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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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
UID:EarlyCareer/13
DESCRIPTION:Title: Hölder regularity up to the boundary for kinetic equations\nby Y
uzhe Zhu (University of Cambridge) as part of Early Career Math Colloquium
\n\n\nAbstract\nWe consider the kinetic Fokker-Planck equation with rough
coefficients in a bounded spatial domain. We will discuss the regularizati
on property of the solutions under inflow or reflection boundary condition
s\, and its application to nonlinear kinetic models.\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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
UID:EarlyCareer/17
DESCRIPTION:Title: Modified scattering of cubic NLS on waveguide manifolds\nby Xueyi
ng Yu (University of Washington) as part of Early Career Math Colloquium\n
\n\nAbstract\nIn this talk\, we will discuss uniqueness properties of solu
tions to the linear generalized fourth-order Schr\\"odinger equations. We
show that a solution with fast enough decay in certain Sobolev spaces at t
wo different times has to be trivial. This is a joint work with Zachary Le
e.\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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
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:20240423T121710Z
UID:EarlyCareer/23
DESCRIPTION:Title: Regularisation by transport noise for 2D fluid dynamics equations
\nby Lucio Galeati (EPFL) as part of Early Career Math Colloquium\n\n\nAbs
tract\nA major open problem in fluid dynamics is to understand whether sol
utions to 2D incompressible Euler equations with $L^p$-valued vorticity ar
e unique\, for some $p\\in [1\,\\infty)$. A related question\, more probab
ilistic in flavour\, is whether one can find a physically meaningful noise
restoring well-posedness of the PDE.\nIn this talk I will present some re
cent advances on the latter problem\, for a class of slightly regularised
2D Euler-type equations (specifically\, logEuler and hypodissipative Navie
r-Stokes)\, in the presence of a rough Kraichnan-type noise\, modelling th
e small scales of a turbulent fluid\; uniqueness in law can then be shown
for solutions with $L^2$-valued vorticity.\nBased on an ongoing joint work
with Dejun Luo (Beijing).\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brennan Sprinkle (Colorado School of Mines)
DTSTART;VALUE=DATE-TIME:20230426T213000Z
DTEND;VALUE=DATE-TIME:20230426T223000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/24
DESCRIPTION:Title: Driving magnetic emulsions with flat tires\nby Brennan Sprinkle (
Colorado School of Mines) as part of Early Career Math Colloquium\n\n\nAbs
tract\nI'll discuss the rolling of active Pickering emulsions - small drop
lets (~10-100 um) covered in smaller (~1um) active particles that can be r
olled along a surface by an external\, AC magnetic field. Curiously\, thes
e droplets roll much faster and more efficiently when they have a larger a
rea of contact with the confining surface. I'll describe experiments done
by collaborators to validate this behavior and numerical simulations that
I developed to quantify it.\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:20240423T121710Z
UID:EarlyCareer/25
DESCRIPTION:Title: Stochastic heat equation with distributional drift\nby Khoa Le (U
niversity of Leeds) as part of Early Career Math Colloquium\n\n\nAbstract\
nWe study stochastic heat equation with a distributional drift b by space-
time white noise. We introduce a notion of a solution to this equation and
obtain the existence and uniqueness of a strong solution whenever b belon
gs to a suitable Besov space which includes measures.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Hernandez (University of Maine)
DTSTART;VALUE=DATE-TIME:20231023T190000Z
DTEND;VALUE=DATE-TIME:20231023T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/26
DESCRIPTION:Title: Splash singularities and magnetic field squeezing for the 2D ideal MH
D equations\nby Matthew Hernandez (University of Maine) as part of Ear
ly Career Math Colloquium\n\n\nAbstract\nA splash singularity is said to o
ccur in the problem of a free boundary fluid model when the boundary of a
fluid starts out as a smooth\, non-self-intersecting curve\, but two once-
distant pieces of the boundary crash into each other in finite time. For t
he 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 singul
arity solutions to the ideal MHD equations for which the external magnetic
field gets squeezed but does not vanish as the splash occurs.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Dolce (EPFL)
DTSTART;VALUE=DATE-TIME:20231120T200000Z
DTEND;VALUE=DATE-TIME:20231120T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/27
DESCRIPTION:by Michele Dolce (EPFL) as part of Early Career Math Colloquiu
m\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel McKenzie (Colorado School of Mines)
DTSTART;VALUE=DATE-TIME:20230918T190000Z
