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PRODID:-//Mathematics Department//NONSGML mathical.php//EN
X-WR-CALNAME:Mathematics Department
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0ad5d@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230429T100000
DTEND;TZID=America/New_York:20230429T130000
CATEGORIES:Special Event
SUMMARY:Thayer Prize Exam for First-Year Students
DESCRIPTION:Dartmouth College’s Mathematics Prize Exam for
First-Year Students. The Mathematics Department Prize fund for this
exam is up to $1000\, to be distributed among the exam winners. The
exam consists of Mathematics Olympiad style problems. Originality
and creativity are heavily weighed.\n
LOCATION:Kemeny 004
URL:https://math.dartmouth.edu/activities/undergrad/thayer-prize/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0adbe@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230502T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:Matt Ellison: Extending a triangulation of the 2-sphere to
the 3-ball
DESCRIPTION:Define the tet-volume of a triangulation of the 2-sphere
to be the minimum number of tetrahedra needed to extend it to a
triangulation of the 3-ball\, and let d(v) be the maximum tet-volume
for v-vertex triangulations. In 1986 Sleator\, Tarjan\, and Thurston
(STT) proved that d(v) = 2v-10 holds for large v\, and conjectured
that it holds for all v >= 13. Their proof used hyperbolic polyhedra
of large volume. They suggested using more general notions of volume
instead\, and I will share our proof of the conjecture using this
idea. This implies STT’s associated conjecture\, proven by Pournin
in 2014\, about the maximum rotation distance between binary
trees. This is joint work with Peter Doyle and Zili Wang.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0adf9@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230502T142500
DTEND;TZID=America/New_York:20230502T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Jonathan Love: On $\\ell$-torsion in superelliptic Jacobians
DESCRIPTION: Let $J$ be the Jacobian of a curve of the form $y^\\ell
= f(t)$ over a finite field $\\mathbb{F}_q$ (with $f(t)$
irreducible\, and $\\ell$ a prime that does not divide either $q$ or
$\\deg(f)$). In this talk we will discuss constraints on the
$\\ell$-rank of $J(\\mathbb{F}_q)$\, including upper bounds\, lower
bounds\, and parity. This is joint work with Wanlin Li and Eric
Stubley.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0ae2f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230502T143000
DTEND;TZID=America/New_York:20230502T153000
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:20230529T130202Z
UID:20230529T0902026474a24a0ae77@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230504T110000
DTEND;TZID=America/New_York:20230504T120000
CATEGORIES:Functional Analysis Seminar
SUMMARY:Claire Valva: Consistent spectral approximation of Koopman
operators using resolvent compactification
DESCRIPTION:Koopman operators and transfer operators transform
nonlinear dynamics in phase space to linear dynamics on vector
spaces of functions\, enabling the use of spectral techniques
without modeling constraints such as linearity. The extraction of
approximate Koopman eigenfunctions (and the associated
eigenfrequencies) from an unknown system is nontrivial\,
particularly if the system has mixed or continuous spectrum. We
discuss a spectrally-accurate approach to approximate the Koopman
operator from data via a “compactification” of the resolvent of
the Koopman generator. This approach employs kernel integral
operators to approximate the skew-adjoint generator in
measure-preserving systems by a family of skew-adjoint operators
with compact resolvent\, whose spectral measures converge in a
suitable asymptotic limit\, and whose eigenfunctions are
approximately periodic. We explore implementations of this technique
using data from several different example systems including Lorenz
63.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~funct-an/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0aeb0@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230504T151500
CATEGORIES:Math Colloquium
SUMMARY:Gary Froyland: Spectral geometry in dynamics
DESCRIPTION:I will describe how elementary constructions from
spectral geometry on manifolds and graphs can be extended to analyse
dynamical evolution on these domains.\n\nI will sketch the numerical
construction of a dynamic Laplace operator and illustrate how its
eigenfunctions can detect coherent regions in convective fluids and
in the ocean.\n\nTechniques to identify regime changes in dynamics
on continuous space and on spatiotemporal networks will also be
discussed.
