, I will introduce our recent
research on the global dynamics of some vector-borne infectious
disease models. We start with a periodic vector-bias malaria model
with constant extrinsic incubation period (EIP). To explore the
temperature sensitivity of the EIP of malaria parasites\, we also
formulate a functional differential equations model with a periodic
time delay. Moreover\, we incorporate the use of insecticide-treated
bed nets (ITNs) into a climate-based mosquito-stage-structured
malaria model. At last\, we develop a time-delayed Lyme disease
model with seasonality. By using the theory of basic reproduction
ratio R0 and the theory of infinite dimensional dynamical systems\,
we derive R0 and establish a threshold type result on the global
dynamics in terms of R0 for each model. By conducting case studies\,
we propose some practical strategies for the control of the
diseases. This talk is based on joint works with Prof. Xiaoqiang
Zhao.
LOCATION:Kemeny 201
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d98087@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170523T160000
CATEGORIES:Geometry and Topology Seminar
SUMMARY:Mary Sandoval: TBD
LOCATION:307 Kemeny
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d98268@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170525T133000
CATEGORIES:Combinatorics Seminar
SUMMARY:Lou Shapiro: The quadratic formula\, ordered trees\, and
Riordan group involutions
DESCRIPTION:We will give some examples of combinatorial interest
that start with the quadratic formula and lead to interpretations in
terms of augmented ordered trees. For Motzkin numbers with
generating function $m = m(z)$ we have as an involution in the
Riordan group $(m\, (-m + \\sqrt{4m-3m^2}/2))$ as one example.
LOCATION:Kemeny 120
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d985ac@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170525T163000
CATEGORIES:Math Colloquium
SUMMARY:Mike Zabrocki: From Robinson–Schensted–Knuth
correspondence to Schur-Weyl duality
DESCRIPTION:I'll show how a combinatorial algorithm attributed to
work of Robinson (1948)\, Schensted (1961) and Knuth (1969) is used
to give a simple and beautiful proof of enumerative results that
were known much earlier in the 20th century because of the
development of representation theory by the work of Schur. I'll
walk historically through some of the extensions of Schur-Weyl
duality that have developed since its introduction and I will
propose an extension of the RSK algorithm that will explain the
corresponding enumerative results.\n\nThis is joint work with Rosa
Orellana.
LOCATION:007 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20170524T211701Z
UID:20170524T1717015925f84d989c7@math.dartmouth.edu
DTSTART;TZID=America/New_York:20170601T133000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Dieter Armbruster: The economics of need based transfers
DESCRIPTION:Need based transfers (NBT) are actions to compensate
losses after disasters. NBT are given based on shared values and
reflect the understanding of the random nature of disasters.
Codified\, they create an economic system that we call the Economics
of Gift Giving. To be specific\, we study an economic system\,
whereby people that fall below a threshold (e.g. welfare threshold)
will receive help from people that are richer. In a series of
projects focused on agent based simulations\, we have studied
different aspects of this economy: i) We have discussed the impact
of the different nature of economic disasters\, specifically the
correlation between disasters. We show that\, all other things being
equal\, spatially correlated disasters have a lower impact than
temporally correlated disasters. ii) We have studied the impact of
the rules of NBT - if multiple agents are in need\, who is allowed
to ask first and whom do they ask. We find that\, for a short time
horizons\, the optimization is similar to a knapsack problem:
Resources are optimally used when an agent with surplus y supports
an agent that needs y − a with a as small as possible. However\,
if disasters happen frequently and a long term horizon is
considered\, this policy leads to extremely bad long term outcomes
whereas a policy that asks the richest agent first seems to be
optimal. iii) In order to go beyond pure simulation studies\, we are
also using kinetic theory to generate Boltzmann-type equations and
their hydrodynamic limits\, leading to Fokker-Planck type equations
for the time evolution of the wealth distributions. Analyses of
these equations show the emergence of egalitarian or very unequal
wealth distributions depending on different priority rules for NBT.
In addition those policies provide different answers to different
optimization problems like how to reduce the number of agents below
the welfare threshold in shortest time vs. how to maximize the
number of survivors.
LOCATION:Kemeny 201
END:VEVENT
END:VCALENDAR