DTEND;VALUE=DATE-TIME:20230918T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/28
DESCRIPTION:Title: Sparse Gradients in Derivative-Free Optimization\nby Daniel McKen
zie (Colorado School of Mines) as part of Early Career Math Colloquium\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marissa Gee (Cornell University)
DTSTART;VALUE=DATE-TIME:20231009T190000Z
DTEND;VALUE=DATE-TIME:20231009T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/29
DESCRIPTION:by Marissa Gee (Cornell University) as part of Early Career Ma
th Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen Feng (Niagara University)
DTSTART;VALUE=DATE-TIME:20231106T200000Z
DTEND;VALUE=DATE-TIME:20231106T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/30
DESCRIPTION:Title: Nonlinear stability for the incompressible MHD system and Oldroyd-B m
odels\nby Wen Feng (Niagara University) as part of Early Career Math C
olloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jin Tan (Cergy Paris University)
DTSTART;VALUE=DATE-TIME:20231113T200000Z
DTEND;VALUE=DATE-TIME:20231113T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/31
DESCRIPTION:Title: Inhomogeneous incompressible Navier-Stokes equations in vacuum: the w
hole 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. Lions\, gl
obal existence results for finite energy weak solutions\nof the inhomogene
ous incompressible Navier-Stokes equations (INS) were proved without assum
ing positive lower bounds on the initial density. In this talk\, I will ta
lk about some regularity and uniqueness results of Lions’ weak solutions
for (INS) supplemented with additional regularity only for initial veloci
ty\, in the whole space case. As an application\, I will explain how these
results enable us to answer Lions’ question\, which concerns preservati
on 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 Christophe P
range (CY Cergy Paris University).\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Albert Ai (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20230925T190000Z
DTEND;VALUE=DATE-TIME:20230925T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/33
DESCRIPTION:Title: Low regularity solutions for quasilinear PDEs\nby Albert Ai (Univ
ersity of Wisconsin-Madison) as part of Early Career Math Colloquium\n\n\n
Abstract\nIn this talk\, we will consider the low regularity well-posednes
s problem for a pair of quasilinear dispersive PDEs: the nonlinear wave eq
uation\, and the water waves equations. Two classical methods\, energy est
imates and Strichartz estimates\, have historically yielded substantial bu
t partial results toward advancing the low regularity theory. We will see
how\, using a special structure of the equations known as a normal form st
ructure\, combined with tools from harmonic and microlocal analysis\, we c
an refine these classical methods to improve the known results for low reg
ularity well-posedness.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margherita Zanella (Polytechnic University of Milan\,)
DTSTART;VALUE=DATE-TIME:20231002T190000Z
DTEND;VALUE=DATE-TIME:20231002T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/34
DESCRIPTION:Title: Uniqueness of the invariant measure and asymptotic stability for 2 th
e 2D Navier-Stokes equations with multiplicative noise\nby Margherita
Zanella (Polytechnic University of Milan\,) as part of Early Career Math C
olloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marissa Gee (Cornell University)
DTSTART;VALUE=DATE-TIME:20231016T190000Z
DTEND;VALUE=DATE-TIME:20231016T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/35
DESCRIPTION:Title: Optimally Navigating a Piecewise-Deterministic World\nby Marissa
Gee (Cornell University) as part of Early Career Math Colloquium\n\n\nAbst
ract\nPiecewise-deterministic Markov processes are a special class\nof hyb
rid systems in which deterministic dynamics are punctuated by\nstochastic
jumps. In this talk\, we will investigate applications of\nthis framework
to optimal path planning problems. Deterministic path\nplanning is a well-
studied problem\, and many efficient methods exist\nfor determining the op
timal policies. However\, computational\nchallenges can arise when applyin
g these methods to the\npiecewise-deterministic setting. We will explore v
arious motivating\napplications\, derive Hamilton-Jacobi-Bellman PDEs that
govern the\noptimal policies\, and address some of the numerical challeng
es posed\nby solving these problems.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bohyun Kim (University of Utah)
DTSTART;VALUE=DATE-TIME:20231030T190000Z
DTEND;VALUE=DATE-TIME:20231030T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/36
DESCRIPTION:Title: A positivity-preserving numerical method for a thin liquid film 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 fl
ows down on a vertical fiber\, one can observe the complex and captivating
interfacial dynamics of an unsteady flow. Such dynamics are applicable in
various fluid experiments due to their high surface area-to-volume ratio.
