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PRODID:-//Mathematics Department//NONSGML mathical.php//EN
X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d61fe6@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230223T110000
DTEND;TZID=America/New_York:20230223T120000
CATEGORIES:Functional Analysis Seminar
SUMMARY:Kameron McCombs: f-Continuous operators on $B(L^2M)$ and the
families index
DESCRIPTION:In 1971 Atiyah and Singer created an index theory for
families of elliptic operators\, where a family of elliptic
operators parametrized by a compact manifold $Y$ is associated with
an element of the K-theory of $Y$. Crucial to this result was the
definition of a continuous family of Fredholm operators indexed by
$Y$. In this talk\, we will define a new class of operators on
$B(L^2M)$ for a compact manifold $M$ called f-continuous operators
in order to derive a new way to define a continuous family of
Fredholm operators. This will allow us to more easily calculate the
index of a continuous family of Fredholm operators.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6203e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230228T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:Maria Dascalu: Tropicalization of graph profiles for some
classes of trees
DESCRIPTION:Many important problems in extremal combinatorics can be
stated as inequalities of graph homomorphism numbers. For a fixed
collection of graphs U\, the tropicalization of the graph profile of
U essentially records all valid binomial inequalities involving
graph homomorphism numbers for graphs in U.\n\nBuilding upon ideas
and techniques described by Blekherman and Raymond in 2021\, I
present progress toward finding the tropicalization for some classes
of trees.
LOCATION:Kemeny 307
URL:https://math.dartmouth.edu/~comb/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62078@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230228T142500
DTEND;TZID=America/New_York:20230228T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Junehyuk Jung: The arithmetic of totally geodesic surfaces
on Bianchi orbifolds
DESCRIPTION:Bianchi subgroups are cofinite non-cocompact lattices in
$PSL_2(C)$\, defined by $\\Gamma_d = PSL_2(O_d)$\, where $O_d$ is
the ring of integers of the imaginary quadratic field of
discriminant $-d$. The Bianchi orbifold $\\Omega_d = \\Gamma_d
\\backslash H^3$ is known to contain infinitely many immersed
totally geodesic surfaces\, which can be identified with integral
binary hermitian forms over $O_d$. In this talk\, I will introduce
basic geometric problems regarding immersed totally geodesic
surfaces\, and explain how some of these problems could be
understood using number theoretic ideas. This talk is partially
based on joint work with Alan Reid.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d620c7@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230228T143000
DTEND;TZID=America/New_York:20230228T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Tyler Maunu: New Approaches to Positive Semidefinite Matrix
Recovery
DESCRIPTION:We study algorithms that exploit constraint geometry to
solve the matrix recovery problem over positive semidefinite
matrices. We consider the problem in two separate settings. In the
first setting\, we study low-rank matrix recovery. We develop a new
connection between this problem and the Wasserstein barycenter
problem. Through this connection\, we derive geometric first-order
methods that have convergence guarantees in Bures-Wasserstein
distance. In the second setting\, we study the problem of graph
Laplacian matrix recovery. In this setting\, we derive first-order
methods that exploit the constraint set geometry that again are
guaranteed to efficiently recover the underlying matrix. Experiments
on simulated and real data demonstrate the advantages of our new
methodologies over existing methods.
LOCATION:Kemeny 307
URL:https://math.dartmouth.edu/~acms
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6210c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230302T110000
DTEND;TZID=America/New_York:20230302T120000
CATEGORIES:Functional Analysis Seminar
SUMMARY:John D. Trout: The algebraic structure of general mechanics
(part 2)
DESCRIPTION:Using ideas of Strocchi\, Iochum & Loupias\, Faddeev &
Yakubovskii\, and Alfsen & Shultz\, we give an operational
derivation of the Jordan-Banach algebra structure of the kinematics
of (bounded) observables in a general theory of mechanics (classical
and quantum) from a set of four axiomatic assumptions. The central
tools are the duality pairing between states and observables given
by expectation values\, the operational association of these
expectation values with measurement outcomes in experiments and
polynomial rescalings of observable measuring devices. This is joint
work with Shadi Ali Ahmad ‘22.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~funct-an/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62144@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230307T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:Greg Warrington: Multivariate chromatic polynomials for
rooted graphs
DESCRIPTION:Abstract: Richard Stanley defined the chromatic
symmetric function X_G of a graph G and conjectured that trees T and
U are isomorphic if and only if X_T=X_U. In this talk we introduce a
variation of the chromatic symmetric function for rooted graphs\,
where we require the root vertex to have a specified color. Our
polynomials satisfy the analogue of Stanley's conjecture: two rooted
trees are isomorphic as rooted graphs if and only if their rooted
chromatic polynomials are equal. This can be proved via an
application of Eisenstein's Criterion and unique factorization or
directly via algebraic transformations to pointed chromatic
functions and rooted U-polynomials. In addition to sketching these
arguments\, we explore some of the combinatorial properties of these
polynomials. This talk is based on joint work with Nick Loehr.