LOCATION:004 Kemeny Hall
URL:https://math.dartmouth.edu/activities/colloquia/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0aee6@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230509T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:Alejandro Galván: On triangular partitions and their
generalizations
DESCRIPTION:An integer partition is said to be triangular if its
Ferrers diagram can be separated from its complement by a straight
line. In this talk\, we will explore various characterizations and
properties of these objects. We will study the poset of triangular
partitions ordered by containment and we will derive some
enumeration formulas\, obtaining an expression to count balanced
words as a corollary. Finally\, we will briefly comment how this
research can be extended to a 3-dimensional analogue\, as well as to
other generalizations which arise by allowing convex or concave
curves instead of straight lines to separate the diagram.\n
LOCATION:Kemeny 242
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0af1f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230509T142500
DTEND;TZID=America/New_York:20230509T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Corey Brooke: Lines on cubic threefold containing a plane
DESCRIPTION:Over an algebraically closed field\, there are two
classical rationality constructions for a cubic threefold $Y$
containing a plane $P$: one is projection from a node\, and the
other uses a line in $Y$ that does not meet $P$. Over an arbitrary
field $k$\, though\, $Y$ might not have any $k$-rational nodes or
$k$-rational lines disjoint from $P$. In this case\, can $Y$ still
be rational via some other construction? I will answer this question
in the negative\, at least in characteristic zero\, using an
intermediate Jacobian torsor obstruction. Concretely\, this entails
studying the Fano variety of lines on a cubic threefold containing a
plane.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0af5e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230509T143000
DTEND;TZID=America/New_York:20230509T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Jason Wei : Scaling unlocks emergent abilities in language
models
DESCRIPTION:Scaling up language models has been shown to predictably
improve performance on a wide range of downstream tasks. In this
talk\, we will instead discuss an unpredictable phenomenon that we
refer to as emergent abilities of large language models. An ability
is considered emergent if it is not present in smaller models but is
present in larger models\, which means that the ability cannot be
predicted simply by extrapolating the performance of smaller models.
With the popularization of large language models such as GPT-3\,
Chinchilla\, and PaLM\, dozens of emergent abilities have been
discovered\, including chain-of-thought prompting\, which enables
state-of-the-art mathematical reasoning\, and instruction
finetuning\, which enables large language models to be usable by the
broader population. The existence of such emergent phenomena raises
the question of whether additional scaling could potentially further
expand the range of capabilities of language models.
LOCATION:Zoom Link
URL:https://dartmouth.zoom.us/j/96317196119?pwd=dG1oSXpTUzhMZG5tdjNlZ2FWVDFldz09
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0af96@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:20230529T130202Z
UID:20230529T0902026474a24a0afcd@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230516T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:GaYee Park: Minimal skew semistandard Young tableaux and the
Hillman--Grassl correspondence
DESCRIPTION:Standard tableaux of skew shape are fundamental objects
in enumerative and algebraic combinatorics and no product formula
for the number is known. Naruse presented a formula as a positive
sum over excited diagrams of products of hook-lengths. Shortly
after\, Morales\, Pak\, and Panova gave a $q$-analogue of Naruse's
formula for semi-standard tableaux of skew shapes in terms of
restricted excited arrays. They also showed\, partly algebraically\,
that the Hillman-Grassl map restricted to skew shapes is the
bijection between skew SSYTs and excited arrays. We study the
problem of making this argument completely bijective. For a skew
shape\, we define a new set of semi-standard Young tableaux\, called
the \\emph{minimal SSYT}\, that are equinumerous with excited
diagrams via a new description of the Hillman--Grassl bijection and
have a version of excited moves. The minimal skew SSYT are the
natural objects to compare with the terms of the Okounkov-Olshanski
formula for counting SYT of skew shape. We prove that the number of
summands in the Okounkov-Olshanski formula is larger than the
excited diagrams in NHLF. This is a joint work with Alejandro
Morales and Greta Panova
LOCATION:Kemeny 242
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b015@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:20230529T130202Z
UID:20230529T0902026474a24a0b04a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230516T143000
DTEND;TZID=America/New_York:20230516T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Maximilian Ramgraber: Adaptive localization in nonlinear
ensemble transport filtering
DESCRIPTION:Most ensemble filtering algorithms today rely on one of
two update strategies. The ensemble Kalman filter (EnKF) and its
many variants are sample-efficient but remain fundamentally
restricted to linear updates\, which limits fidelity in strongly
nonlinear or non-Gaussian settings. Particle filters\, on the other
hand\, can realize arbitrarily nonlinear updates for non-Gaussian
problems\, but often require intractable ensemble sizes to forestall
ensemble collapse. A promising alternative may be found in ensemble
transport methods. Transport methods construct a map from an
unknown\, potentially non-Gaussian target distribution—represented
only through an ensemble of particles—to a well-defined reference
distribution\, often a standard multivariate Gaussian distribution.
