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BEGIN:VEVENT
SUMMARY:Austin Christian (Georgia Institute of Technology)
DTSTART:20220907T213000Z
DTEND:20220907T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/1
DESCRIPTION:Title: Symplectic fillings of lens spaces\nby Austin Christian (Ge
orgia Institute of Technology) as part of Early Career Math Colloquium\n\n
\nAbstract\nIn physics\, the holographic principle suggests that some mani
folds are completely determined by their boundaries --- that the manifold
is somehow a projection of information which is encoded on the boundary.
We will explore this idea in the particular case of symplectic manifolds w
ith contact boundaries\, asking for a count of the exact symplectic fillin
gs of a given contact manifold. Much of our time will be spent pretending
to define these words\, and eventually stating a precise question. Time
permitting\, we will discuss the answer to our question\, which is given b
y joint work with Li\, and was independently obtained by Etnyre-Roy. We w
ill do our best to minimize technical prerequisites.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fizay-Noah Lee (Princeton University)
DTSTART:20220914T213000Z
DTEND:20220914T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/2
DESCRIPTION:Title: Long time behavior of the Nernst-Planck-Navier-Stokes system on
a bounded domain\nby Fizay-Noah Lee (Princeton University) as part of
Early Career Math Colloquium\n\n\nAbstract\nThe Nernst-Planck-Navier-Stok
es (NPNS) system models electrodiffusion of ions in a fluid. After a brief
overview of the state of the art of the relevant global regularity theory
\, we discuss the long time behavior of solutions. In the case of equilibr
ium boundary conditions\, solutions converge to unique steady states\, whi
ch approximately satisfy pointwise electroneutrality in the interior\, awa
y from the boundaries. In the case of nonequilibrium boundary conditions\,
characterized by general Dirichlet boundary conditions for the ionic conc
entrations\, we show that electroneutrality continues to hold in a space-t
ime averaged sense\, for large times. Time permitting\, we also discuss th
e existence of a finite dimensional global attractor for the solution map
to the NPNS system. The topics discussed include joint work with Peter Con
stantin and Mihaela Ignatova.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanye Zhu (Brown University)
DTSTART:20221026T213000Z
DTEND:20221026T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/3
DESCRIPTION:Title: Gradient estimates for singular $p$-Laplace type equations with
measure data\nby Hanye Zhu (Brown University) as part of Early Career
Math Colloquium\n\n\nAbstract\nWe will discuss recent results on gradient
estimates for solutions to singular quasilinear elliptic (or parabolic) e
quations with measure data\, whose prototype is given by the elliptic (or
parabolic) $p$-Laplace equation $-\\Delta_p u=\\mu$ (or $u_t-\\Delta_p u=\
\mu$) with $p\\in(1\,2)$. For these singular nonlinear equations\, we obta
in pointwise gradient estimates via linear elliptic (or parabolic) Riesz p
otential and gradient continuity results via certain assumptions on the li
near Riesz potential. This is based on joint works with Hongjie Dong.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Brusca (New Jersey Institute of Technology)
DTSTART:20221102T213000Z
DTEND:20221102T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/4
DESCRIPTION:Title: Efficient Numerical Methods For The Monge-Ampère Equation\
nby Jake Brusca (New Jersey Institute of Technology) as part of Early Care
er Math Colloquium\n\n\nAbstract\nThe Monge-Ampère equation is a fully no
nlinear degenerate elliptic PDE used in a large number of applications inc
luding mesh generation\, optical design\, and medical image processing. Th
e development of convergent numerical methods for this PDE has been guided
by the Barles and Souganidis framework\, which guarantees a monotone sche
me will converge to the unique weak (viscosity) solution provided the PDE
satisfies a comparison principle. However\, monotone scemes rely on wide s
tencils\, which traditionally suffer from high computational costs and low
accuracy due. We will address these challenges by 1) introducing an impro
ved monotone discretization using an integral representation of the Monge-
Ampère operator and 2) developing highly parallelizable nonlinear root fi
