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BEGIN:VEVENT
SUMMARY:Renming Song (University of Illinois Urbana-Champaign)
DTSTART:20200623T130000Z
DTEND:20200623T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/1/">Factorizations and estimates of Dirichlet heat kernels for non-l
 ocal operators with critical killings</a>\nby Renming Song (University of 
 Illinois Urbana-Champaign) as part of Non-local operators\, probability an
 d singularities\n\n\nAbstract\nIn this talk I will discuss heat kernel est
 imates for critical perturbations \nof non-local operators. To be more pre
 cise\, let $X$ be the reflected \n$\\alpha$-stable process in the closure 
 of a smooth open set $D$\, and \n$X^D$ the process killed upon exiting $D$
 . We consider potentials of the \nform $\\kappa(x)=C\\delta_D(x)^{-\\alpha
 }$ with positive $C$ and the \ncorresponding Feynman-Kac semigroups. Such 
 potentials do not belong \nto the Kato class. We obtain sharp two-sided es
 timates for the heat \nkernel of the perturbed semigroups. The interior es
 timates of the \nheat kernels have the usual $\\alpha$-stable form\, while
  the boundary \ndecay is of the form $\\delta_D(x)^p$ with non-negative \n
 $p\\in [\\alpha-1\, \\alpha)$ depending on the precise value of the \ncons
 tant $C$. Our result recovers the heat kernel estimates of both \nthe cens
 ored and the killed stable process in $D$. Analogous \nestimates are obtai
 ned for the heat kernel of the Feynman-Kac \nsemigroup of the $\\alpha$-st
 able process in \n${\\mathbf R}^d\\setminus \\{0\\}$ through the potential
  $C|x|^{-\\alpha}$. \n\nAll estimates are derived from a more general resu
 lt described as follows: \nLet $X$ be a Hunt process on a locally compact 
 separable metric space in \na strong duality with $\\widehat{X}$. Assume t
 hat transition densities of \n$X$ and $\\widehat{X}$  are comparable to th
 e function $\\widetilde{q}(t\,x\,y)$ \ndefined in terms of the volume of b
 alls and a certain scaling function. \nFor an open set $D$ consider the ki
 lled process $X^D$\, and a critical \nsmooth measure on $D$ with the corre
 sponding positive additive functional \n$(A_t)$.  We show that the heat ke
 rnel of the the Feynman-Kac semigroup \nof $X^D$ through the multiplicativ
 e functional $\\exp(-A_t)$ admits the \nfactorization of the form \n${\\ma
 thbf P}_x(\\zeta >t)\\widehat{\\mathbf P}_y(\\widehat{\\zeta}>t)\\widetild
 e{q}(t\,x\,y)$.\n\nThis talk is based on a joint paper with Soobin Cho\, P
 anki Kim and Zoran Vondracek.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kulik (Wrocław University of Science and Technology)
DTSTART:20200630T130000Z
DTEND:20200630T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/2/">Moment bounds for dissipative semimartingales with heavy jumps</
 a>\nby Alexei Kulik (Wrocław University of Science and Technology) as par
 t of Non-local operators\, probability and singularities\n\n\nAbstract\nTh
 e talk is based on a joint research with Ilya Pavlyukevich. We show that i
 f the jumps of an Ito-semimartingale $X$ admit a finite $p$-moment\, $p>0$
 \,\nthe radial part of its drift is dominated at $\\infty$ by $-|X|^\\kapp
 a$ for some $\\kappa\\geq -1$\, and the balance condition $p+\\kappa>1$ ho
 lds true\, then\nunder some further minor technical assumptions\n$\\sup_{t
 \\geq 0} \\mathbb{E} |X_t|^{p_X}<\\infty$ for each $p_X\\in(0\,p+\\kappa-1
 )$. The upper bound $p+\\kappa-1$ is generically optimal.\nThe proof is ba
 sed on the extension of the method of Lyapunov functions to the semimartin
 gale framework.\n\nOur study of the uniform-in-time moment estimates is st
 rongly motivated by needs of the Stochastic Averaging/Homogenization theor
 y for Levy driven multi-scale systems\, which will be discussed in the tal
 k\, as well.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Jakubowski (Wrocław University of Science and Technology)
DTSTART:20200707T130000Z
DTEND:20200707T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/3/">Critical Schrödinger perturbations of fractional Laplacian</a>\
 nby Tomasz Jakubowski (Wrocław University of Science and Technology) as p
 art of Non-local operators\, probability and singularities\n\n\nAbstract\n
 Let $p(t\,x\,y)$ be the fundamental solution of the equation $\\partial_t 
 u(t\,x) = \\Delta^{\\alpha/2} u(t\,x)$.\nI will consider the integral equa
 tion\n$$\n\\tilde{p}(t\,x\,y) = p(t\,x\,y) + \\int_0^t \\int_{\\mathbb{R}^
 d} p(t-s\,x\,z) q(z) \\tilde{p}(s\,z\,y) dz ds\,\n$$\nwhere $q(z) = \\frac
 {\\kappa}{|z|^{\\alpha}}$ and $\\kappa$ is some constant. The function $\\
 tilde{p}$ solving this equation will be called the Schrödinger perturbati
 ons of the function $p$ by $q$.  I will  present the results concerning th
 e estimates of the function $\\tilde{p}$ in both cases $\\kappa>0$ and $\\
 kappa<0$.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franziska Kühn (Technical University of Dresden)
DTSTART:20200714T130000Z
DTEND:20200714T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/4/">A maximal inequality for martingale problems and applications</a
 >\nby Franziska Kühn (Technical University of Dresden) as part of Non-loc
 al operators\, probability and singularities\n\n\nAbstract\nMartingale pro
 blems aim to characterize stochastic processes by their martingale propert
 ies. A famous example is Lévy's characterization theorem which characteri
 zes Brownian motion by its first two conditional moments. More generally\,
  a wide class of Markov processes and stochastic differential equations ca
 n be described using martingale problems.\n\nIn this talk\, we study marti
 ngale problems associated with Lévy-type operators. We present a maximal 
 inequality\, which goes back to R. Schilling\, and discuss some variants o
 f it. We show that the maximal inequality has many useful applications in 
 the study of distributional and path properties of the corresponding stoch
 astic process\, e.g. criteria for non-explosion in finite time\, existence
  of moments\, ...\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Panki Kim (Seoul National University)
DTSTART:20200721T130000Z
DTEND:20200721T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/5/">Estimates on transition densities of subordinators with jumping 
 density decaying in mixed polynomial orders</a>\nby Panki Kim (Seoul Natio
 nal University) as part of Non-local operators\, probability and singulari
 ties\n\n\nAbstract\nIn this talk\, we discuss the sharp two-sided estimate
 s on the transition densities for subordinators whose Lévy measures are a
 bsolutely continuous and decaying in mixed polynomial orders. Under a weak
 er assumption on Lévy measures\, we also discuss a precise asymptotic beh
 aviors of the transition densities at infinity. Our results cover geometri
 c stable subordinators\, Gamma subordinators and much more. This is a join
 t work with Soobin Cho.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krzysztof Bogdan (Wrocław University of Science and Technology)
DTSTART:20200728T130000Z
DTEND:20200728T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/6/">Nonlinear nonlocal Douglas identity</a>\nby Krzysztof Bogdan (Wr
 ocław University of Science and Technology) as part of Non-local operator
 s\, probability and singularities\n\n\nAbstract\nI will present results fr
 om the joint work with Tomasz Grzywny\, Katarzyna Pietruska-Pałuba\, Artu
 r Rutkowski with the same title (available at https://arxiv.org/abs/2006.0
 1932 ). We give Hardy-Stein and Douglas identities for specific nonlinear 
 nonlocal Sobolev-Bregman integral forms with unimodal Lévy measures. We p
 rove that the corresponding Poisson integral defines an extension operator
  for the Sobolev-Bregman spaces. The results generalizes to the setting of
  $L^p$ spaces the earlier results of the authors\, obtained for the (quadr
 atic) Dirichlet forms and $L^2$ spaces.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Knopova
DTSTART:20200811T130000Z
DTEND:20200811T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/7/">Construction and heat kernel estimates of general stable-like Ma
 rkov processes</a>\nby Victoria Knopova as part of Non-local operators\, p
 robability and singularities\n\n\nAbstract\nStarting with  a non-symmetric
  $\\alpha$-stable- like pseudo-differential operator  $L$ defined  on the 
 test functions\,  we show that the corresponding martingale problem is wel
 l-posed\, and its solution is a strong  Markov process which admits a tran
 sition probability density.  We investigate the structure of this density 
  in the vicinity of the starting point. In particular\,  we show that due 
 to the non-symmetry the respective density is not necessarily bounded\, an
 d one needs additional assumptions  on the Lévy-type  kernel of the opera
 tor  in order to get a point-wise upper bound on the transition probabilit
 y density.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xicheng Zhang (Wuhan)
DTSTART:20200915T130000Z
DTEND:20200915T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/8/">Singular HJB equations with applications to KPZ on the real line
 </a>\nby Xicheng Zhang (Wuhan) as part of Non-local operators\, probabilit
 y and singularities\n\n\nAbstract\nI will talk about the Hamilton-Jacobi-B
 ellman  equations with distribution-valued coefficients\, which is not wel
 l-defined in the classical sense and shall be understood by using paracont
 rolled distribution method introduced by Gubinelli-Imkeller-Perkowski. By 
 a new characterization of weighted Hölder space and Zvonkin's transformat
 ion we prove some new a priori estimates\, and therefore\, establish the g
 lobal well-posedness for singular HJB equations. As an application\, the g
 lobal well-posedness for KPZ equations on the real line in polynomial weig
 hted Hölder spaces is obtained without using Cole-Hopf's transformation. 
 This is a joint work with Rongchan Zhu and Xiangchan Zhu.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoran Vondraček (Zagreb)
DTSTART:20200922T130000Z
DTEND:20200922T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/9/">On the potential theory of Markov processes with jump kernels de
 caying at the boundary</a>\nby Zoran Vondraček (Zagreb) as part of Non-lo
 cal operators\, probability and singularities\n\n\nAbstract\nIn this talk\
 , I will consider some potential theory of the process $Y$ on an open set 
 $D\\subset \\mathbb{R}^d$ associated with a pure jump Dirichlet form whose
  jump kernel has the form $J(x\,y)=B(x\,y)|x-y|^{-d-\\alpha}$\, $0<\\alpha
 <2$. Here $B(x\,y)$ -- the boundary term -- depends on $\\delta_D(x)\, \\d
 elta_D(y)$ and $|x-y|$\, and is allowed to approach 0 at the boundary. Thi
 s is in contrast with previous works where $B(x\,y)$ is assumed to be boun
 ded between two positive constants\, which can be viewed as a uniform elli
 pticity condition for non-local operators. The conditions and the form of 
 the boundary term $B(x\,y)$ are motivated by jump kernels of some subordin
 ate killed Lévy processes.\n\nWe prove that non-negative harmonic functio
 ns of the process satisfy the Harnack inequality and Carleson's estimate. 