Inverting this map permits sampling from the target’s conditional
distributions. Leveraging this operation\, it is possible to derive
true nonlinear generalizations of the EnKF and its smoothing
variants.\nIn this construction\, the complexity of the map’s
parameterization is a critical choice. More complex maps may capture
increasingly complex distributional features but risk unfavourable
bias-variance trade-offs. In this presentation\, we present an
efficient map adaptation scheme which not only (1) identifies an
optimal degree of map complexity\, but also (2) reveals and exploits
conditional independence\, yielding an efficient form of adaptive
localization. We demonstrate the performance of the resulting
adaptive ensemble transport filter in a chaotic and nonlinear
setting and discuss its implications for high-dimensional
environmental systems.
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b08f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230523T110000
CATEGORIES:Combinatorics Seminar
SUMMARY:Tom Roby: Lifting Rowmotion to higher realms and
noncommutative periodicity
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b0be@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230523T142500
DTEND;TZID=America/New_York:20230523T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Nathan McNew: Counting permutations and primitive sets using
the divisor graph of the integers
DESCRIPTION:Recently Pomerance asked how many permutations $\\pi$ of
$n$ satisfy a certain divisibility property\, namely that either $i$
divides $\\pi(i)$ or $\\pi(i)$ divides $i$ for every index $i$. In a
subsequent paper\, he showed that the count is bounded between
$1.93^n$ and $13.6^n$. We discuss an improvement on this result\,
showing that the count is $(c+o(1))^n$ for a constant $2.06 < c <
2.70$. The proof uses bounds on the distribution of smooth numbers
as well as a graph theoretic result on cycle-covers which we prove
and apply to the divisor graph (the graph on vertices $1\,2\,...\,n$
and an edge between two integers if one divides the other). We will
also discuss related enumeration problems\, such as counting
primitive sets of the integers (subsets of the integers in which no
element divides another) which can be approached using similar
methods.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b0f7@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230523T143000
DTEND;TZID=America/New_York:20230523T153000
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:20230529T130202Z
UID:20230529T0902026474a24a0b131@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230525T110000
DTEND;TZID=America/New_York:20230525T120000
CATEGORIES:Functional Analysis Seminar
SUMMARY:John D. Trout: The algebraic structure of general mechanics
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:20230529T130202Z
UID:20230529T0902026474a24a0b16c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230525T142500
DTEND;TZID=America/New_York:20230525T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Amnon Besser: Computing local contributions to Quadratic
Chabauty functions
DESCRIPTION:The Quadratic Chabauty function is a certain function
the rational points of a curve that is used in the Quadratic
Chabauty method for finding all rational points. It is a certain
$p$-adic height and as such has contributions coming from all primes
and it is essential to know in advance what values these can take.
In joint work with Mueller and Srinivasan we use Vologodsky
integration to get a handle on these contributions and we have a
theoretical algorithm to compute these explicitly. I will explain
the method and the algorithm (similar results from a different point
of view are in progress by Betts\, Duque-Rosero\, Hashimoto and
Spelier)
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b1a2@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T023000
DTEND;TZID=America/New_York:20230530T033000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Ethan Levien: Evolution in the presence of large (but
finite) offspring fluctuations
DESCRIPTION:Evolution is driven by a tension between two opposing
forces: random\nfluctuations in the genetic composition of a
population\, known as\ngenetic drift\, and deterministic selection.
Among models of genetic\ndrift\, the classical Wright-Fisher
diffusion (WFD) reigns supreme. The\nsuccess of the WFD can be
attributed to universality: Much like the\nGaussian emerges
universally from sums of iid random variables with\nfinite
variance\, the WFD emerges as a universal large population
size\nlimit from numerous population genetics models in which the
variance\nin offspring numbers is finite. However\, an onslaught of
data from the\nmicrobial world has revealed the limitations of this
model\, motivating\nthe study of evolution in the presence of power
law offspring\ndistributions with infinite variance. In this talk\,
I will present\nresults concerning models of neutral evolution where
the variance in\noffspring is finite\, but large relative to the
population size. In\nparticular\, I will consider offspring
distributions with Weibull log\ntails (the lognormal being a special
case) in a particular\n``thermodynamic’’ limit. These offspring
distributions are motivated\nby biology\, where they appear in
models of microbial pathogens\, but\nalso by a connection to
statistical physics where they appear in the\ncontext of spin
glasses with long range interactions. By leveraging\nresults from
the theory of spin glasses\, I will describe a new class\nof limit
models for genetic drift which generalize the\n$\\Lambda$-Flemming
Viot process – a phenomenological model for neutral\nevolution
with skewed offspring distributions. If time permits I will\nalso
discuss the statistical structure of genealogies emerging
from\nthese models\, which are connected to the forward dynamics
via\nstochastic duality. These genealogies have some
surprising\ncharacteristics including the simultaneous merging of
multiple\nancestral lineages.