LOCATION:Kemeny 307
URL:https://math.dartmouth.edu/~comb/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6217d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230307T142500
DTEND;TZID=America/New_York:20230307T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Holly Paige Chaos: Torsion for CM Elliptic Curves Defined
Over Number Fields of Degree $2p$
DESCRIPTION:Let $E$ be an elliptic curve defined over a number field
$F$. By the Mordell-Weil theorem we know that the points of $E$ with
coordinates in $F$ can be given the structure of a finitely
generated abelian group. We will focus on the subgroups of points
with finite order. For a given prime $p > 3$ and an elliptic curve
$E$ defined over a number field of degree $2p$\, we would like to
know exactly what torsion subgroups arise. Before discussing recent
progress on this query\, specifically in the case of elliptic curves
with complex multiplication (CM)\, I will provide a brief overview
on elliptic curves as well as outline some significant classical
results.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d621b5@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230307T143000
DTEND;TZID=America/New_York:20230307T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Soroush Vosoughi: Unsupervised Structural Graph
Representation Learning
DESCRIPTION:Abstract:\nIn this presentation\, I will discuss our
lab’s research on unsupervised structural graph representation
learning. It is essential to differentiate between representations
that capture structural roles and those that capture local
information in graphs (microscopic representations\, such as
node2vec). Structural embeddings can capture the global roles of
nodes\, edges\, and subgraphs in a graph. This means that nodes that
perform similar functions in a graph will have similar vector
representations\, regardless of their distance from each other in
the graph. Our framework's core feature is its capability for
unsupervised learning of versatile and universal representations
that capture the structural roles of nodes\, edges\, and subgraphs
(communities) in a dynamic attributed graph. These general-purpose
representations eliminate the need for time-consuming and biased
feature engineering and are suitable for both unsupervised and
supervised tasks\, including clustering and classification.
Finally\, I will discuss the potential of these general-purpose
representations for supervised and unsupervised learning in
downstream tasks on various types of graphs\, such as social and
financial networks. \n\n
LOCATION:Kemeny 307
URL:https://math.dartmouth.edu/~acms
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62202@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230308T110000
DTEND;TZID=America/New_York:20230308T130000
CATEGORIES:Special Event
SUMMARY:Directed Reading Program Poster Session
DESCRIPTION:Come hear about all the interesting math that students
have been learning this term as part of the Directed Reading
Program! Topics include matrix groups\, category theory\, Bayesian
inference\, mathematical bioeconomics\, magical mathematics\, and
more! Everyone is welcome. Stop by and see what students have been
reading about this term! Learn more:
https://math.dartmouth.edu/~drp/
LOCATION:Kemeny 300
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62235@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230309T151500
CATEGORIES:Math Colloquium
SUMMARY:Eitan Tadmor: Swarm-Based Gradient Descent Method for
Non-Convex Optimization
DESCRIPTION:We introduce a new swarm-based gradient descent (SBGD)
method for non-convex optimization.\n\nThe swarm consists of
agents\, identified with positions x and masses m. \n\nThe key to
their dynamics is transition of mass from high to lower ground\, and
a time stepping protocol\, h(x\,m)\, which decreases with m.\n\nThe
interplay between positions and masses leads to dynamic distinction
between `leaders’ and `explorers’. Heavier agents lead the swarm
near local minima with small time steps.\n\nLighter agents\, which
explore the landscape by taking large time steps\, are expected to
encounter improved position for the swarm\;\n\nif they do\, then
they assume the role of heavy swarm leaders and so
on.\n\nConvergence analysis and numerical simulations demonstrate
the effectiveness of SBGD method as a global optimizer. \n\n
LOCATION:105 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6226e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230314T100000
DTEND;TZID=America/New_York:20230314T170000
CATEGORIES:Special Event
SUMMARY:The pies say it all: Pi Day
DESCRIPTION:Stop by the grad and faculty lounge for a piece of yummy
pie on Pi day.
