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BEGIN:VEVENT
SUMMARY:Austin Christian (Georgia Institute of Technology)
DTSTART;VALUE=DATE-TIME:20220907T213000Z
DTEND;VALUE=DATE-TIME:20220907T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/1
DESCRIPTION:Title: Symplectic fillings of lens spaces\nby Austin Christian (Georgia I
nstitute of Technology) as part of Early Career Math Colloquium\n\n\nAbstr
act\nIn physics\, the holographic principle suggests that some manifolds a
re completely determined by their boundaries --- that the manifold is some
how a projection of information which is encoded on the boundary. We will
explore this idea in the particular case of symplectic manifolds with con
tact boundaries\, asking for a count of the exact symplectic fillings of a
given contact manifold. Much of our time will be spent pretending to def
ine these words\, and eventually stating a precise question. Time permitt
ing\, we will discuss the answer to our question\, which is given by joint
work with Li\, and was independently obtained by Etnyre-Roy. We will do
our best to minimize technical prerequisites.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fizay-Noah Lee (Princeton University)
DTSTART;VALUE=DATE-TIME:20220914T213000Z
DTEND;VALUE=DATE-TIME:20220914T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/2
DESCRIPTION:Title: Long time behavior of the Nernst-Planck-Navier-Stokes system on a boun
ded domain\nby Fizay-Noah Lee (Princeton University) as part of Early
Career Math Colloquium\n\n\nAbstract\nThe Nernst-Planck-Navier-Stokes (NPN
S) system models electrodiffusion of ions in a fluid. After a brief overvi
ew of the state of the art of the relevant global regularity theory\, we d
iscuss the long time behavior of solutions. In the case of equilibrium bou
ndary conditions\, solutions converge to unique steady states\, which appr
oximately satisfy pointwise electroneutrality in the interior\, away from
the boundaries. In the case of nonequilibrium boundary conditions\, charac
terized by general Dirichlet boundary conditions for the ionic concentrati
ons\, we show that electroneutrality continues to hold in a space-time ave
raged sense\, for large times. Time permitting\, we also discuss the exist
ence of a finite dimensional global attractor for the solution map to the
NPNS system. The topics discussed include joint work with Peter Constantin
and Mihaela Ignatova.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanye Zhu (Brown University)
DTSTART;VALUE=DATE-TIME:20221026T213000Z
DTEND;VALUE=DATE-TIME:20221026T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/3
DESCRIPTION:Title: Gradient estimates for singular $p$-Laplace type equations with measur
e data\nby Hanye Zhu (Brown University) as part of Early Career Math C
olloquium\n\n\nAbstract\nWe will discuss recent results on gradient estima
tes for solutions to singular quasilinear elliptic (or parabolic) equation
s with measure data\, whose prototype is given by the elliptic (or parabol
ic) $p$-Laplace equation $-\\Delta_p u=\\mu$ (or $u_t-\\Delta_p u=\\mu$) w
ith $p\\in(1\,2)$. For these singular nonlinear equations\, we obtain poin
twise gradient estimates via linear elliptic (or parabolic) Riesz potentia
l and gradient continuity results via certain assumptions on the linear Ri
esz potential. This is based on joint works with Hongjie Dong.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Brusca (New Jersey Institute of Technology)
DTSTART;VALUE=DATE-TIME:20221102T213000Z
DTEND;VALUE=DATE-TIME:20221102T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/4
DESCRIPTION:Title: Efficient Numerical Methods For The Monge-Ampère Equation\nby Jak
e Brusca (New Jersey Institute of Technology) as part of Early Career Math
Colloquium\n\n\nAbstract\nThe Monge-Ampère equation is a fully nonlinear
degenerate elliptic PDE used in a large number of applications including
mesh generation\, optical design\, and medical image processing. The devel
opment of convergent numerical methods for this PDE has been guided by the
Barles and Souganidis framework\, which guarantees a monotone scheme will
converge to the unique weak (viscosity) solution provided the PDE satisfi
es a comparison principle. However\, monotone scemes rely on wide stencils
\, which traditionally suffer from high computational costs and low accura