Recent studies verified that when the flow undergoes regime transitions\,
the magnitude of the film thickness changes dramatically\, making numeric
al simulations challenging. In this talk\, we present a computationally ef
ficient numerical method that can maintain the positivity of the film thic
kness as well as conserve the volume of the fluid under the coarse mesh se
tting. A series of comparisons to laboratory experiments and previously pr
oposed numerical methods supports the validity of our numerical method. We
also prove that our method is second-order consistent in space and satisf
ies the entropy estimate.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Agresti (Delft University of Technology)
DTSTART;VALUE=DATE-TIME:20231204T200000Z
DTEND;VALUE=DATE-TIME:20231204T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/37
DESCRIPTION:Title: Reaction-diffusion equations with transport noise\nby Antonio Agr
esti (Delft University of Technology) as part of Early Career Math Colloqu
ium\n\n\nAbstract\nReaction-diffusion equations (RDEs) arise in several ph
ysical and engineering applications as they can be used to model many syst
ems of practical interest\, such as chemical reactions and population dyna
mics. RDEs are mathematically described by a system of parabolic PDEs with
polynomial nonlinearities of high degree. In applications\, transport noi
se is often used to model the effect of a turbulent flow advecting reactan
ts or to take into account local effects in population dynamics. Physicall
y relevant transport noises have typically low regularity in space. It is
a challenging task to handle transport noise and high-order polynomial non
linearities at the same time. In this talk I will review some recent resul
ts on local/global well-posedness of RDEs with transport noise. The keys t
o overcome the difficulties mentioned above are the use of $L^p$ theory fo
r stochastic PDEs and the recent theory of critical spaces for stochastic
evolution equations. If time allows\, then I will discuss how transport ty
pe noise can delay and/or suppress singularities in RDEs. Based on joint w
orks with M. Veraar (TU Delft).\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:None
DTSTART;VALUE=DATE-TIME:20230911T190000Z
DTEND;VALUE=DATE-TIME:20230911T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/38
DESCRIPTION:by None as part of Early Career Math Colloquium\n\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dwight Williams II (Morgan State University)
DTSTART;VALUE=DATE-TIME:20231127T200000Z
DTEND;VALUE=DATE-TIME:20231127T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/41
DESCRIPTION:Title: Extremal equations \\& algebraic methods\nby Dwight Williams II (
Morgan State University) as part of Early Career Math Colloquium\n\n\nAbst
ract\nThe audience is invited to a perspective on reduction algebras\, inc
luding algebraic methods described by Zhelobenko to find solutions of extr
emal equations. The general idea is to realize the solution space of a sys
tem of equations as the representation space of the system's symmetry alge
bra (reduction algebra). In particular\, the representation-theoretic defi
nition of singular/primitive vectors induces a system of extremal equation
s\; similarly\, mathematical models of physical phenomena are characterize
d by extremal equations. Two reduction algebras arising from solving extre
mal equations are given by:\\\\\n\\begin{enumerate}\n\\item Considering th
e Laplace operator in dimension $n$ as an element of the $n$th Weyl algebr
a via a mapping from the Lie algebra $\\mathfrak{sl}(2)$\n\\item Determini
ng primitive vectors in tensor product representations of the Lie superalg
ebra $\\mathfrak{osp}(1|2)$ \\\\\n\\end{enumerate}\nThe speaker's collabor
ation with Jonas T. Hartwig has found success in the second route with 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 their ass
ociated representation spaces as solution spaces to extremal equations is
the focus of multiple ongoing projects.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Phelps (Temple University)
DTSTART;VALUE=DATE-TIME:20240208T200000Z
DTEND;VALUE=DATE-TIME:20240208T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/42
DESCRIPTION:Title: Asymptotic properties and separation rates for local energy solutions
to the Navier-Stokes equations\nby Patrick Phelps (Temple University)
as part of Early Career Math Colloquium\n\n\nAbstract\nWe present recent
results on spatial decay and properties of non-uniqueness for the 3D Navie
r-Stokes equations. We show asymptotics for the ‘non-linear’ part of s
caling invariant flows with data in subcritical classes. Motivated by rece
nt work on non-uniqueness\, we investigate how non-uniqueness of the veloc
ity field would evolve in time in the local energy class. Specifically\, b
y extending our subcritical asymptotics to approximations by Picard iterat