LOCATION:Grad and Faculty Lounges
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d622a1@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230314T143000
DTEND;TZID=America/New_York:20230314T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Ben Allen: Natural selection for collective action
DESCRIPTION:Collective action -- behavior that arises from the
combined actions of multiple individuals -- is observed across
living beings. The question of how and why collective action evolves
has profound implications for behavioral ecology\,
multicellularity\, and human society. Collective action is
challenging to model mathematically\, due to nonlinear fitness
effects and the consequences of spatial\, group\, and/or family
relationships. We derive a simple condition for collective action to
be favored by natural selection. A collective's effect on the
fitness of each individual is weighted by the relatedness between
them\, using a new measure of collective relatedness. If selection
is weak\, this condition can be evaluated using coalescent theory.
More generally\, our result applies to any synergistic social
behavior\, in spatial\, group\, and/or family-structured
populations. We use this result to obtain conditions for the
evolution of collective help among diploid siblings\, subcommunities
of a network\, and hyperedges of a hypergraph. We also obtain a
condition for which of two strategies is favored in a game between
siblings\, cousins\, or other relatives. Our work provides a
rigorous basis for extending the notion of ``actor"\, in the study
of social behavior\, from individuals to collectives.
LOCATION:Kemeny 307
URL:https://math.dartmouth.edu/~acms
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d622e7@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230328T142500
DTEND;TZID=America/New_York:20230328T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Kristin Devleming: Moduli of log Calabi Yau pairs
DESCRIPTION:I will discuss joint work with Kenny Ascher\, Dori
Bejleri\, Harold Blum\, Giovanni Inchiostro\, Yuchen Liu\, and
Xiaowei Wang on construction of moduli stacks and moduli spaces of
log Calabi Yau pairs that can be realized as slc log Fano pairs with
complements. Unlike moduli of canonically polarized varieties
(respectively\, Fano varieties) in which the moduli stack of KSB
stable (respectively\, K semistable) objects is bounded for fixed
volume\, dimension\, the objects here form unbounded families.
Despite this unbounded behavior\, in the case of plane curve pairs
(P2\, C)\, we construct a projective good moduli space
parameterizing S-equivalence classes of these slc Fanos with
complements.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6231e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230328T143000
DTEND;TZID=America/New_York:20230328T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Matt Jones: Nash Equilibrium in a Low-Information Vote
Trading Game
DESCRIPTION:Groups are often asked to make decisions about a wide
range of issues. If each issue is decided by a separate vote\,
voters are incentivized to give away their votes on issues they deem
unimportant in exchange for additional votes on the most critical
issues. This scenario leads to a vote trading game in which voters
must decide which trades to offer to maximize their final utility.
We begin with a discrete model of voter utility and then move to the
more general continuous model. In both cases\, we analyze the game
by studying their Nash equilibria and evaluating how the underlying
utility distribution affects player behavior.
LOCATION:Kemeny 307
URL:https://math.dartmouth.edu/~acms
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62354@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230404T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:J.E. Paguyo: TBD
LOCATION:Zoom
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62383@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230404T140000
DTEND;TZID=America/New_York:20230404T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Eugene Santos. Jr: TBA
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d623b5@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230406T151500
CATEGORIES:Math Colloquium
SUMMARY:Patricia Cahn: Branched Covers and Knot Theory in
Dimensions 3 and 4
DESCRIPTION: There are two fundamental classification problems in
geometric topology: first to classify manifolds up to equivalence
(e.g.\, diffeomorphism)\, and second\, to classify the knotted
objects they contain. Branched covers are a powerful tool for
studying both of these problems. In this talk\, we will discuss
the problem of realizing all manifolds of a given dimension n as
covers of the n-dimensional sphere in dimensions 3 and 4\, and give
a new classification theorem in dimension 4. We will then give new
constructions of branched covers in dimension 4\, and use this to
distinguish knotted surfaces in the 4-dimensional sphere.
