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BEGIN:VEVENT
SUMMARY:Lillian Pierce (Duke University)
DTSTART:20210211T203000Z
DTEND:20210211T213000Z
DTSTAMP:20260422T225926Z
UID:1123112229/1
DESCRIPTION:Title: Counting problems: open questions in number theory\, from the perspecti
ve of moments\nby Lillian Pierce (Duke University) as part of K-State
Mathematics Department Women Lecture Series\n\n\nAbstract\nMany questions
in number theory can be phrased as counting problems. How many number fiel
ds are there? How many elliptic curves are there? How many integral soluti
ons to this system of Diophantine equations are there? If the answer is
“infinitely many\,” we want to understand the order of growth for the
number of objects we are counting in the “family." But in many settings
we are also interested in finer-grained questions\, like: how many number
fields are there\, with fixed degree and fixed discriminant? We know the a
nswer is “finitely many\,” but it would have important consequences if
we could show the answer is always “very few indeed.” In this accessi
ble talk\, we will describe a way that these finer-grained questions can b
e related to the bigger infinite-family questions. Then we will use this p
erspective to survey interconnections between several big open conjectures
in number theory\, related in particular to class groups and number field
s.\n
LOCATION:https://researchseminars.org/talk/1123112229/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu-Ru Liu (University of Waterloo)
DTSTART:20210223T203000Z
DTEND:20210223T213000Z
DTSTAMP:20260422T225926Z
UID:1123112229/2
DESCRIPTION:Title: Diophantine Problems in Function Fields\nby Yu-Ru Liu (University o
f Waterloo) as part of K-State Mathematics Department Women Lecture Series
\n\n\nAbstract\nLet $\\mathbb{Z}$ be the ring of integers\, and let $\\mat
hbb{F}_p[t]$ be the ring of polynomials in one variable defined over the f
inite field $\\mathbb{F}_p$ of $p$ elements. Since the characteristic of $
\\mathbb{Z}$ is $0$\, while that of $\\mathbb{F}_p[t]$ is the positive pri
me number $p$\, it is an interesting phenomenon in arithmetic that these t
wo rings resemble one another so faithfully. The study of the similarity a
nd difference between $\\mathbb{Z}$ and $\\mathbb{F}_p[t]$ lies in the fie
ld that relates number fields to function fields. In this talk\, we will i
nvestigate some Diophantine problems in the settings of $\\mathbb{Z}$ and
$\\mathbb{F}_p[t]$\, including Waring's problem about representations of
elements with fixed powers.\n
LOCATION:https://researchseminars.org/talk/1123112229/2/
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BEGIN:VEVENT
SUMMARY:Svitlana Mayboroada (University of Minnesota)
DTSTART:20210311T203000Z
DTEND:20210311T213000Z
DTSTAMP:20260422T225926Z
UID:1123112229/3
DESCRIPTION:Title: The hidden landscape of wave localization\nby Svitlana Mayboroada (
University of Minnesota) as part of K-State Mathematics Department Women L
ecture Series\n\n\nAbstract\nComplexity of the geometry\, randomness of th
e potential\, and many other irregularities of the system can cause powerf
ul\, albeit quite different\, manifestations of localization\, a phenomeno
n of sudden confinement of waves to a small portion of the original domain
. In the present talk we show that behind a possibly disordered system the
re exists a structure\, referred to as a landscape function\, which predic
ts the location and shape of the localized waves\, a pattern of their deca
y\, and delivers accurate bounds for the corresponding energies.\n
LOCATION:https://researchseminars.org/talk/1123112229/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene Fonseca (Carnegie Melon University)
DTSTART:20210422T193000Z
DTEND:20210422T203000Z
DTSTAMP:20260422T225926Z
UID:1123112229/4
DESCRIPTION:Title: Phase transitions in heterogeneous media: equilibria and geometric flow
s\nby Irene Fonseca (Carnegie Melon University) as part of K-State Mat
hematics Department Women Lecture Series\n\n\nAbstract\nA variational mode
l in the context of the gradient theory for fluid-fluid phase transitions
with small scale heterogeneities is studied. In the case where the scale o
f the small homogeneities is of the same order of the scale governing the
phase transition\, the interaction between homogenization and the phase tr
ansitions process leads to an anisotropic interfacial energy.\n\nThe under
lying gradient flow provides unconditional convergence results for an Alle
n-Cahn type bi-stable reaction diffusion equation in a periodic medium. Th
e limiting dynamics are given by an analog for anisotropic mean curvature