 Furthermore\, in case when $D$ is the half-space we investigate when the b
 oundary Harnack principle holds. This is joint work with Panki Kim (Seoul 
 National University) and Renming Song (University of Illinois).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angkana Rüland (Heidelberg)
DTSTART:20200929T130000Z
DTEND:20200929T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/10/">Uniqueness\, stability and single measurement recovery for the 
 fractional Calderón problem</a>\nby Angkana Rüland (Heidelberg) as part 
 of Non-local operators\, probability and singularities\n\n\nAbstract\nIn t
 his talk I discuss a nonlocal inverse problem\, the\nfractional Calderón 
 problem. This is an inverse problem for a\nfractional Schrödinger equatio
 n in which one seeks to recover\ninformation on an unknown potential by ex
 terior measurements. In the\ntalk\, I prove uniqueness and stability of th
 e "infinite data problem"\nand then address the recovery question. This al
 so yields surprising\ninsights on the  uniqueness properties of the invers
 e problem\, in that it\nturns out that a single measurement suffices to un
 iquely recover the\npotential.\n\nThese properties are based on the very s
 trong unique continuation and\napproximation properties of fractional Schr
 ödinger operators\, which are\nof independent interest and which I also d
 iscuss in the talk.\n\nThis is based on joint work with T. Ghosh\, M. Salo
  and G. Uhlmann.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongjie Dong (Brown)
DTSTART:20201006T130000Z
DTEND:20201006T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/11/">Evolutionary equations with nonlocal time derivatives</a>\nby H
 ongjie Dong (Brown) as part of Non-local operators\, probability and singu
 larities\n\n\nAbstract\nI will present some recent results about fractiona
 l parabolic and wave equations with nonlocal Caputo time derivatives. Unde
 r various vanishing mean oscillation (VMO) conditions on the leading coeff
 icients\, we obtained weighted and mixed-norm Sobolev estimates in the who
 le space\, half space\, or domains.\n\nThis is based on joint work with Do
 yoon Kim (Korea University) and Yanze Liu (Brown University).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daesung Kim (Illinois Urbana-Champaign)
DTSTART:20201013T130000Z
DTEND:20201013T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/12/">Quantitative isoperimetric inequalities arising from stochastic
  processes</a>\nby Daesung Kim (Illinois Urbana-Champaign) as part of Non-
 local operators\, probability and singularities\n\n\nAbstract\nIt is well 
 known that isoperimetric type inequalities hold for a large class of quant
 ities arising from Brownian motion. Banuelos and Mendez-Hernandez showed t
 hat such inequalities can be extended to a wide class of Levy processes. A
  stability question is if the inequality will be about to achieving the eq
 uality when a given domain is close to being a ball. This question can be 
 answered by quantitative improvement of such inequalities in terms of the 
 asymmetry. In this talk\, we discuss the quantitative isoperimetric inequa
 lities for the expected lifetime of Brownian motion and $\\alpha$-stable p
 rocesses\, and some related open problems.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Verbitsky (Missouri)
DTSTART:20201020T140000Z
DTEND:20201020T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/13/">Pointwise estimates of positive solutions to linear and semilin
 ear equations with nonlocal operators</a>\nby Igor Verbitsky (Missouri) as
  part of Non-local operators\, probability and singularities\n\n\nAbstract
 \nRecent results will be presented involving sharp global pointwise estima
 tes  of positive solutions to some linear and semilinear partial different
 ial  equations and inequalities with nonlocal operators satisfying various
  forms of the maximum principle or domination principle. In particular\, e
 quations of the type\n\\[\n(-\\Delta)^{\\frac{\\alpha}{2}} u = g(u) \\sigm
 a +\\mu \\quad \\text{in} \\\, \\\,\n\\Omega\, \\quad u=0 \\\, \\\, \\\, \
 \text{in} \\\, \\\, \\Omega^c\,\n\\]\nwith measure coefficients $\\sigma$\
 , $\\mu$\, where $g(u)=u^q$ and $0< \\alpha < n$ in certain domains $\\Ome
 ga \\subseteq {\\mathbb{R}}^n$\, or Riemannian manifolds\, with positive G
 reen's function will be discussed.\n\nJoint work with Alexander Grigor'yan
 .\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie-Ming Wang (Beijing)
DTSTART:20201103T140000Z
DTEND:20201103T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/14/">Boundary Harnack Principle for Diffusion with Jumps</a>\nby Jie
 -Ming Wang (Beijing) as part of Non-local operators\, probability and sing
 ularities\n\n\nAbstract\nFor $d\\geq 3$\, consider the operator ${\\mathca
 l L}^{\\bf b}={\\mathcal L}^0+b_1\\cdot \\nabla+{\\mathcal S}^{b_2}$\,\nwh
 ere ${\\mathcal L}^0$ is a second order elliptic operator   in non-diverge
 nce form\,\nthe function $b_1$ belongs to some Kato class  and\n$$\n{\\mat
 hcal S}^{b_2} f(x):=\n\\int_{{\\mathbb R}^d} \\left( f(x+z)-f(x)- \\nabla 
 f(x) \\cdot\nz\\\, {\\mathbb 1}_{{|z|\\leq 1}}  \\right) b_2(x\, z)J_0(z) 
 \\\,dz\, \\quad f\\in C_b^2({\\mathbb R}^d)\,\n$$\nwhere $J_0(z)$ satisfie
 s that there exist positive constants $c_1\, c_2$ and $0<\\beta_1\\leq \\b
 eta_2 <2$ such that\n $$c_1 (|z_2|/|z_1|)^{d+\\beta_1}  \\leq J_0(z_1)/J_0
 (z_2)\n\\leq c_2 (|z_2|/|z_1|)^{d+\\beta_2}\n\\quad {f\\!or\\\, any}\\quad
  z_1\, z_2\\in {\\mathbb R}^d \\quad{with}\\quad 0<|z_1|\\leq |z_2|\,$$\n 
 $b_2(x\, z)$  is a  real-valued bounded function\non ${\\mathbb R}^d\\time
 s {\\mathbb R}^d$ satisfying  for each $x\\in {\\mathbb R}^d$\,\n$ b_2(x\,
   \\cdot )\\geq 0$  a.e.  on ${\\mathbb R}^d$\, and\n$$\n1_{\\beta_2=1} \\
 int_{r<|z|\\leq R}z b_2(x\, z) J_0(z)\\\,dz=0 \\quad {f\\!or\\\, every}\\q
 uad x\\in {\\mathbb R}^d\n\\quad {and}\\quad 0< r < R < \\infty.\n$$\nUnde
 r the uniformly ellipticity condition and Hölder condition on the diffusi
 on coefficient $a_{ij}\,$\nthere exists a conservative Feller process $X^{
 \\bf b}$ with its infinitesimal generator ${\\mathcal L}^{\\bf b}$.\nWe gi
 ve the two-sided Green function estimates of $X^{\\bf b}$ on a bounded $C^
 {1\,1}$ domain $D$ and further establish the Martin integral representatio
 n  of harmonic function with respect to $X^{\\bf b}$ on the domain $D$.\nU
 sing the Green function estimates and the Martin  integral formula in $D$\
 , the Harnack principle and the boundary Harnack principle with explicit b
 oundary decay rate for the operator ${\\mathcal L}^{\\bf b}$ under some mi
 ld conditions\nare established.\nThis talk  is based on a joint work with 
 Professor Z.-Q. Chen.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Wang (Fujian)
DTSTART:20201110T140000Z
DTEND:20201110T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/15/">Heat kernel upper bounds for symmetric Markov semigroups</a>\nb
 y Jian Wang (Fujian) as part of Non-local operators\, probability and sing
 ularities\n\n\nAbstract\nIt is well known that Nash-type inequalities for 
 symmetric Dirichlet forms are equivalent to on-diagonal heat kernel upper 
 bounds for associated symmetric Markov semigroups. In this talk\, we show 
 that both imply (and hence are equivalent to) off-diagonal heat kernel upp
 er bounds under some mild assumptions. Our approach is  based on a new gen
 eralized Davies's method. Our results extend that by Carlen-Kusuoka-Strooc
 k for Nash-type inequalities with power order considerably and also extend
  that by Grigor'yan for second order differential operators on a complete 
 non-compact manifold.\n\nThe talk is based on a joint work with Z.-Q. Chen
  (Seattle)\, P. Kim (Seoul) and T. Kumagai (Kyoto).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tadeusz Kulczycki (Wroclaw)
DTSTART:20201117T140000Z
DTEND:20201117T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/16/">On weak solution of SDE driven by inhomogeneous singular Lévy 
 noise.</a>\nby Tadeusz Kulczycki (Wroclaw) as part of Non-local operators\
 , probability and singularities\n\n\nAbstract\nWe study the stochastic dif
 ferential equation\n$dX_t = A_t(X_{t-}) \\\, dZ_t$\, $ X_0 = x$\,\nwhere $
 Z_t = (Z_t^{(1)}\,\\ldots\,Z_t^{(d)})^T$ and for each $i \\in \\{1\,\\ldot
 s\,d\\}$ $Z_t^{(i)}$ is a one-dimensional\, symmetric $\\alpha_i$-stable p
 rocess\, where $\\alpha_i \\in (0\,2)$. Under appropriate conditions on $\
 \alpha_1\,\\ldots\,\\alpha_d$ and on matrices $A_t$  we prove existence an
 d uniqueness of the weak solution of the above SDE\, which will be shown t
 o be a time-inhomogeneous Markov process. We also provide a representation
  of the transition probability density of this process as a sum of explici
 tly given ‘principal part’\, and a ‘residual part’ subject to a se
 t of estimates showing that this part is negligible in a short time. The t
 alk is based on a joint work with A. Kulik and M. Ryznar.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Longmin Wang (Nankai)
DTSTART:20201201T140000Z
DTEND:20201201T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/17/">Branching Random Walks on Hyperbolic Spaces</a>\nby Longmin Wan
 g (Nankai) as part of Non-local operators\, probability and singularities\
 n\n\nAbstract\nThe branching Brownian motion on the hyperbolic plane with 
 binary\nfission at rate $\\lambda > 0$ exhibits a phase transition in\n$\\
 lambda$: For $\\lambda \\leq 1/8$ the number of particles in any\ncompact 
 region is eventually $0$\, w.p.1\, but for $\\lambda > 1/8$\nthe number of
  particles in any open region grows to $\\infty$\nw.p.1. Lalley and Sellke
  (1987) proved that in the subcritical and\ncritical case ($\\lambda \\leq
  1/8$) the set $\\Lambda$ of all limit\npoints in the boundary circle at $
 \\infty$ consisting of particle\ntrails is a Cantor set\, while in the sup
 ercritical case ($\\lambda\n>1/8$) the set $\\Lambda$ has full Lebesgue me
 asure. For $\\lambda\n\\leq 1/8$ the Hausdorff dimension of $\\Lambda$ is 
  at most $1/2$\nand has critical exponent $1/2$ near the critical value $\
 \lambda =\n1/8$. In this talk we will prove the same type of phase transit
 ion\noccurs for branching random walks on hyperbolic spaces.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mateusz Kwaśnicki (Wroclaw)
DTSTART:20201124T140000Z
DTEND:20201124T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/19/">Harmonic extensions\, operators with completely monotone kernel
 s\, and traces of 2-D diffusions</a>\nby Mateusz Kwaśnicki (Wroclaw) as p
 art of Non-local operators\, probability and singularities\n\nAbstract: TB
 A\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerome Goldstein (Memphis)
DTSTART:20201208T150000Z
DTEND:20201208T160000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/20/">The Boderline between Some Good Problems and the Corresponding 
 Bad Problems</a>\nby Jerome Goldstein (Memphis) as part of Non-local opera
 tors\, probability and singularities\n\n\nAbstract\nWe will discuss three 
 problems in PDE for which existence or nonexistence of\ncertain kinds of e
 quations is a delicate issue. Many coauthors are involved\, and the\nprobl
 ems are related to each other.\n\nThe first problem involves work from the
  1970s about uniqueness for certain\nill posed problems involving the Eule
 r-Poisson-Darboux equation. The number of\ninitial conditions required for
  uniqueness involves the size of negative parameter in\nthe singular term 
 and the definition of solution.\n\nThe second problem involves the Schröd
 inger operator with the inverse square\npotential multiplied by a constant