cy due. We will address these challenges by 1) introducing an improved mon
otone discretization using an integral representation of the Monge-Ampère
operator and 2) developing highly parallelizable nonlinear root finders f
or monotone schemes. This presentation is based on joint work with Tadanag
a Takahashi\, Yassine Boubendir\, and Brittany Hamfeldt.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen Feng (Niagara University)
DTSTART;VALUE=DATE-TIME:20221130T213000Z
DTEND;VALUE=DATE-TIME:20221130T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/5
DESCRIPTION:Title: Nonlinear stability and long time behavior for the 2D incompressible M
HD system with partial dissipation\nby Wen Feng (Niagara University) a
s part of Early Career Math Colloquium\n\n\nAbstract\nIn this talk\, we wi
ll discuss the decay results on a 2D magnetohydrodynamic (MHD) system with
only vertical dissipation or horizontal dissipation. For vertical dissipa
tion\, we show that the H^2-norm of any perturbation near a background mag
netic field actually decays algebraically in time. Mathematically this res
ult along with its proof offers a new and effective approach to the large-
time behavior on partially dissipated systems. For horizontal dissipation\
, we show the stability result on the perturbations near a background magn
etic field. In addition\, the solution converges to its horizontal average
asymptotically.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Pasqualotto (Duke University)
DTSTART;VALUE=DATE-TIME:20221116T213000Z
DTEND;VALUE=DATE-TIME:20221116T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/6
DESCRIPTION:Title: Two topics in self-similar singularity formation\nby Federico Pasq
ualotto (Duke University) as part of Early Career Math Colloquium\n\n\nAbs
tract\nSelf-similarity is a powerful tool to investigate the "universal" b
ehavior of certain nonlinear PDEs in which coherent structures (such as si
ngularities) appear. In this talk\, I will describe two results in which s
elf-similarity plays a crucial role.\n\nThe first result\, joint with Sung
-Jin Oh\, concerns singularity formation for a wide class of one-dimension
al models. We construct approximately self-similar "shock forming" solutio
ns to a class of dispersive and dissipative perturbations of the classical
Burgers equation. This class includes the Whitham equation arising in wat
er waves and the fractional KdV equation with dispersive term of order $\\
alpha \\in [0\,1)$. Our result appears to be the first construction of gra
dient blow-up for fractional KdV in the range $\\alpha \\in [2/3\,1)$.\n\n
In the second result\, joint with Tarek Elgindi\, we focus on the axisymme
tric 3D Euler equations in the whole space $\\mathbb{R}^3$ (and its 2D app
roximate model\, the Boussinesq system) . We provide a novel mechanism for
self-similar singularity formation starting from $C^{1\,\\alpha}$ initial
data with non-trivial swirl. Unlike previous constructions\, the blow-up
happens away from the symmetry axis.\n\nhttps://arizona.zoom.us/j/82763762
677\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Havva Yoldaş (TU Delft)
DTSTART;VALUE=DATE-TIME:20221123T213000Z
DTEND;VALUE=DATE-TIME:20221123T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/7
DESCRIPTION:Title: A variational approach to the existence problem for a degenerate 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-diffusion
system consisting of two Fokker-Planck equations where the gradient of th
e density for each species acts as a potential for the other one. The syst
em is the gradient flow for the Wasserstein distance of a functional 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 s
uitable sense for the gradient flow of the corresponding relaxed functiona
l. The talk is based on a joint work with R. Ducasse and F. Santambrogio (
Calc Var PDE\, 2022).\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samy Wu Fung (Colorado School of Mines)
DTSTART;VALUE=DATE-TIME:20220921T213000Z
DTEND;VALUE=DATE-TIME:20220921T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
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 Early Car
eer Math Colloquium\n\n\nAbstract\nComputing tasks may often be posed as o
ptimization problems. The objective functions for real-world scenarios are
often nonconvex and/or nondifferentiable. State-of-the-art methods for so
lving 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 minima\, a