flow\, of the formulation due to Ken Brakke. As an essential ingredient in
the analysis\, an explicit expression for the effective surface tension\,
which dictates the limiting anisotropic mean curvature\, is obtained.\n\n
This is joint work with Riccardo Cristoferi (Radboud University\, The Neth
erlands)\, Adrian Hagerty\, Cristina Popovici\, Rustum Choksi (McGill)\, J
essica Lin (McGill)\, and Raghavendra Venkatraman (CMU).\n
LOCATION:https://researchseminars.org/talk/1123112229/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betsy Stovall (University of Wisconsin)
DTSTART:20210330T193000Z
DTEND:20210330T203000Z
DTSTAMP:20260422T225926Z
UID:1123112229/5
DESCRIPTION:Title: Maximizers and near-maximizers for Fourier restriction inequalities
\nby Betsy Stovall (University of Wisconsin) as part of K-State Mathematic
s Department Women Lecture Series\n\n\nAbstract\nFourier restriction pheno
mena allow us to make sense out of the restriction of the Fourier transfor
m of an $L^p$ function (nominally only defined almost everywhere) on measu
re zero sets\, provided these sets possess sufficient curvature. In the d
ual formulation\, "tubes" whose directions are restricted to lie along som
e curved set can only overlap with one another on a relatively small regio
n of space. More quantitatively\, such phenomena are reflected by Lebesgu
e space bounds for the Fourier restriction operator. In this talk\, we wi
ll describe some open questions and recent results regarding the existence
of functions that provide a worst-case scenario by saturating these Lebes
gue space bounds.\n
LOCATION:https://researchseminars.org/talk/1123112229/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Blair Sullivan (University of Utah)
DTSTART:20210506T193000Z
DTEND:20210506T203000Z
DTSTAMP:20260422T225926Z
UID:1123112229/6
DESCRIPTION:Title: Putting parameterization into practice\nby Blair Sullivan (Universi
ty of Utah) as part of K-State Mathematics Department Women Lecture Series
\n\n\nAbstract\nThe field of network science has burgeoned in the last two
decades\, developing new methods for analyzing complex network data of ev
er-increasing scale. Surprisingly\, few approaches draw on the wealth of e
fficient algorithms arising from structural graph theory and parameterized
complexity. In part\, this is due to the primarily theoretical nature of
the related literature\, unrealistic structural assumptions\, and a lack o
f cross-pollination of the research communities. In this talk\, we survey
the key ingredients for bridging this theory-practice gap\, and describe s
everal applications which demonstrate the potential of parameterized graph
algorithms in computational genomics.\n
LOCATION:https://researchseminars.org/talk/1123112229/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Riehl (Johns Hopkins University)
DTSTART:20210916T193000Z
DTEND:20210916T203000Z
DTSTAMP:20260422T225926Z
UID:1123112229/7
DESCRIPTION:Title: Contractibility as uniqueness\nby Emily Riehl (Johns Hopkins Unive
rsity) as part of K-State Mathematics Department Women Lecture Series\n\n\
nAbstract\nWhat does it mean for something to exist uniquely? Classically\
, to say that a set A has a unique element means that there is an element
x of A and any other element y of A equals x. When this assertion is appli
ed to a space A\, instead of a mere set\, and interpreted in a continuous
fashion\, it encodes the statement that the space is contractible\, i.e.\,
that A is continuously deformable to a point. This talk will explore this
notion of contractibility as uniqueness and its role in generalizing from
ordinary categories to infinite-dimensional categories.\n
LOCATION:https://researchseminars.org/talk/1123112229/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Balakrishnan (Boston University)
DTSTART:20210928T193000Z
DTEND:20210928T203000Z
DTSTAMP:20260422T225926Z
UID:1123112229/8
DESCRIPTION:Title: Questions about rational points on curves\nby Jennifer Balakrishnan
(Boston University) as part of K-State Mathematics Department Women Lectu
re Series\n\n\nAbstract\nA rational point on a curve is a point whose coor
dinates are both rational numbers. When a curve has genus 2 or more\, by a
theorem of Faltings\, there are always only finitely many rational points
. Yet many more questions remain: how many rational points are there exact
ly? Is there an algorithm to find them all? I'll discuss these questions a
nd more (ranging from the time of the ancient Greeks to the present)\, off
er some answers\, and highlight a selection of illustrative examples.\n