  c. The spectrum of this operator on $L^2(\\mathbb{R}^n)$ is\neither $\\ma
 thbb{R}$ or $\\mathbb{R}^+$\, depending on the choice of c: In the 1980s\,
  it was proved that the corresponding heat equation has instantaneous blow
  up and no positive solutions\nwhen the spectrum is $\\mathbb{R}$. The cor
 responding result is true when Euclidean space is\nreplaced by the Heisenb
 erg group\; this was proved in 2020.\n\nThe final problem is nonlinear and
  involves the parabolic problem for the fast\ndiffusion equation or the p-
 Laplacian heat equation\, perturbed in various ways\, on\nEuclidean space 
 or on a Riemannaian manifold. In some cases one can show the\nabsence of n
 onnegative solutions (except for the zero function).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moritz Kassmann (Bielefeld)
DTSTART:20210112T140000Z
DTEND:20210112T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/21/">Heat kernel estimates for mixed systems of diffusions and jump 
 processes</a>\nby Moritz Kassmann (Bielefeld) as part of Non-local operato
 rs\, probability and singularities\n\n\nAbstract\nWe prove sharp heat kern
 el estimates for symmetric Markov processes that are independent copies of
  one-dimensional jump or diffusion processes.  The result can be seen as a
  robustness result for heat kernels like the one of Aronson (1968) for dif
 fusions or the one of Chen/Kumagai (2003) for isotropic jump processes. Th
 e talk is based on a joint work together with Jaehoon Kang (KAIST).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guohuan Zhao (Bielefeld)
DTSTART:20201215T140000Z
DTEND:20201215T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/22/">Regularity properties of jump diffusions with irregular coeffic
 ients</a>\nby Guohuan Zhao (Bielefeld) as part of Non-local operators\, pr
 obability and singularities\n\n\nAbstract\nIn this talk\, I plan to presen
 t some results about the regularity properties of strong solutions to SDEs
  driven by Lévy processes with irregular drift coefficients. In short\, I
  will show the Malliavin differentiability of the unique strong solutions 
 as well as the differentiability of the stochastic flows with respect to t
 he spatial variable. Meanwhile\, I will also talk about the Schauder's est
 imate for the resolvent equations corresponding to the SDEs.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carina Geldhauser (Lund)
DTSTART:20210119T140000Z
DTEND:20210119T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/23/">The fractional Green function in atmospheric turbulence models<
 /a>\nby Carina Geldhauser (Lund) as part of Non-local operators\, probabil
 ity and singularities\n\n\nAbstract\nIn this talk we discuss a family of d
 iscrete models for atmospheric turbulence\, often called point vortex mode
 ls.\n\nWe state some of it basic properties and show how we can derive an 
 effective PDE\, the so-called mean field limit\, from the discrete Hamilto
 nian system\, by using a variational principle.  Furthermore\, we discuss 
 the usage and interpretation of these models in statistical physics.\n\nTh
 e content of this talk is based joint work with Marco Romito (Uni Pisa).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damir Kinzebulatov (Quebec)
DTSTART:20210126T140000Z
DTEND:20210126T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/25/">Fractional Kolmogorov operator and desingularizing weights</a>\
 nby Damir Kinzebulatov (Quebec) as part of Non-local operators\, probabili
 ty and singularities\n\n\nAbstract\nThe subject of this talk are sharp two
 -sided bounds on the heat kernel of the fractional Laplacian perturbed by 
 a Hardy-type drift\, which we establish by transferring the operator to an
  appropriate weighted space with singular weight. The talk is based on joi
 nt papers with Yu.A.Semenov and K.Szczypkowski.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vanja Wagner (Zagreb)
DTSTART:20210202T140000Z
DTEND:20210202T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/26/">Semilinear equations for non-local operators: beyond the fracti
 onal Laplacian</a>\nby Vanja Wagner (Zagreb) as part of Non-local operator
 s\, probability and singularities\n\n\nAbstract\nWe study semilinear probl
 ems in general bounded open sets for non-local operators with exterior and
  boundary conditions\, where the operators are more general than the fract
 ional Laplacian. We also give results in case of bounded $C^{1\,1}$ open s
 ets. The talk is based on joint work with Ivan Biočić and Zoran Vondrač
 ek.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (The University of Chicago)
DTSTART:20210316T140000Z
DTEND:20210316T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/27/">Regularity estimates for the Boltzmann equation without cutoff<
 /a>\nby Luis Silvestre (The University of Chicago) as part of Non-local op
 erators\, probability and singularities\n\n\nAbstract\nWe study the regula
 rization effect of the inhomogeneous Boltzmann equation without cutoff. We
  obtain a priori estimates for all derivatives of the solution depending o
 nly on bounds of its hydrodynamic quantities: mass density\, energy densit
 y and entropy density. As a consequence\, a classical solution to the equa
 tion may fail to exist after a certain time T only if at least one of thes
 e hydrodynamic quantities blows up. Our analysis applies to the case of mo
 derately soft and hard potentials. We use methods that originated in the s
 tudy of nonlocal elliptic and parabolic equations: a weak Harnack inequali
 ty in the style of De Giorgi\, and a Schauder-type estimate.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gisèle Goldstein (The University of Memphis)
DTSTART:20210323T140000Z
DTEND:20210323T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/28/">On Thomas-Fermi Theory and Extensions</a>\nby Gisèle Goldstein
  (The University of Memphis) as part of Non-local operators\, probability 
 and singularities\n\n\nAbstract\nOf concern to quantum chemists and solid 
 state physicists is the approximate numerical computation of the ground st
 ate wave function\, and the ground state energy and density for molecular 
 and other quantum mechanical systems. Since the number of molecules in bul
 k matter is of the order of 1026\, direct computation is too cumbersome or
  impossible in many situations. In 1927\, L. Thomas and E. Fermi proposed 
 replacing the ground state wave function by the ground state density\, whi
 ch is a function of only three variables. Independently\, each found an ap
 proximate expansion for the energy associated with a density. (The wave fu
 nction uniquely determines the density\, but not conversely.)\n\nA computa
 tionally better approximate expansion was found in the 1960’s by W. Kohn
  and his collaborators\; for this work Kohn got the Nobel Prize in Chemist
 ry in 1998. A successful attempt to put Thomas-Fermi theory into a rigorou
 s mathematical framework was begun in the 1970’s by E. Lieb and B. Simon
  and was continued and expanded by Ph. Benilan\, H. Brezis and others. Ver
 y little rigorous mathematics supporting Kohn density functional theory is
  known. In this talk I will present a survey of rigorous Thomas-Fermi theo
 ry\, including recent developments and open problems (in the\ncalculus of 
 variations and semilinear elliptic systems).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazuhiro Kuwae (Fukuoka University)
DTSTART:20210330T130000Z
DTEND:20210330T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/29/">Lp-Kato class measures for symmetric Markov processes under hea
 t kernel estimates</a>\nby Kazuhiro Kuwae (Fukuoka University) as part of 
 Non-local operators\, probability and singularities\n\n\nAbstract\nI will 
 talk on the coincidence of two classes of $L^p$-Kato class measures\nin th
 e framework of symmetric Markov processes admitting upper and lower estima
 tes of heat kernel under mild conditions. One class of $L^p$-Kato class me
 asures is defined by the $p$-th power of positive order resolvent kernel\,
  another is defined in terms of the $p$-th power of Green kernel depending
  on some exponents related to the heat kernel estimates. We also prove tha
 t $q$-th integrable functions on balls with radius $1$ having uniformity o
 f its norm with respect to centers are of $L^p$-Kato class if $q$ is great
 er than a constant related to $p$ and the constants appeared in the upper 
 and lower estimates of the heat kernel. These are complete extensions of s
 ome results\nby Aizenman-Simon and the recent results by the second named 
 author in the framework of Brownian motions on Euclidean space. We further
  give necessary and sufficient conditions\nfor a Radon measure with Ahlfor
 s regularity to belong to $L^p$-Kato class. Our results can be applicable 
 to many examples\, for instance\, symmetric (relativistic) stable processe
 s\, jump processes on $d$-sets\, Brownian motions on Riemannian manifolds\
 , diffusions on fractals and so on.\nJoint work with Takahiro Mori.\n\nThe
  details can be seen in  https://arxiv.org/abs/2008.10934\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qi Zhang (University of California\, Riverside)
DTSTART:20210504T130000Z
DTEND:20210504T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/31/">Time analyticity and reversibility of some parabolic equations<
 /a>\nby Qi Zhang (University of California\, Riverside) as part of Non-loc
 al operators\, probability and singularities\n\n\nAbstract\nWe describe a 
 concise way to prove time analyticity for solutions of parabolic equations
  including the heat and Navier Stokes equations. In some cases\, results u
 nder sharp conditions are obtained. An application is a necessary and suff
 icient condition for the solvability of the backward heat equation which i
 s ill-posed\, helping to remove an old obstacle in control theory.\n\nPart
  of the work is joint with Hongjie Dong\, which is related to earlier join
 t work with F. H. Lin.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Krylov (University of Minnesota)
DTSTART:20210416T140000Z
DTEND:20210416T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/32/">(joint with Montreal-Quebec Analsyis Seminar)</a>\nby Nicolai K
 rylov (University of Minnesota) as part of Non-local operators\, probabili
 ty and singularities\n\n\nAbstract\nFind out more details:\n\nhttps://rese
 archseminars.org/seminar/MathematicalAnalysis\n\nhttps://www.math.mcgill.c
 a/jakobson/analysish/seminar.html\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jamil Chaker (Bielefeld University)
DTSTART:20210420T130000Z
DTEND:20210420T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/33/">On nonlocal operators with anisotropic kernels</a>\nby Jamil Ch
 aker (Bielefeld University) as part of Non-local operators\, probability a
 nd singularities\n\n\nAbstract\nIn this talk we study a class of (linear a
 nd nonlinear) integro-differential operators with anisotropic and singular
  kernels. We present local robust regularity estimates for weak solutions 
 in the general framework of bounded measurable coefficients. \nThe results
  in this talk are based on joint works with Moritz Kassmann\, Minhyun Kim 
 and Marvin Weidner.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Grzywny (Wroclaw University of Science and Technology)
DTSTART:20210615T130000Z
DTEND:20210615T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/35/">Subordinated Markov processes: estimates for heat kernels and G
 reen functions</a>\nby Tomasz Grzywny (Wroclaw University of Science and T
 echnology) as part of Non-local operators\, probability and singularities\
 n\n\nAbstract\nLet (M\, d) be a metric space and μ a Radon measure on M. 