LOCATION:004 Kemeny Hall
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d623ec@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230411T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6241a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230411T140000
DTEND;TZID=America/New_York:20230411T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Tyler Maunu: New Approaches to Positive Semidefinite Matrix
Recovery
DESCRIPTION:We study algorithms that exploit constraint geometry to
solve the matrix recovery problem over positive semidefinite
matrices. We consider the problem in two separate settings. In the
first setting\, we study low-rank matrix recovery. We develop a new
connection between this problem and the Wasserstein barycenter
problem. Through this connection\, we derive geometric first-order
methods that have convergence guarantees in Bures-Wasserstein
distance. In the second setting\, we study the problem of graph
Laplacian matrix recovery. In this setting\, we derive first-order
methods that exploit the constraint set geometry that again are
guaranteed to efficiently recover the underlying matrix. Experiments
on simulated and real data demonstrate the advantages of our new
methodologies over existing methods.
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62451@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230411T142500
DTEND;TZID=America/New_York:20230411T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Juliette Bruce: TBD
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62481@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230413T100000
CATEGORIES:Topology Seminar
SUMMARY:Liam Kahmeyer: A homotopy invariant of image simple fold
maps to oriented surfaces
DESCRIPTION:In 2019\, Osamu Saeki showed that for two homotopic
generic fold maps $f\,g:S^3 \\rightarrow S^2$ with respective
singular sets $\\Sigma(f)$ and $\\Sigma(g)$ whose respective images
$f(\\Sigma)$ and $g(\\Sigma)$ are smoothly embedded\, the number of
components of the singular sets\, respectively denoted
$\\#|\\Sigma(f)|$ and $\\#|\\Sigma(g)|$\, need not have the same
parity. From Saeki's result\, a natural question arises: For generic
fold maps $f:M \\rightarrow N$ of a smooth manifold $M$ of dimension
$m \\geq 2$ to an oriented surface $N$ of finite genus with
$f(\\Sigma)$ smoothly embedded\, under what conditions (if any) is
$\\#|\\Sigma(f)|$ a $\\Z/2$-homotopy invariant? The goal of this
talk is to explore this question. Namely\, I will show that for
smooth generic fold maps $f:M \\rightarrow N$ of a smooth closed
oriented manifold $M$ of dimension $m\\geq 2$ to an oriented surface
$N$ of finite genus with $f(\\Sigma)$ smoothly embedded\,
$\\#|\\Sigma(f)|$ is a modulo two homotopy invariant provided one of
the following conditions is satisfied: (a) $\\textrm{dim}(M) = 2q$
for $ q \\geq 1$\, (b) the singular set of the homotopy is an
orientable manifold\, or (c) the image of the singular set of the
homotopy does not have triple self-intersection points.\n\n
LOCATION:Zoom ID 870 912 2782\, ask Vladimir Chernov for the
Password.
URL:https://math.dartmouth.edu/~topology
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d624c0@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230417T180000
CATEGORIES:⋆ Kemeny Lecture ⋆
SUMMARY:Alex Lubotzky: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/kemeny-lectures/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d624f0@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230418T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6251f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230418T140000
DTEND;TZID=America/New_York:20230418T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:TBA: TBA
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6254e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230418T151500
CATEGORIES:⋆ Kemeny Lecture ⋆
SUMMARY:Alex Lubotzky: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/kemeny-lectures/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6257d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230419T151500
CATEGORIES:⋆ Kemeny Lecture ⋆
SUMMARY:Alex Lubotzky: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/kemeny-lectures/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d625ac@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230420T151500
CATEGORIES:Math Colloquium
SUMMARY:Daniela Calvetti: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/calendar/agenda-colloq.php
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d625db@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230425T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62608@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230425T140000
DTEND;TZID=America/New_York:20230425T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Soroush Vosoughi: Unsupervised Structural Graph
Representation Learning
DESCRIPTION:We study algorithms that exploit constraint geometry to
solve the matrix recovery problem over positive semidefinite
matrices. We consider the problem in two separate settings. In the
first setting\, we study low-rank matrix recovery. We develop a new
connection between this problem and the Wasserstein barycenter
problem. Through this connection\, we derive geometric first-order
methods that have convergence guarantees in Bures-Wasserstein
distance. In the second setting\, we study the problem of graph
Laplacian matrix recovery. In this setting\, we derive first-order
methods that exploit the constraint set geometry that again are
guaranteed to efficiently recover the underlying matrix. Experiments
on simulated and real data demonstrate the advantages of our new
methodologies over existing methods.