nders for monotone schemes. This presentation is based on joint work with
Tadanaga Takahashi\, Yassine Boubendir\, and Brittany Hamfeldt.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen Feng (Niagara University)
DTSTART:20221130T213000Z
DTEND:20221130T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/5
DESCRIPTION:Title: Nonlinear stability and long time behavior for the 2D incompres
sible MHD system with partial dissipation\nby Wen Feng (Niagara Univer
sity) as part of Early Career Math Colloquium\n\n\nAbstract\nIn this talk\
, we will discuss the decay results on a 2D magnetohydrodynamic (MHD) syst
em with only vertical dissipation or horizontal dissipation. For vertical
dissipation\, we show that the H^2-norm of any perturbation near a backgro
und magnetic field actually decays algebraically in time. Mathematically t
his result along with its proof offers a new and effective approach to the
large-time behavior on partially dissipated systems. For horizontal dissi
pation\, we show the stability result on the perturbations near a backgrou
nd magnetic field. In addition\, the solution converges to its horizontal
average asymptotically.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Pasqualotto (Duke University)
DTSTART:20221116T213000Z
DTEND:20221116T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/6
DESCRIPTION:Title: Two topics in self-similar singularity formation\nby Federi
co Pasqualotto (Duke University) as part of Early Career Math Colloquium\n
\n\nAbstract\nSelf-similarity is a powerful tool to investigate the "unive
rsal" behavior of certain nonlinear PDEs in which coherent structures (suc
h as singularities) appear. In this talk\, I will describe two results in
which self-similarity plays a crucial role.\n\nThe first result\, joint wi
th Sung-Jin Oh\, concerns singularity formation for a wide class of one-di
mensional models. We construct approximately self-similar "shock forming"
solutions to a class of dispersive and dissipative perturbations of the cl
assical Burgers equation. This class includes the Whitham equation arising
in water waves and the fractional KdV equation with dispersive term of or
der $\\alpha \\in [0\,1)$. Our result appears to be the first construction
of gradient blow-up for fractional KdV in the range $\\alpha \\in [2/3\,1
)$.\n\nIn the second result\, joint with Tarek Elgindi\, we focus on the a
xisymmetric 3D Euler equations in the whole space $\\mathbb{R}^3$ (and its
2D approximate model\, the Boussinesq system) . We provide a novel mechan
ism for self-similar singularity formation starting from $C^{1\,\\alpha}$
initial data with non-trivial swirl. Unlike previous constructions\, the b
low-up happens away from the symmetry axis.\n\nhttps://arizona.zoom.us/j/8
2763762677\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Havva Yoldaş (TU Delft)
DTSTART:20221123T213000Z
DTEND:20221123T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/7
DESCRIPTION:Title: A variational approach to the existence problem for a degenerat
e cross-diffusion model\nby Havva Yoldaş (TU Delft) as part of Early
Career Math Colloquium\n\n\nAbstract\nIn this talk\, we look at a cross-di
ffusion system consisting of two Fokker-Planck equations where the gradien
t of the density for each species acts as a potential for the other one. T
he system is the gradient flow for the Wasserstein distance of a functiona
l which is not lower semi-continuous\, thus it is not well-posed. We then
compute the convexification of the integral and provide an existence proof
in a suitable sense for the gradient flow of the corresponding relaxed fu
nctional. The talk is based on a joint work with R. Ducasse and F. Santamb
rogio (Calc Var PDE\, 2022).\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samy Wu Fung (Colorado School of Mines)
DTSTART:20220921T213000Z
DTEND:20220921T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/8
DESCRIPTION:Title: Global Solutions to Nonconvex Problems by Evolution of Hamilton
-Jacobi PDEs\nby Samy Wu Fung (Colorado School of Mines) as part of Ea
rly Career Math Colloquium\n\n\nAbstract\nComputing tasks may often be pos
ed as optimization problems. The objective functions for real-world scenar
ios are often nonconvex and/or nondifferentiable. State-of-the-art methods
for solving these problems typically only guarantee convergence to local
minima. This work presents Hamilton-Jacobi-based Moreau Adaptive Descent (