 Assume that {S(t)}_{t\\in T} is a Markov process on M such that its transi
 tion function is absolutely continuous with μ\, where T is a set of non-n
 egative integers or a set of non-negative real numbers. By A we denote the
  semigroup generator associated with the transition function of {S(t)}.  F
 or a Bernstein function f we define a new semigroup with generator -f(-A) 
 that is a semigroup for the Markov process {S(K_t)}\, where {K_t} is a sub
 ordinator on  T associated with the function f. During the talk\, there wi
 ll be discussed  estimates of the haet kernel/transition function and Gree
 n function of {S(K_t)}. The proofs are elementary and do not use estimates
  for transition probability of  the subordinator. The talk is based on joi
 nt work with Bartosz Trojan.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timur Yastrzhembskiy (Brown University)
DTSTART:20210601T130000Z
DTEND:20210601T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/37/">Global $L_p$-estimates for kinetic Kolmogorov-Fokker-Planck equ
 ation</a>\nby Timur Yastrzhembskiy (Brown University) as part of Non-local
  operators\, probability and singularities\n\n\nAbstract\nWe  study the de
 generate  Kolmogorov equation (also known as kinetic Fokker-Planck equatio
 n) in both nondivergence and divergence forms:\n$$\n	\\partial_t u - v \\c
 dot D_x u - a^{i j} (z) D_{v_i v_j} u + \\lambda u = f\,\n$$\n$$\n	\\parti
 al_t u - v \\cdot D_x u - D_{v_i} (a^{i j} (z) D_{v_j} u) + \\lambda u = D
 _{v_i} f_i + f_0.\n$$\nThe leading coefficients are merely measurable in $
 t$ and  satisfy the VMO condition in $x\, v$  with respect to some quasi-m
 etric. We also assume boundedness and uniform nondegeneracy of $a$. We pro
 ve global a priori estimates in some weighted mixed-norm Lebesgue spaces a
 nd solvability results. Our proof does not rely on kernel estimates.\n\nTh
 e talk is based on a joint work with Hongjie Dong\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stjepan Šebek (University of Zagreb)
DTSTART:20210608T130000Z
DTEND:20210608T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/38/">Limit theorems for a stable sausage</a>\nby Stjepan Šebek (Uni
 versity of Zagreb) as part of Non-local operators\, probability and singul
 arities\n\n\nAbstract\nIn this talk\, we study fluctuations of the volume 
 of a stable sausage defined via a d-dimensional rotationally invariant alp
 ha-stable process. As the main results\, we establish a central limit theo
 rem and functional central limit theorem (in the case when d/alpha > 3/2) 
 with a standard one-dimensional Brownian motion in the limit\, and Khintch
 ine’s and Chung’s laws of the iterated logarithm (in the case when d/a
 lpha > 9/5).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Maurelli (Università degli Studi di Milano)
DTSTART:20210427T130000Z
DTEND:20210427T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/39/">Regularization by noise for transport PDEs: two results</a>\nby
  Mario Maurelli (Università degli Studi di Milano) as part of Non-local o
 perators\, probability and singularities\n\n\nAbstract\nWe say that a regu
 larization by noise phenomenon occurs for a possibly ill-posed differentia
 l equation if this equation becomes well-posed (in a pathwise sense) under
  addition of a suitable noise term. The long-term aim of regularization by
  noise is to show this phenomenon for PDEs coming from physics\, especiall
 y fluid dynamics.\n\nIn this talk we consider regularization by noise for 
 transport-type PDEs. A transport-type PDE is a prototype for many PDEs fro
 m physics and takes the form\n$$\n\\partial_t u(t\,x) +b(t\,x\,u)\\cdot\\n
 abla u(t\,x) =0\,\\quad t>0\,x\\in\\mathbb{R}^d\,u(t\,x)\\in\\mathbb{R}\,\
 \qquad (1)\n$$\nwith $b$ given vector field. We focus on two cases\,\n$$\n
 b(t\,x\,u) = \\tilde b(t\,x) \\text{ and } b(t\,x\,u)=\\tilde b(t\,x)u\,\\
 qquad (2)\n$$\ncorresponding respectively to the linear transport equation
  and a scalar conservation law. For irregular vector fields $\\tilde{b}$\,
  the corresponding deterministic transport equations (1) are in general il
 l-posed. We add to the transport equation the so-called transport noise\, 
 namely we consider the stochastic PDE\n$$\ndu(t\,x\,\\omega) +b\\cdot\\nab
 la u\\\,dt +\\nabla u\\circ dW =0\,\\\,t>0\,x\\in\\mathbb{R}^d\,u\\in\\mat
 hbb{R}\, \\qquad (3)\n$$\nwhere $W$ is a $d$-dimensional Brownian motion a
 nd $\\circ$ stands for Stratonovich integration. We show that\, for $b$ of
  the form (2) for some classes of irregular vector fields $\\tilde{b}$\, t
 he corresponding stochastic transport PDEs (3) are well-posed.\n\nThe proo
 fs are based on a combination of the renormalization argument by DiPerna-L
 ions and some parabolic bounds.\n\nThis talk is based on the works Attanas
 io-Flandoli 2011 and Gess-M. 2018.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katarzyna Pietruska-Pałuba (University of Warsaw)
DTSTART:20210511T130000Z
DTEND:20210511T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/40/">Properties of the integrated density of states for random Schr
 ödinger operators driven by nonlocal processes</a>\nby Katarzyna Pietrusk
 a-Pałuba (University of Warsaw) as part of Non-local operators\, probabil
 ity and singularities\n\n\nAbstract\nWe will discuss asymptotic properties
  of the integrated density of states for random systems whose hamiltonians
  are driven by nonlocal processes\, and the random field is either of Pois
 sonian or alloy type. In both cases the IDS exhibits unusually fast decay 
 near the bottom of the spectrum (called the Lifschitz singularity). If tim
 e permits\, we will also discuss the relation of the asymptotic behaviour 
 of the IDS to the long-time behaviour of solutions of the nonlocal parabol
 ic Anderson problem.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Klimsiak (Institute of Mathematics Polish Academy of Scienc
 es)
DTSTART:20210525T130000Z
DTEND:20210525T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/41/">Schrödinger equations with smooth measure potential and genera
 l measure data</a>\nby Tomasz Klimsiak (Institute of Mathematics Polish Ac
 ademy of Sciences) as part of Non-local operators\, probability and singul
 arities\n\n\nAbstract\nWe study equations driven by Schrödinger operators
  consisting of a self-adjoint Dirichlet operator and a singular potential\
 , which belongs to a class of positive Borel measures absolutely continuou
 s with respect to a capacity generated by the operator. In particular\, we
  cover positive potentials exploding on a set of capacity zero. The right-
 hand side of equations is allowed to be a general bounded Borel measure. T
 he class of self-adjoint Dirichlet operators is quite large. Examples incl
 ude integro-differential operators with the local part of divergence form.
  \n\nWe give a necessary and sufficient condition for the existence of a s
 olution\, and prove some regularity and stability results.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minhyun Kim (Bielefeld University)
DTSTART:20210622T130000Z
DTEND:20210622T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/42/">The concentration-compactness principle for the nonlocal anisot
 ropic $p$-Laplacian of mixed order</a>\nby Minhyun Kim (Bielefeld Universi
 ty) as part of Non-local operators\, probability and singularities\n\n\nAb
 stract\nIn this talk\, we introduce a new class of operators with an ortho
 tropic structure having different exponents of integrability and different
  orders of differentiability. We prove a robust Sobolev-type inequality an
 d establish the existence of minimizers of the Sobolev quotient. The metho
 d for the existence of minimizers is based on the concentration-compactnes
 s principle which we extend to this class of operators. One consequence of
  the main result is the existence of a nontrivial nonnegative solution to 
 the corresponding critical problem.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikola Sandrić (University of Zagreb)
DTSTART:20210629T130000Z
DTEND:20210629T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/43/">Periodic homogenization of linear degenerate PDEs</a>\nby Nikol
 a Sandrić (University of Zagreb) as part of Non-local operators\, probabi
 lity and singularities\n\n\nAbstract\nIn this talk\, we discuss functional
  CLT for a class of degenerate diffusion processes with periodic coefficie
 nts\, thus generalizing the already classical results in the context of un
 iformly elliptic diffusions. As an application\, we obtain periodic homoge
 nization of a class of linear degenerate elliptic and parabolic PDEs. The 
 talk is based on joint work with Ivana Valentić.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wolfgang Arendt (Ulm University)
DTSTART:20210706T130000Z
DTEND:20210706T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/44/">Variational Methods for the Dirichlet-to-Neumann Operator and F
 ractional Powers</a>\nby Wolfgang Arendt (Ulm University) as part of Non-l
 ocal operators\, probability and singularities\n\n\nAbstract\nUsually the 
 DtN operator is considered as a pseudo-differential operator on C-infinity
  domains.\nWe will present a variational approach which works for Lipschit
 z domains and even domains with finite surface. The same approach allows o
 ne to give a functional framework of the Caffarelli-Silvestre extension le
 ading to the fractional laplacian. We will realize the fractional power of
  any sectorial operator on a Hilbert space (in the sense of Kato) as a DtN
  operator with precise description of the domains.\n\nReferences:\n\nW. Ar
 endt\, A.F.M. ter Elst: The Dirichlet-to-Neumann operator on C. Ann. Sc. N
 orm. Super. Pisa Cl. Sci. 20 (2020) 1169-1196\n\nW. Arendt\, A.F.M. ter El
 st\, M. Warma: Fractional powers of sectorial operators via the Dirichlet-
 to-Neumann operator.\nComm. PDE 43 (2018) 1-24\n\nJ. Galé\, P. Miana\, P.