LOCATION:https://researchseminars.org/talk/1123112229/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juanita Pinzón Caicedo (University of Notre Dame)
DTSTART:20211014T193000Z
DTEND:20211014T202000Z
DTSTAMP:20260422T225926Z
UID:1123112229/9
DESCRIPTION:Title: Instantons and knot concordance\nby Juanita Pinzón Caicedo (Univer
sity of Notre Dame) as part of K-State Mathematics Department Women Lectur
e Series\n\nLecture held in Room 122 in Cardwell Hall.\n\nAbstract\nKnot c
oncordance can be regarded as the study of knots as boundaries of surfaces
embedded in spaces of dimension 4. Specifically\, two knots $K_0$ and $K_
1$ are said to be smoothly concordant if there is a smooth embedding of th
e annulus $S^1 \\times [0\, 1]$ into the “cylinder” $S^3 \\times [0\,
1]$ that restricts to the given knots at each end. Smooth concordance is a
n equivalence relation\, and the set C of smooth concordance classes of kn
ots is an abelian group with connected sum as the binary operation. The al
gebraic structure of $C$\, the concordance class of the unknot\, and the s
et of knots that are topologically slice but not smoothly slice are much s
tudied objects in low-dimensional topology. Gauge theoretical results on t
he nonexistence of certain definite smooth 4-manifolds can be used to bett
er understand these objects. In particular\, the study of anti-self dual c
onnections on 4-manifolds can be used to shown that the group of topologic
ally slice knots up to smooth concordance contains a subgroup isomorphic t
o $Z^\\infty.$\n
LOCATION:https://researchseminars.org/talk/1123112229/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Billey (University of Washington)
DTSTART:20211028T193000Z
DTEND:20211028T202000Z
DTSTAMP:20260422T225926Z
UID:1123112229/10
DESCRIPTION:Title: Some Theorems in Asymptotic Algebraic Combinatorics\nby Sara Bille
y (University of Washington) as part of K-State Mathematics Department Wom
en Lecture Series\n\n\nAbstract\nAsymptotic Combinatorics is a branch of M
athematics that looks at limiting distributions of combinatorial formulas.
Our recent work has focused on generalizations of a classic formula for
standard Young tableaux called the Hook Length Formula and its generalizat
ions to using the major index statistic. Further examples include Stanley
’s q-hook-content formula for semistandard tableaux and q-hook length fo
rmulas of Björner–Wachs related to linear extensions of labeled forests
. We show that\, while these limiting distributions are “generically”
asymptotically normal\, there are uncountably many non-normal limit laws.
More precisely\, we introduce and completely describe the compact closure
of the moduli space of distributions of these statistics in several regime
s. The additional limit distributions involve generalized uniform sum dist
ributions which are topologically parameterized by certain decreasing sequ
ence spaces with bounded 2-norm. The closure of the moduli space of these
distributions in the Lévy metric gives rise to the moduli space of DUSTPA
N distributions. As an application\, we completely classify the limiting d
istributions of the size statistic on plane partitions fitting in a box. T
his talk is based on joint work with Joshua Swanson at USC (https://arxiv.
org/abs/2010.12701).\n
LOCATION:https://researchseminars.org/talk/1123112229/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nageswari Shanmugalingam (University of Cincinnati)
DTSTART:20211118T203000Z
DTEND:20211118T212000Z
DTSTAMP:20260422T225926Z
UID:1123112229/11
DESCRIPTION:Title: A multitude of formulations of Dirichlet problem for least gradient fu
nctional\nby Nageswari Shanmugalingam (University of Cincinnati) as pa
rt of K-State Mathematics Department Women Lecture Series\n\nLecture held
in Cardwell 101.\n\nAbstract\nWe are always trying to optimize things in p
ractice: taking the shortest path\, maximizing productivity\, minimizing e
nergy spent. A class of elliptic PDEs would have us minimizing energy. For
example\, when $1 < p < \\infty$\, minimizing the energy $\\int_\\Omega |
\\nabla u|^p d\\mu$ subject to some boundary constraint is equivalent to s
olving the problem $-\\Delta_p u=0$ in $\\Omega$ with Dirichlet boundary d
ata. Solutions to this problem are now relatively well-understood. When $p
=1$\, the minimization problem becomes purely geometric\, and is related t
o minimal surfaces. However\, the corresponding Dirichlet type condition c
an fail for this problem. We will discuss various ways of re-formulating t
he Dirichlet problem to obtain reasonable solutions\, even in weighted Euc
lidean settings.\n
LOCATION:https://researchseminars.org/talk/1123112229/11/
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