es\, we may bound the rate at which two solutions\, evolving from the same
data\, may separate pointwise. We conclude by extending this separation r
ate to solutions with no scaling assumption. Joint work with Zachary Brads
haw.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amélie Loher (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20240222T200000Z
DTEND;VALUE=DATE-TIME:20240222T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/44
DESCRIPTION:by Amélie Loher (University of Cambridge) as part of Early Ca
reer Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Liu (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20240229T200000Z
DTEND;VALUE=DATE-TIME:20240229T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/45
DESCRIPTION:by Xin Liu (Texas A&M University) as part of Early Career Math
Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chunyin Siu (Cornell University)
DTSTART;VALUE=DATE-TIME:20240314T190000Z
DTEND;VALUE=DATE-TIME:20240314T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/46
DESCRIPTION:Title: Detecting Weak Topological Signals in Noisy Environments\nby Chun
yin Siu (Cornell University) as part of Early Career Math Colloquium\n\n\n
Abstract\nTopological signals refer to global nonlinear structures in data
sets like components\, cycles and holes. While traditional approaches are
well adapted to identifying strong topological signals in clean datasets\,
they tend to struggle when the signal-to-noise ratio is low. We introduce
a novel method to distinguish\, from noise\, small holes surrounded by hi
gh-density regions of a probability density function. The proposed method
is robust against additive noise and outliers. We will introduce the metho
d after a high-level overview of topological structures. Numerical experim
ents will be presented to demonstrate the proposed method's utility. This
is joint work with Gennady Samorodnitsky\, Christina Lee Yu and Andrey Yao
\, and it is based on the preprint https://arxiv.org/abs/2204.07821\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhongkai Tao (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20240328T190000Z
DTEND;VALUE=DATE-TIME:20240328T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/47
DESCRIPTION:by Zhongkai Tao (University of California\, Berkeley) as part
of Early Career Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Rosati (University of Warwick)
DTSTART;VALUE=DATE-TIME:20240404T190000Z
DTEND;VALUE=DATE-TIME:20240404T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/48
DESCRIPTION:by Tommaso Rosati (University of Warwick) as part of Early Car
eer Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurélie Paull (Institut Élie Cartan de Lorraine)
DTSTART;VALUE=DATE-TIME:20240411T190000Z
DTEND;VALUE=DATE-TIME:20240411T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
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://researchseminars.org/talk/EarlyCareer/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaxin Jin (Ohio State University)
DTSTART;VALUE=DATE-TIME:20240418T190000Z
DTEND;VALUE=DATE-TIME:20240418T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/50
DESCRIPTION:by Jiaxin Jin (Ohio State University) as part of Early Career
Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yupei Huang (Duke University)
DTSTART;VALUE=DATE-TIME:20240425T190000Z
DTEND;VALUE=DATE-TIME:20240425T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/51
DESCRIPTION:by Yupei Huang (Duke University) as part of Early Career Math
Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yeor Hafouta (University of Florida)
DTSTART;VALUE=DATE-TIME:20240502T190000Z
DTEND;VALUE=DATE-TIME:20240502T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/52
DESCRIPTION:by Yeor Hafouta (University of Florida) as part of Early Caree
r Math Colloquium\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Son Tu (Michigan State University)
DTSTART;VALUE=DATE-TIME:20240321T190000Z
DTEND;VALUE=DATE-TIME:20240321T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T121710Z
UID:EarlyCareer/53
DESCRIPTION:Title: Properties of the effective Hamiltonian and homogenization of the Ham
ilton-Jacobi equation\nby Son Tu (Michigan State University) as part o
f Early Career Math Colloquium\n\n\nAbstract\nThe homogenization of Hamilt
on-Jacobi equations in the periodic setting was pioneered by Lions\, Papan
icolaou\, and Varadhan in the 1980s. However\, understanding the intricate
properties of the effective Hamiltonian and its impact on the homogenizat
ion limit across various settings remains a substantial open problem. In t
his presentation\, we will discuss recent developments that highlight a co
nnection between this phenomenon and weak KAM theory on a qualitative leve
l\, as well as present some quantitative results.\n
LOCATION:https://researchseminars.org/talk/EarlyCareer/53/
END:VEVENT
END:VCALENDAR