 R. Stinga: Extension problem and fractional operators: semigroups and wave
  equation. J. Evol. Eqn. 13 (2013) 343-368.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yehuda Pinchover (Technion – Israel Institute of Technology)
DTSTART:20210713T130000Z
DTEND:20210713T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/45/">Optimal Hardy inequalities for Schrodinger operators on graphs<
 /a>\nby Yehuda Pinchover (Technion – Israel Institute of Technology) as 
 part of Non-local operators\, probability and singularities\n\n\nAbstract\
 nFor a given subcritical discrete Schrödinger operator $H$ on a weighted 
 infinite graph $X$\, we construct a Hardy-weight $w$ which is optimal in t
 he following sense. The operator $H − \\lambda w$ is subcritical in $X$ 
 for all $\\lambda < 1$\, null-critical in $X$ for $\\lambda = 1$\, and sup
 ercritical near any neighborhood of infinity in $X$ for any $\\lambda>1$. 
 Our results rely on a criticality theory for Schrödinger operators on gen
 eral weighted graphs.\n\nThis is a joint work with Matthias Keller and Fel
 ix Pogorzelski.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yana Butko (Universität des Saarlandes)
DTSTART:20210720T130000Z
DTEND:20210720T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/46/">Stochastic solutions of generalized time-fractional evolution e
 quations</a>\nby Yana Butko (Universität des Saarlandes) as part of Non-l
 ocal operators\, probability and singularities\n\n\nAbstract\nThis is a jo
 int work with Christian Bender\, Saarland University.  We consider a gener
 al class of integro-differential evolution equations which includes the go
 verning equation of the generalized grey Brownian motion and the time- and
  space-fractional heat equation:\n\n$$u(t\,x) = u_0(x) + \\int_0^t k(t\,s)
 Lu(s\,x)ds\, \\qquad t>0\,\\quad x\\in\\mathbb{R}^d\, \\qquad (1)$$\n\nwhe
 re $L$ is a pseudo-differential operator associated to a Lévy process and
  \n$k(t\,s)$\, $0 < s < t < \\infty$\, is a general memory kernel. Such eq
 uations arise in models of anomalous diffusion.\n\nWe present a general re
 lation between the parameters of the equation  and the distribution of any
  stochastic process\, which provides a stochastic solution of Feynman-Kac 
 type.  More precisely\, we derive a series representation in terms of the 
 time kernel $k$ and the symbol $-\\psi$ of the pseudodifferential operator
  $L$ for the characteristic function of the one-dimensional marginals of a
 ny stochastic solution. We explain how this series simplifies in the impor
 tant case of homogeneous kernels which includes the kernel $k(t\,s)=(t-s)^
 {\\beta-1}/\\Gamma(\\beta)$ for time-fractional evolution equations and\, 
 more generally\, kernels corresponding to  Saigo-Maeda fractional diffinte
 gration operators. The connection between Saigo-Maeda fractional diffinteg
 ration operators and positive random variables with Laplace transform give
 n by Prabhakar's three parameter generalization of the Mittag-Leffler func
 tion is established. These results   yield a stochastic representation for
  (1) with a Saigo-Maeda kernel in terms of a randomly slowed down Lévy pr
 ocess $(Y_{At^\\beta})_{t\\geq 0}$\, where $Y$ is a Lévy process with inf
 initesimal generator $L$\, $A$ is an independent random variable with Lapl
 ace transform given by the three-parameter Mittag-Leffler function\, and $
 \\beta$ corresponds to the degree of homogeneity of the kernel. If $Y$ has
  a stable distribution (e.g.\, in the case of a symmetric fractional Lapla
 cian in space)\, the randomly slowed down Lévy process can be replaced by
  a randomly scaled linear fractional stable motion\,  providing a stochast
 ic solution in terms of a self-similar process with stationary increments.
  Similar results hold also in the case  of equation (1) with more general 
 operator $L$ (it is enough to assume that $L$ generates a strongly continu
 ous semigroup on some Banach space) and lead to Feynman-Kac formulae for s
 uch equations (if $L:=L_0+V$ where $L_0$ generates a Markov process and $V
 $ is a suitable potential). \n\n[1] Ch. Bender\, Ya.A. Butko.  Stochastic 
 solutions of generalized time-fractional evolution equations// arXiv:2102.
 00117 (2021)\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grzegorz Karch (University of Wrocław)
DTSTART:20210928T130000Z
DTEND:20210928T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/47/">Concentration phenomena in a model of chemotaxis</a>\nby Grzego
 rz Karch (University of Wrocław) as part of Non-local operators\, probabi
 lity and singularities\n\n\nAbstract\nIn this talk\, I shall discuss resul
 ts obtained in the papers:\n\nBiler\, Piotr\; Karch\, Grzegorz\; Zienkiewi
 cz\, Jacek\, Large\nglobal-in-time solutions to a nonlocal model of chemot
 axis. Adv. Math.\n330 (2018)\, 834–875.\n\nBiler\, Piotr\; Karch\, Grzeg
 orz\; Pilarczyk\, Dominika\, Global radial\nsolutions in classical Keller-
 Segel model of chemotaxis. J.\nDifferential Equations 267 (2019)\, no. 11\
 , 6352–6369.\n\nthe both on solutions to certain parabolic-elliptic mode
 ls of\nchemotaxis. In these papers\, criteria for existence and nonexisten
 ce\nof global-in-time solutions have been obtained.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathav Murugan (University of British Columbia)
DTSTART:20211026T140000Z
DTEND:20211026T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/48/">On the comparison between jump processes and subordinated diffu
 sions</a>\nby Mathav Murugan (University of British Columbia) as part of N
 on-local operators\, probability and singularities\n\n\nAbstract\nA well k
 nown method to obtain heat kernel estimates and Harnack inequalities for j
 ump processes is to compare the given jump process with a subordinated dif
 fusion process. On any space that admits a diffusion which satisfies sub-G
 aussian heat kernel bounds\, we show that a large family of jump processes
  have a jump kernel comparable to that of a subordinated diffusion process
 . If time permits\, I will also discuss another recent result that the par
 abolic Harnack inequality implies that the jump kernel admits a density. T
 his is joint work with Guanhua Liu (Tsinghua University).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Marinelli (University College London)
DTSTART:20211102T140000Z
DTEND:20211102T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/49/">On the Malliavin differentiability of solutions to reaction-dif
 fusion equations with multiplicative noise</a>\nby Carlo Marinelli (Univer
 sity College London) as part of Non-local operators\, probability and sing
 ularities\n\n\nAbstract\nWe discuss some recent results about existence an
 d regularity of the Malliavin derivative of the solution\, evaluated at fi
 xed points in time and space\, to a parabolic dissipative stochastic PDE o
 n $L^2(G)$\, where $G$ is an open bounded domain in $\\mathbb{R}^d$ with s
 mooth boundary. The equation is driven by a multiplicative Wiener noise an
 d the nonlinear drift term is the superposition operator associated to a r
 eal function which is assumed to be monotone\, locally Lipschitz continuou
 s\, and growing not faster than a polynomial. The arguments are based on t
 he well-posedness theory in the mild sense for stochastic evolution equati
 ons in Banach spaces\, as well as on monotonicity techniques and on a maxi
 mum principle for stochastic evolution equations.\n\nPartly based on joint
  work with Ll. Quer-Sardanyons.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Nowak (Bielefeld University)
DTSTART:20211012T130000Z
DTEND:20211012T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/50/">Regularity theory for nonlocal equations with VMO coefficients<
 /a>\nby Simon Nowak (Bielefeld University) as part of Non-local operators\
 , probability and singularities\n\n\nAbstract\nWe present some higher regu
 larity results for nonlocal equations with possibly discontinuous coeffici
 ents of VMO-type in fractional Sobolev spaces. While for corresponding loc
 al elliptic equations with VMO coefficients it is only possible to obtain 
 higher integrability\, in our nonlocal setting we are able to also prove a
  substantial amount of higher differentiability. Therefore\, our results a
 re in some sense of purely nonlocal type\, following the recent trend of s
 uch results in the literature.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Röckner (Bielefeld University)
DTSTART:20211109T140000Z
DTEND:20211109T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/51/">Strong dissipativity of generalized time-fractional derivatives
  and quasi-linear (stochstic) partial differential equations</a>\nby Micha
 el Röckner (Bielefeld University) as part of Non-local operators\, probab
 ility and singularities\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Stollmann (Chemnitz University of Technology)
DTSTART:20211019T130000Z
DTEND:20211019T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/52/">On the decomposition principle and a Persson type theorem for g
 eneral regular Dirichlet forms</a>\nby Peter Stollmann (Chemnitz Universit
 y of Technology) as part of Non-local operators\, probability and singular
 ities\n\n\nAbstract\nWe present a decomposition principle for general regu
 lar Dirichlet forms satisfying a spatial local compactness condition. We u
 se the decomposition principle to derive a Persson type theorem for the\nc
 orresponding Dirichlet forms.  Our setting covers non-local forms as well 
 as local ones.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pascal Auscher (University of Paris-Saclay)
DTSTART:20211116T140000Z
DTEND:20211116T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/53/">On regularity of weak solutions to linear parabolic systems wit
 h measurable coefficients</a>\nby Pascal Auscher (University of Paris-Sacl
 ay) as part of Non-local operators\, probability and singularities\n\n\nAb
 stract\nWe discuss what can be seen as an old and seemingly closed problem
  in regularity theory for parabolic systems. Still novel phenomenons show 
 up. Namely\, what is the regularity of weak solutions to equations or syst
 ems of the form $\\partial_t u - div A\\\, grad\\\, u = f+ div F$ on a par
 abolic cylinder assuming minimal  conditions on A and (parabolic) scale in
 variant integrability on f and F? Of course\, it depends on how one define
 s a weak solution. We show\, and it seems that was not noticed under minim
 al assumptions\, that  local square integrability of u and its gradient im
 plies local  $L^2$ bounds  uniformly in  time and more. Further\, with fur
 ther integrability property on f and F\, we also obtain  Hölder continuit
 y in time with values in $L^p$  for some $p>2$\, which is new\, as well as
  higher integrability for the gradient which was due to Giaquinta and Stru
 we.  This uses of half-order time derivatives with some non-local estimate
 s. \n\nJoint work with S. Bortz\, M. Egert and O. Saari (JMPA\, 2019).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Veraar (Delft University of Technology)
DTSTART:20211214T140000Z
DTEND:20211214T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/54/">Stochastic Navier-Stokes equations with gradient noise in criti
 cal spaces</a>\nby Mark Veraar (Delft University of Technology) as part of
  Non-local operators\, probability and singularities\n\n\nAbstract\nIn thi
 s talk I will present some recent results on the stochastic Navier-Stokes 
 equations on the d-dimensional torus with gradient noise\, which arises in
  the study of turbulent flows. Under very weak smoothness assumptions on t
 he data one has local well-posedness. Moreover\, using a new bootstrap met
 hod new regularization results for solution are obtained. New blow-up crit
 eria are introduced and can be seen as stochastic versions of the Serrin b