ssuming continuity of the objective function. The core idea is to compute
gradients of the Moreau envelope of the objective (which is “piece-wise
convex”) with adaptive smoothing parameters. Gradients of the Moreau env
elope are approximated by employing the Hopf-Lax formula for the viscous H
amilton Jacobi equation. Provided numerical examples illustrate global con
vergence.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Miller (Oden Institute at UT Austin)
DTSTART;VALUE=DATE-TIME:20221109T213000Z
DTEND;VALUE=DATE-TIME:20221109T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/10
DESCRIPTION:Title: Ensuring Exploration in Graph-Based Active Learning\nby Kevin Mil
ler (Oden Institute at UT Austin) as part of Early Career Math Colloquium\
n\n\nAbstract\nUncertainty sampling has traditionally been the de facto\,
simplest acquisition function for active learning in semi-supervised learn
ing. Comparatively cheap to compute and straightforward to interpret\, unc
ertainty sampling has been known to suffer from myopic sampling bias that
fails to properly explore the extent of geometric structure of the dataset
prior to exploiting learning decision boundaries. As such\, most work in
active learning for graph-based learning has focused on the design of more
intricate acquisition functions that are explorative in nature\, though a
re almost always more costly to compute. We show that exploration and expl
oitation in graph-based semi-supervised learning can be achieved by ensuri
ng that the underlying graph-based model reflects uncertainty at unlabeled
nodes that in turn captures the underlying clustering structure of the da
taset. We present theoretical results and empirical evidence to demonstrat
e that Poisson reweighted Laplacian learning\, which has a well-defined co
ntinuum limit model\, allows us to ensure exploration by simply applying a
specific form of uncertainty sampling.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evan Miller (University of British Columbia and the PIMS)
DTSTART;VALUE=DATE-TIME:20221019T213000Z
DTEND;VALUE=DATE-TIME:20221019T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/11
DESCRIPTION:Title: On the regularity of the axisymmetric\, swirl-free solutions of the E
uler equation in four and higher dimensions\nby Evan Miller (Universit
y of British Columbia and the PIMS) as part of Early Career Math Colloquiu
m\n\n\nAbstract\nIn this talk\, we will discuss the axisymmetric\, swirl-f
ree Euler\nequation in four and higher dimensions. We will show that in fo
ur and\nhigher dimensions the axisymmetric\, swirl-free Euler equation has
\nproperties which could allow finite-time singularity formation of a form
\nthat is excluded in three dimensions. We will also consider a model\nequ
ation that is obtained by taking the infinite-dimensional limit of the\nvo
rticity equation in this setup. This model exhibits finite-time blowup of\
na Burgers shock type. The blowup result for the infinite dimensional mode
l\nequation heavily suggests that smooth solutions of the Euler equation\n
exhibit finite-time blowup in sufficiently high dimensions.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo Bongarti (Weierstrass Institute for Applied Analysis and S
tochastics)
DTSTART;VALUE=DATE-TIME:20221012T213000Z
DTEND;VALUE=DATE-TIME:20221012T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/12
DESCRIPTION:Title: Boundary stabilization of nonlinear dynamics of acoustics waves under
the JMGT equation\nby Marcelo Bongarti (Weierstrass Institute for Ap
plied Analysis and Stochastics) as part of Early Career Math Colloquium\n\
n\nAbstract\nThe Jordan–Morse–Gibbson–Thompson (JMGT) equation is a
third-order in time partial differential equation (PDE) model describing n
onlinear propagation of sound in an acoustic medium. Its study is motivate
d by a large array of applications arising in engineering and medical scie
nces\, especially high intensity focused ultrasound (HIFU) technologies. T
he important feature is that the model avoids the infinite speed of propag
ation paradox associated with the classical second order in time equation
known as Westervelt’s equation. The third order in time derivative is du
e to the shift from parabolic to the hyperbolic model\, the latter being a
singular perturbation (w.r.t the thermal time relaxation) of the former.