HJ-MAD)\, a zero-order algorithm with guaranteed convergence to global min
ima\, assuming continuity of the objective function. The core idea is to c
ompute gradients of the Moreau envelope of the objective (which is “piec
e-wise convex”) with adaptive smoothing parameters. Gradients of the Mor
eau envelope are approximated by employing the Hopf-Lax formula for the vi
scous Hamilton Jacobi equation. Provided numerical examples illustrate glo
bal convergence.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Miller (Oden Institute at UT Austin)
DTSTART:20221109T213000Z
DTEND:20221109T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/10
DESCRIPTION:Title: Ensuring Exploration in Graph-Based Active Learning\nby Ke
vin Miller (Oden Institute at UT Austin) as part of Early Career Math Coll
oquium\n\n\nAbstract\nUncertainty sampling has traditionally been the de f
acto\, simplest acquisition function for active learning in semi-supervise
d learning. Comparatively cheap to compute and straightforward to interpre
t\, uncertainty sampling has been known to suffer from myopic sampling bia
s that fails to properly explore the extent of geometric structure of the
dataset prior to exploiting learning decision boundaries. As such\, most w
ork in active learning for graph-based learning has focused on the design
of more intricate acquisition functions that are explorative in nature\, t
hough are almost always more costly to compute. We show that exploration a
nd exploitation in graph-based semi-supervised learning can be achieved by
ensuring that the underlying graph-based model reflects uncertainty at un
labeled nodes that in turn captures the underlying clustering structure of
the dataset. We present theoretical results and empirical evidence to dem
onstrate that Poisson reweighted Laplacian learning\, which has a well-def
ined continuum limit model\, allows us to ensure exploration by simply app
lying a specific form of uncertainty sampling.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evan Miller (University of British Columbia and the PIMS)
DTSTART:20221019T213000Z
DTEND:20221019T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/11
DESCRIPTION:Title: On the regularity of the axisymmetric\, swirl-free solutions o
f the Euler equation in four and higher dimensions\nby Evan Miller (Un
iversity of British Columbia and the PIMS) as part of Early Career Math Co
lloquium\n\n\nAbstract\nIn this talk\, we will discuss the axisymmetric\,
swirl-free Euler\nequation in four and higher dimensions. We will show tha
t in four and\nhigher dimensions the axisymmetric\, swirl-free Euler equat
ion has\nproperties which could allow finite-time singularity formation of
a form\nthat is excluded in three dimensions. We will also consider a mod
el\nequation that is obtained by taking the infinite-dimensional limit of
the\nvorticity equation in this setup. This model exhibits finite-time blo
wup of\na Burgers shock type. The blowup result for the infinite dimension
al model\nequation heavily suggests that smooth solutions of the Euler equ
ation\nexhibit finite-time blowup in sufficiently high dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo Bongarti (Weierstrass Institute for Applied Analysis and S
tochastics)
DTSTART:20221012T213000Z
DTEND:20221012T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/12
DESCRIPTION:Title: Boundary stabilization of nonlinear dynamics of acoustics wave
s under the JMGT equation\nby Marcelo Bongarti (Weierstrass Institute
for Applied Analysis and Stochastics) as part of Early Career Math Colloq
uium\n\n\nAbstract\nThe Jordan–Morse–Gibbson–Thompson (JMGT) equatio
n is a third-order in time partial differential equation (PDE) model descr
ibing nonlinear propagation of sound in an acoustic medium. Its study is m
otivated by a large array of applications arising in engineering and medic
al sciences\, especially high intensity focused ultrasound (HIFU) technolo
gies. The important feature is that the model avoids the infinite speed of
propagation paradox associated with the classical second order in time eq
uation known as Westervelt’s equation. The third order in time derivativ
e is due to the shift from parabolic to the hyperbolic model\, the latter
being a singular perturbation (w.r.t the thermal time relaxation) of the f
ormer. In this talk we will present several results pertinent to the model
\, mostly from the point of view of boundary stabilization. These include:
(i) local and global wellposedness\, (ii) asymptotic analysis when the th
ermal relaxation parameter vanishes\, and (iii) boundary stabillizability
of JMGT in the critical and degenerate case.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuzhe Zhu (University of Cambridge)
DTSTART:20230201T213000Z
DTEND:20230201T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/13
DESCRIPTION:Title: Hölder regularity up to the boundary for kinetic equations\nby Yuzhe Zhu (University of Cambridge) as part of Early Career Math Col
loquium\n\n\nAbstract\nWe consider the kinetic Fokker-Planck equation with
rough coefficients in a bounded spatial domain. We will discuss the regul
arization property of the solutions under inflow or reflection boundary co
nditions\, and its application to nonlinear kinetic models.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Zhiyuan Zhang (Courant Institute)
DTSTART:20230405T213000Z
DTEND:20230405T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/14
DESCRIPTION:Title: Outflow Problems in Plasmas and Fluids\nby Katherine Zhiyu
an Zhang (Courant Institute) as part of Early Career Math Colloquium\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Strikwerda (North Carolina State University)
DTSTART:20230208T213000Z
DTEND:20230208T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/15
DESCRIPTION:Title: Optimal Control in Fluid Flows through Deformable Porous Media
\nby Sarah Strikwerda (North Carolina State University) as part of Ear
ly Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mengxuan Yang (UC Berkeley)
DTSTART:20230329T213000Z
DTEND:20230329T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/16
DESCRIPTION:Title: Magic angles and high Chern number flat band of a twisted mult
ilayer graphene model\nby Mengxuan Yang (UC Berkeley) as part of Early
Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xueying Yu (University of Washington)
DTSTART:20230412T213000Z
DTEND:20230412T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/17
DESCRIPTION:Title: Modified scattering of cubic NLS on waveguide manifolds\nb
y Xueying Yu (University of Washington) as part of Early Career Math Collo
quium\n\n\nAbstract\nIn this talk\, we will discuss uniqueness properties
of solutions to the linear generalized fourth-order Schr\\"odinger equatio
ns. We show that a solution with fast enough decay in certain Sobolev spac
es at two different times has to be trivial. This is a joint work with Zac
hary Lee.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quyuan Lin (UC Santa Barbara)
DTSTART:20230322T213000Z
DTEND:20230322T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/19
DESCRIPTION:Title: Primitive equations: mathematical analysis and machine learnin
g algorithm\nby Quyuan Lin (UC Santa Barbara) as part of Early Career
Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elliot Cartee (University of Chicago)
DTSTART:20230215T213000Z
DTEND:20230215T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/20
DESCRIPTION:Title: Quantifying and Managing Uncertainty in Piecewise-Deterministi
c Markov Processes\nby Elliot Cartee (University of Chicago) as part o
f Early Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lindstrom (University of Texas Rio Grande Valley)
DTSTART:20230301T213000Z
DTEND:20230301T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/21
DESCRIPTION:Title: Anomalies and Commonalities\nby Michael Lindstrom (Univers
ity of Texas Rio Grande Valley) as part of Early Career Math Colloquium\n\
n\nAbstract\nThis talk will cover two research projects. In the first\, we
seek to identify contextual anomalies among time series with possible mis
sing data. By generalizing Kernel Density Estimation to Hilbert Spaces\, w
e develop tools to identify anomalous time series\, test them against comp
eting methods on synthetic data\, and then employ the tools to identify an
omalous event records among airplane fleets. In the second project\, we co
mbine topic modelling through Nonnegative Matrix Factorization and regress
ion on a continuous observation variable. Previous authors have covered th
e case of topic modelling for classification\; here\, we show the idea can
be extended to regression\, applying it to Rate My Professors reviews and
predicting an instructors mean rating from the written comments. We ident
ify interpretable groups of words (topics)\, such that their level of repr
esentation in a review has a quantifiable effect on the associated rating.