 low-up criteria. The latter is used to prove global well-posedness with hi
 gh probability for small initial data in critical spaces in any dimensions
  $d\\geq 2$. Moreover\, for d=2 we obtain new global well-posedness result
 s and regularization phenomena\, which unify and extend several earlier re
 sults.\n\nThe talk is based on joint work with Antonio Agresti https://arx
 iv.org/abs/2107.03953\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert Frank (University of Munich)
DTSTART:20220118T140000Z
DTEND:20220118T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/55/">Sobolev norms involving fractional Hardy operators</a>\nby Rupe
 rt Frank (University of Munich) as part of Non-local operators\, probabili
 ty and singularities\n\n\nAbstract\nWe consider the fractional Schrödinge
 r operator with Hardy potential and critical or subcritical coupling const
 ant. This operator generates a natural scale of homogeneous Sobolev spaces
  which we compare with the ordinary homogeneous Sobolev spaces. As a bypro
 duct\, we obtain generalized and reversed Hardy inequalities for this oper
 ator. Our results extend those obtained recently for ordinary (non-fractio
 nal) Schrödinger operators and have an important application in the treat
 ment of large relativistic atoms. \n\nThe talk is based on joint work with
  K. Merz and H. Siedentop\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Quastel (University of Toronto)
DTSTART:20220208T140000Z
DTEND:20220208T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/56/">Integrable fluctuations in random growth</a>\nby Jeremy Quastel
  (University of Toronto) as part of Non-local operators\, probability and 
 singularities\n\n\nAbstract\nWe survey models in the KPZ universality clas
 s and the integrable Markov process which governs their asymptotic fluctua
 tions.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fritz Gesztesy (Baylor University)
DTSTART:20211130T140000Z
DTEND:20211130T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/57/">Continuity properties of the spectral shift function for massle
 ss Dirac operators and an application to the Witten index</a>\nby Fritz Ge
 sztesy (Baylor University) as part of Non-local operators\, probability an
 d singularities\n\n\nAbstract\nWe report on recent results regarding the l
 imiting absorption principle for multi-dimensional\, massless Dirac-type o
 perators (implying absence of singularly continuous spectrum) and continui
 ty properties of the associated spectral shift function.\n\nWe will motiva
 te our interest in this circle of ideas by briefly describing the connecti
 on to index theory for non-Fredholm operators\, particularly\, to the noti
 on of the Witten index.\n\nThis is based on various joint work with A. Car
 ey\, J. Kaad\, G. Levitina\, R. Nichols\, D. Potapov\, F. Sukochev\, and D
 . Zanin.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Lin (McGill University)
DTSTART:20220308T140000Z
DTEND:20220308T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/58/">Asymmetric and Symmetric Cooperative Motion</a>\nby Jessica Lin
  (McGill University) as part of Non-local operators\, probability and sing
 ularities\n\n\nAbstract\nWe prove distributional convergence for a family 
 of random processes on $\\mathbb{Z}$\, which describe a type of random wal
 k with dependent delay. The model generalizes the "hipster random walks" s
 tudied by Addario-Berry et al [Probability Theory and Related Fields\, '20
 ]. We introduce a novel approach which relies on convergence results for f
 inite difference schemes of certainly fully nonlinear PDEs. This talk is b
 ased on joint work with Louigi Addario-Berry and Erin Beckman.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stéphane Menozzi (Université d'Évry Val d'Essonne)
DTSTART:20220315T140000Z
DTEND:20220315T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/59/">Heat kernel of supercritical SDEs with unbounded drifts</a>\nby
  Stéphane Menozzi (Université d'Évry Val d'Essonne) as part of Non-loca
 l operators\, probability and singularities\n\n\nAbstract\nWe consider SDE
 s driven by isotropic α-stable processes\, 0<α<2\, where:\n- the coeffic
 ients are Hölder continuous in space\n- the "diffusion" coefficient is bo
 unded and uniformly elliptic\n- the drift can be unbounded\n\nIf β is the
  spatial Hölder regularity index of the coefficients\, we obtain under th
 e condition α+β>1 existence of the density for such SDEs. Furthermore th
 is density enjoys sharp two-sided estimates and we derive as well sharp bo
 unds for its logarithmic derivative.\n\nImportantly\, we cover the whole s
 upercritical range. The proof relies on ad hoc parametrix expansions and p
 robabilistic techniques.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Metafune (Università del Salento)
DTSTART:20220322T140000Z
DTEND:20220322T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/60/">A unified approach to degenerate problems in the half-space</a>
 \nby Giorgio Metafune (Università del Salento) as part of Non-local opera
 tors\, probability and singularities\n\n\nAbstract\nWe study elliptic and 
 parabolic problems governed by the singular elliptic operators\n\n$\n\\mat
 hcal L =y^{\\alpha_1}\\Delta_{x} +y^{\\alpha_2}\\left(D_{yy}+\\frac{c}{y}D
 _y -\\frac{b}{y^2}\\right)\,\\qquad\\alpha_1\, \\alpha_2 \\in\\R\n$\n\nin 
 the half-space $\\R^{N+1}_+=\\{(x\,y): x \\in \\R^N\, y>0\\}$. This is a j
 oint paper with\n L. Negro and  C. Spina.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Friesen (Dublin City University)
DTSTART:20220405T130000Z
DTEND:20220405T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/61/">Continuous affine Volterra processes</a>\nby Martin Friesen (Du
 blin City University) as part of Non-local operators\, probability and sin
 gularities\n\n\nAbstract\nRecent empirical observations on intra-day stock
  market data suggest that volatilities defined as short-term fluctuations 
 of asset prices exhibit a highly rough behavior on smaller time scales. Wh
 ile such an effect is neither adequately captured nor predicted by Markovi
 an models\, recent analysis has shown that their rough counterparts based 
 on the fractional Brownian motion or on Volterra processes perfectly captu
 re these effects.\n\n \nIn this talk\, we focus on the particular class of
  affine Volterra processes being characterized by the feature that their c
 haracteristic function can be expressed in a semi-explicit form in terms o
 f a solution of a Volterra Riccati equation.\n\nFor this equation\, we pro
 vide a priori growth bounds\, Sobolev regularity in time\, continuous depe
 ndence on parameters\, and differentiability in the initial state. Based o
 n these findings\, we derive the existence of limiting distributions for a
  large class of affine Volterra processes. To each of these distributions\
 , we construct the associated stationary non-Markovian Volterra process an
 d finally analyze the regularity of its law.\n\nThis is joint work with P.
  Jin (BNU-HKBU)\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peixue Wu (University of Illinois at Urbana-Champaign)
DTSTART:20220412T130000Z
DTEND:20220412T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/62/">Heat kernel estimates for non-local operators with multi-singul
 ar killing potential.</a>\nby Peixue Wu (University of Illinois at Urbana-
 Champaign) as part of Non-local operators\, probability and singularities\
 n\n\nAbstract\nWe study the heat kernel estimates for non-local operators 
 with multi-singular killing potential. To be specific\, given an open set 
 $D$ with boundary $\\partial D = \\cup_{k=1}^d \\cup_{j=1}^{m_k} \\Gamma_{
 k\,j}$\, where for any $1\\leq k$\, $1 \\leq j \\leq m_k$\, $\\Gamma_{k\,j
 }$ is a $C^{1\,\\beta}$ submanifold without boundary of codimension $1\\le
  k\\le d$ and $\\{\\Gamma_{k\,j}\\}_{1\\le k\\le d\, 1\\le j \\le m_k}$ ar
 e disjoint. We show that the heat kernel $p^D(t\,x\,y)$ of the following n
 on-local operator with multi-singular critical killing potential \n\n\n$$\
 n\\big( (\\Delta|_D)^{\\alpha/2} - \\kappa\\big)(f)(x):= p.v. {A}_{d\,-\\a
 lpha} \\int_D \\frac{f(y)-f(x)}{|y-x|^{d+\\alpha}}dy - \\sum_{k=1}^d \\sum
 _{j=1}^{m_k} \\lambda_{k\,j} \\delta_{\\Gamma_{k\,j}}(x)^{-\\alpha}\,\n$$\
 n\nwhere $ \\lambda_{k\,j}>0\, \\alpha \\in (0\,2)$ has the following esti
 mates: for any given $T>0$\, \n\n$$\np^D(t\,x\,y) \\asymp p(t\,x\,y) \\pro
 d_{k=1}^d \\prod_{j=1}^{m_k} (\\frac{\\delta_{\\Gamma_{k\,j}}(x)}{t^{1/\\a
 lpha}} \\wedge 1)^{p_{k\,j}}(\\frac{\\delta_{\\Gamma_{k\,j}}(y)}{t^{1/\\al
 pha}} \\wedge 1)^{p_{k\,j}}\, \\quad \\forall t\\in (0\,T)\, x\,y\\in D\,\
 n$$\n\nwhere $p(t\,x\,y)$ is the heat kernel of the $\\alpha$-stable proce
 ss on $\\mathbb{R}^d$ and $p_{k\,j}$ and $\\lambda_{k\,j}$ are related thr
 ough a strictly increasing function $\\lambda = C(k\,\\alpha\,p)$. Our met
 hod is based on the result established in [Cho et al. Journal de Mathémat
 iques Pures et Appliquées 143(2020): 208-256] and a detailed analysis of 
 $C^{1\,\\beta}$ manifolds. \n\nThis is joint work with Renming Song and Sh
 ukun Wu: arXiv:2203.03891.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soobin Cho (Seoul National University)
DTSTART:20220510T130000Z
DTEND:20220510T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/63/">General law of iterated logarithm for Markov processes</a>\nby 
 Soobin Cho (Seoul National University) as part of Non-local operators\, pr
 obability and singularities\n\n\nAbstract\nIn this talk\, we discuss gener
 al criteria and forms of both liminf and limsup laws of\niterated logarith
 m (LIL) for continuous-time Markov processes. We establish LILs under loca
 l assumptions near zero (near in finity\, respectively) on uniform bounds 
 of the  first exit time from balls in terms of a function $\\phi$ and unif
 orm bounds on the tails of the jumping measure in terms of a function $\\p
 si$. One of the main results is that a simple ratio test in terms of the f
 unctions $\\phi$ and $\\psi$ completely determines whether there exists a 
 positive nondecreasing function $R(t)$ such that $limsup|X_t|/R(t)$ is pos
 itive and finite a.s.\, or not. Our results cover a large class of subordi
 nate dffusions\, jump processes with mixed polynomial local growths and ra
 ndom conductance models with long range jumps.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Bonforte (University of Madrid)
DTSTART:20220426T130000Z
DTEND:20220426T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/64/">Nonlinear and Nonlocal Diffusions. Smoothing effects\, Green fu
 nctions and functional inequalities</a>\nby Matteo Bonforte (University of
  Madrid) as part of Non-local operators\, probability and singularities\n\
 n\nAbstract\nWe will consider the Cauchy problem for Nonlinear Diffusion e
 quations of porous medium type $u_t=-\\mathcal{L} u^m$\, with $m>1$ and in
 vestigate whether or not integrable data produce bounded solutions. The di
 ffusion operator belongs to a quite general class of nonlocal operators\, 
 and we will see how different assumption on the operator imply (or not) sm
 oothing properties. We will briefly compare the approach based on Moser it
 eration and the approach through Green functions. On one hand\, we show th
 at if the linear case ($m=1$) enjoys smoothing properties\, also the nonli
 near will do. On the other hand\, we see that in some cases the nonlinear 
 diffusion enjoys the smoothing properties also when the linear counterpart
  does not\, thanks to the convex nonlinearity.\n\nFollowing Nash' ideas\, 
 we see how smoothing properties are often equivalent to the validity of Ga
 gliardo-Nirenberg-Sobolev (and Nash) inequalities: we explore these implic
 ations also in the nonlinear and nonlocal context and the connection with 
 dual inequalities (Hardy-Littlewood-Sobolev) and Green function estimates.