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b1e1@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T090000
DTEND;TZID=America/New_York:20230530T093000
CATEGORIES:Thesis Defence
SUMMARY:Love Tsai: Expanding the Schelling Agent-Based Model: De
Jure Segregation Dynamics on a Network
DESCRIPTION:\n
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b216@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T100000
DTEND;TZID=America/New_York:20230530T103000
CATEGORIES:Thesis Defence
SUMMARY:Jenny Song: Chromatic Symmetric Functions of Trees with
Restriction on the Number of Colors Used
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b245@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T103000
DTEND;TZID=America/New_York:20230530T110000
CATEGORIES:Thesis Defence
SUMMARY:Michael Gonzalez: The chromatic symmetric function in the
star basis
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b274@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T110000
DTEND;TZID=America/New_York:20230530T113000
CATEGORIES:Thesis Defence
SUMMARY:Varun Malladi: Bounded Adjointable Operators on Dense
Subspaces of Separable Hilbert Spaces
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b2a3@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T120000
DTEND;TZID=America/New_York:20230530T123000
CATEGORIES:Thesis Defence
SUMMARY:Brian Wang: Capturing dynamical systems using deep learning
and understanding optimal data size in training time series
prediction models
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b2d2@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T123000
DTEND;TZID=America/New_York:20230530T130000
CATEGORIES:Thesis Defence
SUMMARY:Noah Schwartz: Expanding the Legendrian knot atlas
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b300@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T130000
DTEND;TZID=America/New_York:20230530T133000
CATEGORIES:Thesis Defence
SUMMARY:Jonah Weinbaum: “A census of cubic fourfolds over the
field with two elements”
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b32f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T133000
DTEND;TZID=America/New_York:20230530T140000
CATEGORIES:Thesis Defence
SUMMARY:Henry Wildermuth: Aspects of Alexander Duality
LOCATION:Haldeman 041
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b35e@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:20230529T130202Z
UID:20230529T0902026474a24a0b38b@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T142500
DTEND;TZID=America/New_York:20230530T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Pete Clark: Group-Theoretic Ax-Katz Theorems
DESCRIPTION:The Chevalley-Warning Theorem is a 1935 result asserting
that for a "low degree" polynomial system over a finite field of
characteristic p\, the number of solutions is divisible by p. The
original proof of this beautiful result was a few pages\, but in
1964 James Ax gave a spectacular ten line argument. He also
addressed the question of divisibility by higher powers of p. The
definitive result was given in 1971 by Nick Katz: the celebrated
Ax-Katz Theorem gives the optimal p-adic divisibility for all fixed
parameter values (number of variables\, number and degrees of the
polynomials). Simpler proofs of the Ax-Katz Theorem are now known\,
but none as simple as Ax's proof of Chevalley-Warning.\n\nMy
favorite proof of Ax-Katz is a 2006 argument by Richard Wilson\,
which works only over the prime field F_p. The proof is extremely
"concrete" but hints at additional algebraic structure. The
foundation for this structure was provided in a 2021 paper of
Aichinger-Moosbauer\, who develop a calculus of finite differences
for maps between commutative groups and deduce a purely
group-theoretic result that implies the Chevalley-Warning Theorem.
\n\nBy synthesizing the work of Wilson and Aichinger-Moosbauer\, Uwe
Schauz and I proved an Ax-Katz type p-adic congruence for maps
between arbitrary finite commutative groups (Ax-Katz is the special
case in which the domain has prime exponent). But even the general
statement is rather complicated. If we take a step back\, already
Ax's work implies a striking qualitative result -- for polynomial
systems over F_q\, if one fixes the number and degrees of the
polynomials\, then the amount of p-adic divisibility in the solution
locus goes to infinity with the number of variables -- that I call
the Ax Effect. I will end by discussing joint work with Nicholas
Triantafillou that gives a group-theoretic generalization of Ax's
"ten line" proof. From this we deduce that the Ax Effect holds over
any finite ring. When we restrict our bounds to the case of
polynomial systems over F_p we recover precisely Ax's part of the
Ax-Katz Theorem.