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6263f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230427T100000
CATEGORIES:Topology Seminar
SUMMARY:Sergey Maksimenko: Homotopy types of diffeomorphisms groups
of simplest Morse-Bott foliations on lens spaces
DESCRIPTION:Let $\\mathcal{F}$ the Morse-Bott foliation on the solid
torus $T =\nS^1\\times D^2$ into $2$-tori parallel to the boundary
and one singular\ncircle $S^1\\times 0$.\nA diffeomorphism $h:T \\to
T$ is called foliated (resp.\\ leaf preserving)\nif for each leaf
$\\omega\\in\\mathcal{F}$ its image $h(\\omega)$ is also\nleaf of
$\\mathcal{F}$ (resp. $h(\\omega)=\\omega$).\nGluing two copies of
$T$ by some diffeomorphism between their\nboundaries\, one gets a
lens space $L_{p\,q}$ with a Morse-Bott
foliation\n$\\mathcal{F}_{p\,q}$ obtained from $\\mathcal{F}$ on
each copy of $T$.\nDenote by $\\mathcal{D}_{fol}(T\,\\partial T)$
and\n$\\mathcal{D}_{lp}(T\,\\partial T)$ respectively the groups of
foliated and\nleaf preserving diffeomorphisms of $T$ fixed on
$\\partial T$.\nSimilarly\, let $\\mathcal{D}_{fol}(L_{p\,q})$
and\n$\\mathcal{D}_{lp}(L_{p\,q})$ be respectively the groups of
foliated and\nleaf preserving diffeomorphisms of
$\\mathcal{F}_{p\,q}$.\nEndow all those groups with the
corresponding $C^{\\infty}$ Whitney\ntopologies.\nThe aim of the
talk is give a complete description the homotopy types of\nthe above
groups $\\mathcal{D}_{fol}(T\,\\partial
T)$\,\n$\\mathcal{D}_{lp}(T\,\\partial T)$\,
$\\mathcal{D}_{fol}(L_{p\,q})$\,\n$\\mathcal{D}_{lp}(L_{p\,q})$ for
all $p\,q$.
LOCATION:Zoom ID 870 912 2782 ask Vladimir Chernov for the Password
URL:https://math.dartmouth.edu/~topology/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6267e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230502T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d626ad@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230502T140000
DTEND;TZID=America/New_York:20230502T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Qian Zhang : Gradcurl-Conforming Finite Elements Based on De
Rham Complexes for the Fourth-Order Curl Problems
DESCRIPTION:The fourth-order curl operator appears in various
models\, such as electromagnetic interior transmission eigenvalue
problems\, magnetohydrodynamics in hot plasmas\, and couple stress
theory in linear elasticity. The key to discretizing these problems
is to discretize the fourth-order curl operator. In this talk\, I
will present the conforming finite element method for a simplified
fourth-order curl model. Discretizing the quad-curl equations using
smoother elements (such as H^2-conforming elements) would lead to
wrong solutions. Speciﬁc ﬁnite elements need to be designed for
the fourth-order curl operator. However\, constructing such elements
is a challenging task because of the continuity required by the
curlcurl-conformity and the naturally divergence-free property of
the curl operator. In this presentation\, we provide the
construction of the curlcurl-conforming elements in both 2D and 3D
based on the de Rham complex. In 2D\, the lowest-order grad
curl-conforming element has only 6 and 8 degrees of freedom on a
triangle and a rectangle\, respectively. In 3D\, we relate the
fourth-order curl problem to fluid mechanics and a de Rham complex
with higher regularity. The lowest-order element has only 18
degrees of freedom on a tetrahedron. As a by-product\, we construct
a family of stable and mass-preserving finite element pairs for
solving the Navier-Stokes equations.