   \n\nThis is a work in progress with J. Endal (UAM\, Madrid).\n\nIf time 
 allows\, we will complete the panorama by showing related results on Eucli
 dean bounded domains (joint works with Figalli\, Ros-Oton\, Sire\, Vazquez
 ) and/or on Riemannian Manifolds (joint works with Berchio\, Ganguly\, Gri
 llo\, Muratori)\, together with a small detour on the Fast diffusion case 
 $m<1$ (joint work with Ibarrondo and Ispizua).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Spina (University of Salento)
DTSTART:20220531T130000Z
DTEND:20220531T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/65/">$L^p$ estimates  for a class of  degenerate  operators</a>\nby 
 Chiara Spina (University of Salento) as part of Non-local operators\, prob
 ability and singularities\n\n\nAbstract\nWe prove $L^p$-estimates for the 
    operator\n$$\\mathcal L=\\Delta_x+\\Delta_y +c\\frac{y}{|y|^2}\\cdot\\n
 abla_y-\\frac{b}{|y|^{2}}=\\Delta_x+L_y\,$$\nwhere $L_y=\\Delta_y +c\\frac
 {y}{|y|^2}\\cdot\\nabla_y-\\frac{b}{|y|^{2}}$. The parameters   $b\,\\ c$ 
 are constant real coefficients subject to the condition $ D:=b+\\left(\\fr
 ac{M-2+c}{2}\\right)^2> 0$. \n\nWe work in the space $L^p_c:=L^p(\\R^{N+M}
 \, |y|^c\\\, dxdy)$\, motivated by the fact that  the weight $|y|^c$ makes
  the operator symmetric in $L^2_c$ and we assume $M+c>0$\, so that the mea
 sure $d\\mu=|y|^c\\\, dx\\\, dy$ is locally finite on $\\R^{N+M}$.\n\n\n\n
 \nThe operators $\\Delta_x$\, $L_y$ commute  and the whole operator $\\mat
 hcal L$ satisfies the scaling property $I_s^{-1}\\mathcal L I_s=s^2\\mathc
 al L$\, if $I_s u(x\,y)=u(sx\,sy)$. It is not difficult to see that $\\mat
 hcal L$ generates a semigroup in $L^p_c$ if and only if $L_y$ generates in
  $L^p(\\R^M\, |y|^c\\\, dy)$ and this is equivalent to $(M+c)\\\, \\left|\
 \frac{1}{2}-\\frac 1 p\\right|<1+\\sqrt D$.\n\n\nWhen $M=1$ and $b=0$\,  $
 L_y$ is a Bessel operator and both $\\mathcal L=\\Delta_x+B_y$ and $D_t-\\
 mathcal L$ play a major role in the investigation of the fractional powers
  $(-\\Delta_x)^s$ and  $(D_t-\\Delta_x)^s$\, $s=(1-c)/2$\, through the  ``
 extension procedure" of Caffarelli and Silvestre [1]. \n\n\nWhen $M=1$\, t
 hat is in the half-space $\\R^{N+1}_+$\,  all the results of this paper\, 
 and much more\, have been proved  in [4] by taking advantage of sophistica
 ted tools from operator valued harmonic analysis.  More general\, non symm
 etrizing weights $|y|^m\\\, dx\\\, dy$ are therein considered and both Dir
 ichlet and Neumann boundary conditions. We refer the reader also to  [2]\,
  [3] for the case $b=0$  and with variable coefficients. \n\n\nHere we use
  a different strategy and show that $L^p$-estimates for the pure $x$-deriv
 atives\, that is the boundedness of the operators $D_{x_ix_j}\\mathcal L^{
 -1}$\, follow from sub-solution estimates through an interpolation theorem
  in absence of kernels in homogeneous spaces due to Z. Shen. Sub-solution 
 estimates\, that is improving of integrability for (sub) solutions of the 
 homogeneous equation $\\mathcal Lu=0$\, are proved by combining Cacciopoli
  estimates\, weighted Sobolev embeddings and Moser iteration.\n\n[1] L. Ca
 ffarelli\,L. Silvestre: An extension problem related to the fractional Lap
 lacean\,\nComm. Partial Differential Equations\, 32 (2007)\, no. 7-9 1245-
 1260.\n\n[2] H. Dong\, T. Phan: On parabolic and elliptic equations with s
 ingular or degenerate coeff-\ncients\, arxiv: 2007.04385 2020\n\n[3] H. Do
 ng\, T. Phan:Weighted mixed-norm Lp estimates for equations in non-diverge
 nce form\nwith singular coeffcients: the Dirichlet problem arxiv: 2103.080
 33 2021\n\n[4] G. Metafune\, L. Negro\, C. Spina: Lp estimates for the Caf
 farelli-Silvestre extension\noperators\, Journal of Differential Equations
  Volume 316\, (2022)\, Pages 290-345.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Błażej Wróbel (University of Wroclaw)
DTSTART:20220621T130000Z
DTEND:20220621T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/66/">On Lp estimates for positivity-preserving Riesz transforms rela
 ted to Schrödinger operators</a>\nby Błażej Wróbel (University of Wroc
 law) as part of Non-local operators\, probability and singularities\n\n\nA
 bstract\nWe study $L^p$ boundedness properties of positivity preserving Ri
 esz transforms related to a \nSchrödinger operator. Using interpolation t
 echnique we establish $L^p$ boundedness for general non-negative potential
 s. Then we present a counterexample showing that the $L^{\\infty}$ bounded
 ness may fail. Next we give integral type conditions on the potential $V$ 
 that guarantee the boundedness on the endpoints $p=1$ and $p=\\infty$. Our
  conditions depend only on the global properties of V and are resistant to
  small perturbations. In particular $V$ may have a power growth or an expo
 nential growth. \n\nThe talk is based on a joint work with Maciej Kucharsk
 i.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Xiao (Memorial University)
DTSTART:20220628T130000Z
DTEND:20220628T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/67/">Energy formulae for fractional Schrodinger-Poisson system</a>\n
 by Jie Xiao (Memorial University) as part of Non-local operators\, probabi
 lity and singularities\n\n\nAbstract\nThrough a geometric-capacity-theoret
 ic approach\, this talk presents two new formulas for the fractional energ
 y of a quantum particle arising from the fractional  Schrodinger-Poisson s
 ystem which models the behavior of a quantum particle within an unknown el
 ectrostatic field.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xue-Mei Li (EPFL and Imperial College London)
DTSTART:20221115T140000Z
DTEND:20221115T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/70/">Hessian estimates of the logarithmic heat kernel</a>\nby Xue-Me
 i Li (EPFL and Imperial College London) as part of Non-local operators\, p
 robability and singularities\n\n\nAbstract\nHessian estimates on the heat 
 kernel and its logarithmic estimates for important first steps toward unde
 rstanding\ntoe Brownian bridge measure\, a natural measure on loop spaces.
  It also find applications in studying the existence of Lipschitz\ntranspo
 rt maps. I shall discuss some new techniques in these studies and results.