LOCATION:Kemeny 343
URL:https://math.dartmouth.edu/~zahlen
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b3cf@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230530T143000
DTEND;TZID=America/New_York:20230530T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Ethan Levien: TBA
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b3fe@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
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b42c@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230601T142500
DTEND;TZID=America/New_York:20230601T152500
CATEGORIES:Algebra and Number Theory Seminar
SUMMARY:Shiang Tang: Compatible systems of Galois representations
over function fields
DESCRIPTION:For a global function field F and a semisimple algebraic
group G\, we construct compatible systems of p-adic representations
of the absolute Galois group over F valued in G with Zariski-dense
images. More precisely\, we show that any continuous mod-p
representation of the absolute Galois group over F valued in G
satisfying mild conditions lifts to characteristic zero\, which can
then be placed into a compatible system of p-adic representations.
\nAs an application\, we deduce new instances of the inverse Galois
problem for finite groups of Lie type over global function fields.
The main ingredients are a lifting theorem of
Fakhruddin-Khare-Patrikis and a classical theorem of L. Lafforgue on
the Langlands correspondence for global function fields.
LOCATION:Kemeny 343
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b462@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230606T143000
DTEND;TZID=America/New_York:20230606T153000
CATEGORIES:Applied and Computational Mathematics Seminar
SUMMARY:Raghav Singal: TBA
LOCATION:Kemeny 307
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b491@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230914T151500
CATEGORIES:Math Colloquium
SUMMARY:Jakob Hedicke: TBA
LOCATION:TBA
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b4bf@math.dartmouth.edu
DTSTART;TZID=America/New_York:20230926T151500
CATEGORIES:Math Colloquium
SUMMARY:Paul Pollack: TBA
LOCATION:TBA
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b4ee@math.dartmouth.edu
DTSTART;TZID=America/New_York:20231005T151500
CATEGORIES:Math Colloquium
SUMMARY:Thibault Lefeuvre: TBA
LOCATION:TBA
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b51f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20231018T180000
CATEGORIES:∾ Prosser Lecture ∾
SUMMARY:Michael Lopez: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/prosser-lectures/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b54f@math.dartmouth.edu
DTSTART;TZID=America/New_York:20231102T151500
CATEGORIES:Math Colloquium
SUMMARY:Pamela Estephania Harris: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/prosser-lectures/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b57e@math.dartmouth.edu
DTSTART;TZID=America/New_York:20231102T180000
CATEGORIES:∿ Lahr Lecture ∿
SUMMARY:Pamela Estephania Harris: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/prosser-lectures/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b5ad@math.dartmouth.edu
DTSTART;TZID=America/New_York:20240208T151500
CATEGORIES:Math Colloquium
SUMMARY:Sarah Mason: TBA
LOCATION:TBA
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b5dc@math.dartmouth.edu
DTSTART;TZID=America/New_York:20240222T151500
CATEGORIES:Math Colloquium
SUMMARY:Christopher Jones: TBA
LOCATION:TBA
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b60a@math.dartmouth.edu
DTSTART;TZID=America/New_York:20240328T151500
CATEGORIES:Math Colloquium
SUMMARY:Mason Porter: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/colloquia/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b639@math.dartmouth.edu
DTSTART;TZID=America/New_York:20240515T180000
CATEGORIES:⋆ Kemeny Lecture ⋆
SUMMARY:Anne Schilling: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/kemeny-lectures/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b668@math.dartmouth.edu
DTSTART;TZID=America/New_York:20240516T151500
CATEGORIES:⋆ Kemeny Lecture ⋆
SUMMARY:Anne Schilling: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/kemeny-lectures/
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230529T130202Z
UID:20230529T0902026474a24a0b697@math.dartmouth.edu
DTSTART;TZID=America/New_York:20240517T151500
CATEGORIES:⋆ Kemeny Lecture ⋆
SUMMARY:Anne Schilling: TBA
LOCATION:TBA
URL:https://math.dartmouth.edu/activities/kemeny-lectures/
END:VEVENT
END:VCALENDAR