\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yotam Yaniv (UCLA)
DTSTART:20230315T213000Z
DTEND:20230315T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/22
DESCRIPTION:Title: Construction of Hierarchically Semi-Separable Matrix Represent
ation using Adaptive Johnson-Lindenstrauss Sketching\nby Yotam Yaniv (
UCLA) as part of Early Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucio Galeati (EPFL)
DTSTART:20230419T213000Z
DTEND:20230419T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/23
DESCRIPTION:Title: Regularisation by transport noise for 2D fluid dynamics equati
ons\nby Lucio Galeati (EPFL) as part of Early Career Math Colloquium\n
\n\nAbstract\nA major open problem in fluid dynamics is to understand whet
her solutions to 2D incompressible Euler equations with $L^p$-valued vorti
city are unique\, for some $p\\in [1\,\\infty)$. A related question\, more
probabilistic in flavour\, is whether one can find a physically meaningfu
l noise restoring well-posedness of the PDE.\nIn this talk I will present
some recent advances on the latter problem\, for a class of slightly regul
arised 2D Euler-type equations (specifically\, logEuler and hypodissipativ
e Navier-Stokes)\, in the presence of a rough Kraichnan-type noise\, model
ling the small scales of a turbulent fluid\; uniqueness in law can then be
shown for solutions with $L^2$-valued vorticity.\nBased on an ongoing joi
nt work with Dejun Luo (Beijing).\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brennan Sprinkle (Colorado School of Mines)
DTSTART:20230426T213000Z
DTEND:20230426T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/24
DESCRIPTION:Title: Driving magnetic emulsions with flat tires\nby Brennan Spr
inkle (Colorado School of Mines) as part of Early Career Math Colloquium\n
\n\nAbstract\nI'll discuss the rolling of active Pickering emulsions - sma
ll droplets (~10-100 um) covered in smaller (~1um) active particles that c
an be rolled along a surface by an external\, AC magnetic field. Curiously
\, these droplets roll much faster and more efficiently when they have a l
arger area of contact with the confining surface. I'll describe experiment
s done by collaborators to validate this behavior and numerical simulation
s that I developed to quantify it.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khoa Le (University of Leeds)
DTSTART:20230503T213000Z
DTEND:20230503T223000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/25
DESCRIPTION:Title: Stochastic heat equation with distributional drift\nby Kho
a Le (University of Leeds) as part of Early Career Math Colloquium\n\n\nAb
stract\nWe study stochastic heat equation with a distributional drift b by
space-time white noise. We introduce a notion of a solution to this equat
ion and obtain the existence and uniqueness of a strong solution whenever
b belongs to a suitable Besov space which includes measures.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Hernandez (University of Maine)
DTSTART:20231023T190000Z
DTEND:20231023T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/26
DESCRIPTION:Title: Splash singularities and magnetic field squeezing for the 2D i
deal MHD equations\nby Matthew Hernandez (University of Maine) as part
of Early Career Math Colloquium\n\n\nAbstract\nA splash singularity is sa
id to occur in the problem of a free boundary fluid model when the boundar
y of a fluid starts out as a smooth\, non-self-intersecting curve\, but tw
o once-distant pieces of the boundary crash into each other in finite time
. For the ideal MHD equations\, such a phenomenon forces a magnetic field
outside of the fluid either to vanish or to get squeezed as the moment of
splash approaches. In this talk we will discuss the construction of splash
singularity solutions to the ideal MHD equations for which the external m
agnetic field gets squeezed but does not vanish as the splash occurs.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Dolce (EPFL)
DTSTART:20231120T200000Z
DTEND:20231120T210000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/27
DESCRIPTION:by Michele Dolce (EPFL) as part of Early Career Math Colloquiu
m\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel McKenzie (Colorado School of Mines)
DTSTART:20230918T190000Z
DTEND:20230918T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/28
DESCRIPTION:Title: Sparse Gradients in Derivative-Free Optimization\nby Danie
l McKenzie (Colorado School of Mines) as part of Early Career Math Colloqu
ium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marissa Gee (Cornell University)
DTSTART:20231009T190000Z
DTEND:20231009T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/29
DESCRIPTION:by Marissa Gee (Cornell University) as part of Early Career Ma
th Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen Feng (Niagara University)
DTSTART:20231106T200000Z
DTEND:20231106T210000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/30
DESCRIPTION:Title: Nonlinear stability for the incompressible MHD system and Oldr
oyd-B models\nby Wen Feng (Niagara University) as part of Early Career
Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jin Tan (Cergy Paris University)
DTSTART:20231113T200000Z
DTEND:20231113T210000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/31
DESCRIPTION:Title: Inhomogeneous incompressible Navier-Stokes equations in vacuum
: the whole space case\nby Jin Tan (Cergy Paris University) as part of