In this talk we will present several results pertinent to the model\, most
ly from the point of view of boundary stabilization. These include: (i) lo
cal and global wellposedness\, (ii) asymptotic analysis when the thermal r
elaxation parameter vanishes\, and (iii) boundary stabillizability of JMGT
in the critical and degenerate case.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuzhe Zhu (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20230201T213000Z
DTEND;VALUE=DATE-TIME:20230201T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/13
DESCRIPTION:by Yuzhe Zhu (University of Cambridge) as part of Early Career
Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Zhiyuan Zhang (Courant Institute)
DTSTART;VALUE=DATE-TIME:20230405T213000Z
DTEND;VALUE=DATE-TIME:20230405T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/14
DESCRIPTION:Title: Outflow Problems in Plasmas and Fluids\nby Katherine Zhiyuan Zhan
g (Courant Institute) as part of Early Career Math Colloquium\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Strikwerda (North Carolina State University)
DTSTART;VALUE=DATE-TIME:20230208T213000Z
DTEND;VALUE=DATE-TIME:20230208T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/15
DESCRIPTION:Title: Optimal Control in Fluid Flows through Deformable Porous Media\nb
y Sarah Strikwerda (North Carolina State University) as part of Early Care
er Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mengxuan Yang (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20230329T213000Z
DTEND;VALUE=DATE-TIME:20230329T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/16
DESCRIPTION:Title: Magic angles and high Chern number flat band of a twisted multilayer
graphene model\nby Mengxuan Yang (UC Berkeley) as part of Early Career
Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xueying Yu (University of Washington)
DTSTART;VALUE=DATE-TIME:20230412T213000Z
DTEND;VALUE=DATE-TIME:20230412T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/17
DESCRIPTION:by Xueying Yu (University of Washington) as part of Early Care
er Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quyuan Lin (UC Santa Barbara)
DTSTART;VALUE=DATE-TIME:20230322T213000Z
DTEND;VALUE=DATE-TIME:20230322T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/19
DESCRIPTION:Title: Primitive equations: mathematical analysis and machine learning algor
ithm\nby Quyuan Lin (UC Santa Barbara) as part of Early Career Math Co
lloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elliot Cartee (University of Chicago)
DTSTART;VALUE=DATE-TIME:20230215T213000Z
DTEND;VALUE=DATE-TIME:20230215T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/20
DESCRIPTION:Title: Quantifying and Managing Uncertainty in Piecewise-Deterministic Marko
v Processes\nby Elliot Cartee (University of Chicago) as part of Early
Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lindstrom (University of Texas Rio Grande Valley)
DTSTART;VALUE=DATE-TIME:20230301T213000Z
DTEND;VALUE=DATE-TIME:20230301T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/21
DESCRIPTION:Title: Anomalies and Commonalities\nby Michael Lindstrom (University of
Texas Rio Grande Valley) as part of Early Career Math Colloquium\n\n\nAbst
ract\nThis talk will cover two research projects. In the first\, we seek t
o identify contextual anomalies among time series with possible missing da
ta. By generalizing Kernel Density Estimation to Hilbert Spaces\, we devel
op tools to identify anomalous time series\, test them against competing m
ethods on synthetic data\, and then employ the tools to identify anomalous
event records among airplane fleets. In the second project\, we combine t
opic modelling through Nonnegative Matrix Factorization and regression on
a continuous observation variable. Previous authors have covered the case
of topic modelling for classification\; here\, we show the idea can be ext
ended to regression\, applying it to Rate My Professors reviews and predic
ting an instructors mean rating from the written comments. We identify int
erpretable groups of words (topics)\, such that their level of representat
ion in a review has a quantifiable effect on the associated rating.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yotam Yaniv (UCLA)
DTSTART;VALUE=DATE-TIME:20230315T213000Z
DTEND;VALUE=DATE-TIME:20230315T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/22
DESCRIPTION:Title: Construction of Hierarchically Semi-Separable Matrix Representation u
sing Adaptive Johnson-Lindenstrauss Sketching\nby Yotam Yaniv (UCLA) a
s part of Early Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucio Galeati (EPFL)
DTSTART;VALUE=DATE-TIME:20230419T213000Z
DTEND;VALUE=DATE-TIME:20230419T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/23
DESCRIPTION:by Lucio Galeati (EPFL) as part of Early Career Math Colloquiu
m\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brenna Sprinkle (Colorado School of Mines)
DTSTART;VALUE=DATE-TIME:20230426T213000Z
DTEND;VALUE=DATE-TIME:20230426T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/24
DESCRIPTION:by Brenna Sprinkle (Colorado School of Mines) as part of Early
Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khoa Le (University of Leeds)
DTSTART;VALUE=DATE-TIME:20230503T213000Z
DTEND;VALUE=DATE-TIME:20230503T223000Z
DTSTAMP;VALUE=DATE-TIME:20230331T103604Z
UID:EarlyCareer/25
DESCRIPTION:by Khoa Le (University of Leeds) as part of Early Career Math
Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/25/
END:VEVENT
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