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d626e9@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230502T142500
DTEND;TZID=America/New_York:20230502T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Jonathan Love: TBD
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6271b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230504T151500
CATEGORIES:Math Colloquium
SUMMARY:Gary Froyland: TBA
LOCATION:Kemeny 004
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6274a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230509T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62778@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230509T140000
DTEND;TZID=America/New_York:20230509T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:TBA: TBA
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d627a6@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230509T142500
DTEND;TZID=America/New_York:20230509T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Corey Brooke: TBD
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d627d5@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230511T151500
CATEGORIES:Math Colloquium
SUMMARY:Jonathan Bloom: Strictly increasing and decreasing sequences
in subintervals of words
DESCRIPTION:In this talk we discuss our proof of a recent conjecture
of Guo and Poznanovi\\'{c} concerning chains in certain 01-fillings
of moon polyominoes. A key ingredient of our proof is a
correspondence between words $w$ and pairs $(W(w)\, M(w))$ of
increasing tableaux such that $M(w)$ determines the lengths of the
longest strictly increasing and strictly decreasing sequences in
every subinterval of $w$. (It will be noted that similar and
well-studied correspondences like RSK insertion and Hecke insertion
fail in this regard.) To define our correspondence we make use of
Thomas and Yong's K-infusion operator and then use it to obtain the
bijections that prove the conjecture of Guo and Poznanovi\\'{c}.
(Joint work with D. Saracino.)
LOCATION:004 Kemeny Hall
URL:https://math.dartmouth.edu/calendar/agenda-colloq.php
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6280d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230516T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6283b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230516T140000
DTEND;TZID=America/New_York:20230516T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:TBA: TBA
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62869@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230516T142500
DTEND;TZID=America/New_York:20230516T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Adriana Salerno and Ursula Whitcher: Combinatorial pencils
and Hasse–Witt invariants
DESCRIPTION:Using a natural combinatorial generalization of the
Fermat quartic and\nthe Batyrev mirror symmetry construction\, we
obtain a collection of $K3$\nsurface pencils of generic Picard rank
19 in Gorenstein Fano toric\nvarieties. We characterize point counts
on these varieties over finite\nfields using Picard-Fuchs equations
and classical hypergeometric\nfunctions. We use similar techniques
to study the periods and arithmetic\nof highly symmetric Calabi-Yau
hypersurfaces in Grassmannians.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6289e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230523T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d628d1@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230523T140000
DTEND;TZID=America/New_York:20230523T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Ben Allen Emmanuel College: Natural selection for collective
action
DESCRIPTION:Collective action -- behavior that arises from the
combined actions of multiple individuals -- is observed across
living beings. The question of how and why collective action evolves
has profound implications for behavioral ecology\,
multicellularity\, and human society. Collective action is
challenging to model mathematically\, due to nonlinear fitness
effects and the consequences of spatial\, group\, and/or family
relationships. We derive a simple condition for collective action to
be favored by natural selection. A collective's effect on the
fitness of each individual is weighted by the relatedness between
them\, using a new measure of collective relatedness. If selection
is weak\, this condition can be evaluated using coalescent theory.
More generally\, our result applies to any synergistic social
behavior\, in spatial\, group\, and/or family-structured
populations. We use this result to obtain conditions for the
evolution of collective help among diploid siblings\, subcommunities
of a network\, and hyperedges of a hypergraph. We also obtain a
condition for which of two strategies is favored in a game between
siblings\, cousins\, or other relatives. Our work provides a
rigorous basis for extending the notion of "actor"\, in the study
of social behavior\, from individuals to collectives.
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6290e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230523T142500
DTEND;TZID=America/New_York:20230523T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Nathan McNew: TBD
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6293e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T090000
DTEND;TZID=America/New_York:20230530T140000
CATEGORIES:Thesis Defence
SUMMARY:Senors: Senior Thesis Presentations
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6296d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:TBD
LOCATION:TBD
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d6299b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T140000
DTEND;TZID=America/New_York:20230530T150000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:TBA: TBA
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d629ca@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T140000
DTEND;TZID=America/New_York:20230530T170000
CATEGORIES:Special Event
SUMMARY:Undergraduate Poster Session
LOCATION:Kemeny/Haldeman hallways
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d629f8@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T142500
DTEND;TZID=America/New_York:20230530T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Pete Clark: TBD
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230324T101701Z
UID:20230324T061701641d789d62a28@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230601T120000
DTEND;TZID=America/New_York:20230601T133000
CATEGORIES:Special Event
SUMMARY:Math Majors BBQ
LOCATION:Kemeny/Haldeman Patio
END:VEVENT
END:VCALENDAR