Early Career Math Colloquium\n\n\nAbstract\nIn a famous book of P.-L. Lio
ns\, global existence results for finite energy weak solutions\nof the inh
omogeneous incompressible Navier-Stokes equations (INS) were proved withou
t assuming positive lower bounds on the initial density. In this talk\, I
will talk about some regularity and uniqueness results of Lions’ weak so
lutions for (INS) supplemented with additional regularity only for initial
velocity\, in the whole space case. As an application\, I will explain ho
w these results enable us to answer Lions’ question\, which concerns pre
servation of boundary regularity of density patch and vacuum bubble in the
whole space. The talk is based on a very recent work with my mentor Chris
tophe Prange (CY Cergy Paris University).\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Albert Ai (University of Wisconsin-Madison)
DTSTART:20230925T190000Z
DTEND:20230925T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/33
DESCRIPTION:Title: Low regularity solutions for quasilinear PDEs\nby Albert A
i (University of Wisconsin-Madison) as part of Early Career Math Colloquiu
m\n\n\nAbstract\nIn this talk\, we will consider the low regularity well-p
osedness problem for a pair of quasilinear dispersive PDEs: the nonlinear
wave equation\, and the water waves equations. Two classical methods\, ene
rgy estimates and Strichartz estimates\, have historically yielded substan
tial but partial results toward advancing the low regularity theory. We wi
ll see how\, using a special structure of the equations known as a normal
form structure\, combined with tools from harmonic and microlocal analysis
\, we can refine these classical methods to improve the known results for
low regularity well-posedness.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margherita Zanella (Polytechnic University of Milan\,)
DTSTART:20231002T190000Z
DTEND:20231002T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/34
DESCRIPTION:Title: Uniqueness of the invariant measure and asymptotic stability f
or 2 the 2D Navier-Stokes equations with multiplicative noise\nby Marg
herita Zanella (Polytechnic University of Milan\,) as part of Early Career
Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marissa Gee (Cornell University)
DTSTART:20231016T190000Z
DTEND:20231016T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/35
DESCRIPTION:Title: Optimally Navigating a Piecewise-Deterministic World\nby M
arissa Gee (Cornell University) as part of Early Career Math Colloquium\n\
n\nAbstract\nPiecewise-deterministic Markov processes are a special class\
nof hybrid systems in which deterministic dynamics are punctuated by\nstoc
hastic jumps. In this talk\, we will investigate applications of\nthis fra
mework to optimal path planning problems. Deterministic path\nplanning is
a well-studied problem\, and many efficient methods exist\nfor determining
the optimal policies. However\, computational\nchallenges can arise when
applying these methods to the\npiecewise-deterministic setting. We will ex
plore various motivating\napplications\, derive Hamilton-Jacobi-Bellman PD
Es that govern the\noptimal policies\, and address some of the numerical c
hallenges posed\nby solving these problems.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bohyun Kim (University of Utah)
DTSTART:20231030T190000Z
DTEND:20231030T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/36
DESCRIPTION:Title: A positivity-preserving numerical method for a thin liquid fil
m on a vertical cylindrical fiber\nby Bohyun Kim (University of Utah)
as part of Early Career Math Colloquium\n\n\nAbstract\nWhen a thin liquid
film flows down on a vertical fiber\, one can observe the complex and capt
ivating interfacial dynamics of an unsteady flow. Such dynamics are applic
able in various fluid experiments due to their high surface area-to-volume
ratio. Recent studies verified that when the flow undergoes regime transi
tions\, the magnitude of the film thickness changes dramatically\, making
numerical simulations challenging. In this talk\, we present a computation
ally efficient numerical method that can maintain the positivity of the fi
lm thickness as well as conserve the volume of the fluid under the coarse
mesh setting. A series of comparisons to laboratory experiments and previo
usly proposed numerical methods supports the validity of our numerical met
hod. We also prove that our method is second-order consistent in space and
satisfies the entropy estimate.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Agresti (Delft University of Technology)
DTSTART:20231204T200000Z
DTEND:20231204T210000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/37
DESCRIPTION:Title: Reaction-diffusion equations with transport noise\nby Anto
nio Agresti (Delft University of Technology) as part of Early Career Math
Colloquium\n\n\nAbstract\nReaction-diffusion equations (RDEs) arise in sev
eral physical and engineering applications as they can be used to model ma
ny systems of practical interest\, such as chemical reactions and populati
on dynamics. RDEs are mathematically described by a system of parabolic PD
Es with polynomial nonlinearities of high degree. In applications\, transp
ort noise is often used to model the effect of a turbulent flow advecting
reactants or to take into account local effects in population dynamics. Ph
ysically relevant transport noises have typically low regularity in space.
It is a challenging task to handle transport noise and high-order polynom
ial nonlinearities at the same time. In this talk I will review some recen
t results on local/global well-posedness of RDEs with transport noise. The
keys to overcome the difficulties mentioned above are the use of $L^p$ th
eory for stochastic PDEs and the recent theory of critical spaces for stoc
hastic evolution equations. If time allows\, then I will discuss how trans
port type noise can delay and/or suppress singularities in RDEs. Based on
joint works with M. Veraar (TU Delft).\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:None
DTSTART:20230911T190000Z
DTEND:20230911T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/38
DESCRIPTION:by None as part of Early Career Math Colloquium\n\nAbstract: T
BA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dwight Williams II (Morgan State University)
DTSTART:20231127T200000Z
DTEND:20231127T210000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/41
DESCRIPTION:Title: Extremal equations \\& algebraic methods\nby Dwight Willia
ms II (Morgan State University) as part of Early Career Math Colloquium\n\
n\nAbstract\nThe audience is invited to a perspective on reduction algebra
s\, including algebraic methods described by Zhelobenko to find solutions
of extremal equations. The general idea is to realize the solution space o
f a system of equations as the representation space of the system's symmet
ry algebra (reduction algebra). In particular\, the representation-theoret
ic definition of singular/primitive vectors induces a system of extremal e
quations\; similarly\, mathematical models of physical phenomena are chara
cterized by extremal equations. Two reduction algebras arising from solvin
g extremal equations are given by:\\\\\n\\begin{enumerate}\n\\item Conside
ring the Laplace operator in dimension $n$ as an element of the $n$th Weyl
algebra via a mapping from the Lie algebra $\\mathfrak{sl}(2)$\n\\item De
termining primitive vectors in tensor product representations of the Lie s
uperalgebra $\\mathfrak{osp}(1|2)$ \\\\\n\\end{enumerate}\nThe speaker's c
ollaboration with Jonas T. Hartwig has found success in the second route w
ith the introduction of the diagonal reduction superalgebra of $\\mathfrak
{osp}(1|2)$. The first example runs throughout the writings of Zhelobenko
and was the subject of Irmak Bukey's undergraduate thesis\, as supervised
by the speaker.\nThe pursuit of more examples of reduction algebras and th
eir associated representation spaces as solution spaces to extremal equati
ons is the focus of multiple ongoing projects.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Phelps (Temple University)
DTSTART:20240208T200000Z
DTEND:20240208T210000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/42
DESCRIPTION:Title: Asymptotic properties and separation rates for local energy so
lutions to the Navier-Stokes equations\nby Patrick Phelps (Temple Univ
ersity) as part of Early Career Math Colloquium\n\n\nAbstract\nWe present
recent results on spatial decay and properties of non-uniqueness for the 3
D Navier-Stokes equations. We show asymptotics for the ‘non-linear’ pa
rt of scaling invariant flows with data in subcritical classes. Motivated
by recent work on non-uniqueness\, we investigate how non-uniqueness of th
e velocity field would evolve in time in the local energy class. Specifica
lly\, by extending our subcritical asymptotics to approximations by Picard
iterates\, we may bound the rate at which two solutions\, evolving from t
he same data\, may separate pointwise. We conclude by extending this separ
ation rate to solutions with no scaling assumption. Joint work with Zachar
y Bradshaw.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amélie Loher (University of Cambridge)
DTSTART:20240222T200000Z
DTEND:20240222T210000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/44
DESCRIPTION:by Amélie Loher (University of Cambridge) as part of Early Ca
reer Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Liu (Texas A&M University)
DTSTART:20240229T200000Z
DTEND:20240229T210000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/45
DESCRIPTION:by Xin Liu (Texas A&M University) as part of Early Career Math
Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chunyin Siu (Cornell University)
DTSTART:20240314T190000Z
DTEND:20240314T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/46
DESCRIPTION:Title: Detecting Weak Topological Signals in Noisy Environments\n
by Chunyin Siu (Cornell University) as part of Early Career Math Colloquiu
m\n\n\nAbstract\nTopological signals refer to global nonlinear structures
in datasets like components\, cycles and holes. While traditional approach
es are well adapted to identifying strong topological signals in clean dat
asets\, they tend to struggle when the signal-to-noise ratio is low. We in
troduce a novel method to distinguish\, from noise\, small holes surrounde
d by high-density regions of a probability density function. The proposed
method is robust against additive noise and outliers. We will introduce th
e method after a high-level overview of topological structures. Numerical
experiments will be presented to demonstrate the proposed method's utility
. This is joint work with Gennady Samorodnitsky\, Christina Lee Yu and And
rey Yao\, and it is based on the preprint https://arxiv.org/abs/2204.07821
\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhongkai Tao (University of California\, Berkeley)
DTSTART:20240328T190000Z
DTEND:20240328T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/47
DESCRIPTION:by Zhongkai Tao (University of California\, Berkeley) as part
of Early Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Rosati (University of Warwick)
DTSTART:20240404T190000Z
DTEND:20240404T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/48
DESCRIPTION:by Tommaso Rosati (University of Warwick) as part of Early Car
eer Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurélie Paull (Institut Élie Cartan de Lorraine)
DTSTART:20240411T190000Z
DTEND:20240411T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/49
DESCRIPTION:by Aurélie Paull (Institut Élie Cartan de Lorraine) as part
of Early Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaxin Jin (Ohio State University)
DTSTART:20240418T190000Z
DTEND:20240418T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/50
DESCRIPTION:by Jiaxin Jin (Ohio State University) as part of Early Career
Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yupei Huang (Duke University)
DTSTART:20240425T190000Z
DTEND:20240425T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/51
DESCRIPTION:by Yupei Huang (Duke University) as part of Early Career Math
Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yeor Hafouta (University of Florida)
DTSTART:20240502T190000Z
DTEND:20240502T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/52
DESCRIPTION:by Yeor Hafouta (University of Florida) as part of Early Caree
r Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Son Tu (Michigan State University)
DTSTART:20240321T190000Z
DTEND:20240321T200000Z
DTSTAMP:20260404T111324Z
UID:EarlyCareer/53
DESCRIPTION:Title: Properties of the effective Hamiltonian and homogenization of
the Hamilton-Jacobi equation\nby Son Tu (Michigan State University) as
part of Early Career Math Colloquium\n\n\nAbstract\nThe homogenization of
Hamilton-Jacobi equations in the periodic setting was pioneered by Lions\
, Papanicolaou\, and Varadhan in the 1980s. However\, understanding the in
tricate properties of the effective Hamiltonian and its impact on the homo
genization limit across various settings remains a substantial open proble
m. In this presentation\, we will discuss recent developments that highlig
ht a connection between this phenomenon and weak KAM theory on a qualitati
ve level\, as well as present some quantitative results.\n
LOCATION:https://stable.researchseminars.org/talk/EarlyCareer/53/
END:VEVENT
END:VCALENDAR