  This is joint work with Xin Chen and Bo Wu.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Longjie Xie (Jiangsu Normal University)
DTSTART:20221011T130000Z
DTEND:20221011T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/71/">Weak and strong well-posedness of critical and supercritical SD
 Es with singular coefficients</a>\nby Longjie Xie (Jiangsu Normal Universi
 ty) as part of Non-local operators\, probability and singularities\n\n\nAb
 stract\nConsider the following time-dependent stable-like operator with dr
 ift:\n$$\n\\mathscr{L}_t\\varphi(x)=\\int_{\\mathbb{R}^d}\\big[\\varphi(x+
 z)-\\varphi(x)-z^{(\\alpha)}\\cdot\\nabla\\varphi(x)\\big]\\sigma(t\,x\,z)
 \\nu_\\alpha(d z)+b(t\,x)\\cdot\\nabla \\varphi(x)\,\n$$\nwhere $d\\geq 1$
 \, $\\nu_\\alpha$ is an $\\alpha$-stable type Lévy measure with $\\alpha\
 \in(0\,1]$ and $z^{(\\alpha)}=1_{\\alpha=1}1_{|z|\\leq1}z$\, $\\sigma$ is 
 a real-valued Borel function on $\\mathbb{R}_+\\times\\mathbb{R}^d\\times\
 \mathbb{R}^d$ and $b$ is an $\\mathbb{R}^d$-valued Borel function\non $\\m
 athbb{R}_+\\times\\mathbb{R}^d$. By using the Littlewood-Paley theory\, we
  establish the well-posedness for the martingale problem associated with $
 \\mathscr{L}_t$ under the sharp balance condition $\\alpha+\\beta\\geq1$\,
  where $\\beta$ is the Hölder index of $b$ with respect to $x$.\nMoreover
 \, we also study a class of stochastic differential equations driven by Ma
 rkov processes with generators of the form $\\mathscr{L}_t$.\nWe prove the
  pathwise uniqueness of strong solutions for such equations when the coeff
 icients are in certain Besov spaces.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Anh Bui (Macquarie University)
DTSTART:20221213T140000Z
DTEND:20221213T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/72/">On Sobolev norms involving generalized Hardy operators</a>\nby 
 The Anh Bui (Macquarie University) as part of Non-local operators\, probab
 ility and singularities\n\n\nAbstract\nConsider the operator on $L^{2}(\\m
 athbb{R}^d)\, d\\ge 1$\n  $$\n  \\mathcal L_a = (-\\Delta)^{\\alpha/2}+a|x
 |^{-\\alpha} \\quad \\text{with} \\quad 0<\\alpha<\\min\\{2\, d\\}.\n  $$\
 n  Under the condition $a\\ge -\\frac{2^\\alpha\\Gamma((d+\\alpha)/4)^2}{\
 \Gamma((d-\\alpha)/4)^2}$ the operator is non negative and self-adjoint.\n
   We prove that fractional powers {$\\mathcal{L}^{s/2}_a$}\n  for $s\\in(0
 \,2]$ satisfy the estimates\n  $$\n    \\|\\mathcal{L}_{a}^{s/2}f\\|_{L^{p
 }}\n      \\lesssim\\|(-\\Delta)^{\\alpha s/4}f\\|_{L^{p}}\,\n    \\qquad\
 n    \\|(-\\Delta)^{s/2}f\\|_{L^{p}}\n      \\lesssim \\|\\mathcal{L}_{a}^
 {\\alpha s/4}f\\|_{L^{p}}\n  $$\n  for suitable ranges of $p$. Our result 
 fills the remaining gap\n  in earlier results. The method of proof is base
 d on square function estimates for operators whose heat kernel has a weak 
 decay. This talk is based on joint work with P. D'Ancona.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrice Baudoin (University of Connecticut)
DTSTART:20221206T140000Z
DTEND:20221206T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/73/">Asymptotic windings of the unitary Brownian motion</a>\nby Fabr
 ice Baudoin (University of Connecticut) as part of Non-local operators\, p
 robability and singularities\n\n\nAbstract\nWe study several matrix diffus
 ion processes constructed from a unitary Brownian motion. In particular\, 
 we use the Stiefel fibration to lift the Brownian motion of the complex Gr
 assmannian to the complex Stiefel manifold and deduce a skew-product decom
 position of the Stiefel Brownian motion. As an application\, we prove asym
 ptotic laws for the determinants of the block entries of the unitary Brown
 ian motion. This is a joint work with Jing Wang (Purdue University).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Polidoro (University of Modena and Reggio Emilia)
DTSTART:20221220T140000Z
DTEND:20221220T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/74
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/74/">Asymptotic bounds for the relativistic Fokker-Planck operator</
 a>\nby Sergio Polidoro (University of Modena and Reggio Emilia) as part of
  Non-local operators\, probability and singularities\n\n\nAbstract\nWe con
 sider a class of second order degenerate kinetic operators L in the framew
 ork of special relativity. We first describe L as an Hörmander operator w
 hich is invariant with respect to Lorentz transformations. Then we prove a
  Lorentz-invariant Harnack type inequality\, and we derive accurate asympt
 otic lower bounds for positive solutions to Lf=0. As a consequence we obta
 in upper and  lower bounds for the density of the relativistic stochastic 
 process associated to L.\n\nThis is a joint work with Francesca Anceschi a
 nd Annalaura Rebucci.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abdelaziz Rhandi (University of Salerno)
DTSTART:20221108T130000Z
DTEND:20221108T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/75
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/75/">Bounds for the gradient of the transition kernel for elliptic o
 perators with unbounded diffusion\, drift and potential terms</a>\nby Abde
 laziz Rhandi (University of Salerno) as part of Non-local operators\, prob
 ability and singularities\n\n\nAbstract\nWe prove global Sobolev regularit
 y and pointwise upper bounds for the gradient of transition densities asso
 ciated with second order differential operators in R^d with unbounded diff
 usion\, drift and potential terms.\n\nThis is joint work with Markus Kunze
  and Marianna Porfido.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaj Nyström (Uppsala University)
DTSTART:20221025T130000Z
DTEND:20221025T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/76
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/76/">Parabolic uniform rectifiability and caloric measure I: $A_\\in
 fty$ implies parabolic uniform rectifiability of a parabolic Lipschitz gra
 ph</a>\nby Kaj Nyström (Uppsala University) as part of Non-local operator
 s\, probability and singularities\n\n\nAbstract\nWe prove that if a parabo
 lic Lipschitz graph domain has the property that its caloric measure is a 
 parabolic $A_\\infty$ weight with respect to surface measure\, then the fu
 nction defining the graph has a half-order time derivative in the space of
  (parabolic) bounded mean oscillation. Equivalently\, we prove that the $A
 _\\infty$ property of caloric measure implies that the boundary is parabol
 ic uniformly rectifiable. Consequently\, by combining our result with the 
 work of Lewis and Murray we resolve\, in the setting of parabolic Lipschit
 z graph domains\, a longstanding open problem in the field by proving that
  the $L^p$ solvability (for some $p > 1$) of the Dirichlet problem for the
  heat equation is equivalent to parabolic uniformly rectifiability.  This 
 is joint work with S. Bortz\, S. Hofmann\, and J.M. Martell.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-François Jabir (Higher School of Economics)
DTSTART:20230117T140000Z
DTEND:20230117T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/77/">Multidimensional stable-driven McKean-Vlasov SDEs with distribu
 tional interaction kernel</a>\nby Jean-François Jabir (Higher School of E
 conomics) as part of Non-local operators\, probability and singularities\n
 \n\nAbstract\nThis talk will be focused on presenting existence and unique
 ness results\, in a weak and a strong sense\, for McKean-Vlasov models dri
 ven by alpha-stable Lévy processes and an interaction kernel lying in a B
 esov space with non-positive exponent.  In this specific setting\, we exhi
 bit how\, quantitatively\, the McKean non-linearity\, together with the no
 ise\, provides a regularisation effect allowing to pass beyond classical -
  or more recently established - characteristic thresholds ensuring the wel
 lposedness of linear SDEs with singular derive. Application to physically-
 based McKean-Vlasov models and the propagation of chaos property of some r
 elated particle approximation will be also discussed. \n\n\n(This work is 
 a joint collaboration with P-E. Chaudru de Raynal\,  Laboratoire de Mathé
 matiques Jean Leray\, Nantes\, and S. Menozzi\, LaMME\, Univ. Evry Val d
 ’Essonne - Paris Saclay.)\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xicheng Zhang (Beijing Institute of Technology)
DTSTART:20230131T140000Z
DTEND:20230131T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/78/">Second order fractional  mean-field  SDEs with singular kernels
  and measure initial data</a>\nby Xicheng Zhang (Beijing Institute of Tech
 nology) as part of Non-local operators\, probability and singularities\n\n
 \nAbstract\nIn this work we establish the local and global well-posedness 
 of weak and strong solutions to second order fractional mean-field SDEs wi
 th singular/distribution interaction kernels and measure initial value\, w
 here the kernel can be\nNewton or Coulomb potential\, Riesz potential\, Bi
 ot-Savart law\, etc. Moreover\, we also show the stability\, smoothness an
 d the short time singularity and large time decay estimates of the density
 .\nOur results reveal a phenomenon that for nonlinear mean-field equations
 \, the regularity of the initial distribution could balance the singularit
 y of the kernel. The precise relationship between the singularity of kerne
 ls and the regularity of\ninitial value are calculated\, which belongs to 
 the subcritical regime in scaling sense. In particular\, our results  prov
 ide microscopic probability explanation and establish a unified treatment 
 for\nmany physical models such as fractional Vlasov-Poisson-Fokker-Planck 
 system\, the vorticity formulation of 2D-fractal Navier-Stokes equations\,
  surface quasi-geostrophic models\, fractional porous medium equation with
  viscosity\, etc.\n(This is a joint work with Zimo Ham and Michael Rockner
 .)\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Marino (Polish Academy of Sciences)
DTSTART:20230124T140000Z
DTEND:20230124T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/79
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/79/">Weak regularisation by degenerate Lévy noise</a>\nby Lorenzo M
 arino (Polish Academy of Sciences) as part of Non-local operators\, probab
 ility and singularities\n\n\nAbstract\nThe current talk presents some new 
 results about the regularisation by noise phenomena for multidimensional O
 DEs\, where the random disturbance stands as a Lévy process (with suitabl
 e properties) and it perturbs the dynamics only on some components. In par
 ticular\, we aim to exhibit the minimal Hölder regularity on the determin
 istic drift ensuring the well-posedness\, in a weak probabilistic sense\, 
 of the associated SDE. Due to the noise degeneracy\, an hypoelliptic-type 
 framework is implemented assuming a weak Hörmander condition on the drift
 . As a by-product of our method of proof\, Krylov-type estimates for the c
 anonical solution process are also established. In conclusion\, we also sh
 ow through suitable counter-examples that there exists indeed an (almost) 
 sharp threshold on the Hölder regularity exponents of the drift ensuring 
 the weak well-posedness for the SDE.\n\n\nThe work this talk is based upon
  is a joint collaboration with S. Menozzi (LaMME\, Université d’Evry Va
 l d’Essonne).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renming Song (University of Illinois Urbana-Champaign)
DTSTART:20230207T140000Z
DTEND:20230207T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/80
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/80/">Potential theory of Dirichlet forms with jump kernels blowing u
 p at the boundary</a>\nby Renming Song (University of Illinois Urbana-Cham
 paign) as part of Non-local operators\, probability and singularities\n\n\
 nAbstract\nIn this talk\, I will present some recent results on potential 
 theory of Dirichlet forms on the half-space $\\R^d_+$ defined by the jump 
 kernel $J(x\,y)=|x-y|^{-d-\\alpha}\\mathcal{B}(x\,y)$\, where $\\alpha\\in
  (0\,2)$ and $\\mathcal{B}(x\,y)$ can blow up to infinity at the boundary.
  The main results include boundary Harnack principle and sharp two-sided G
 reen function estimates.\n\nThis talk is based on a joint paper with Panki
  Kim and Zoran Vondracek.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krzysztof Bogdan (Wroclaw University of Science and Technology)
DTSTART:20230314T140000Z
DTEND:20230314T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/81
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/81/">The fractional Laplacian with reflections</a>\nby Krzysztof Bog
 dan (Wroclaw University of Science and Technology) as part of Non-local op
 erators\, probability and singularities\n\n\nAbstract\nMotivated by the no
 tion of isotropic $\\alpha$-stable Lévy process confined\, by ''reflectio
 ns''\, to a bounded open Lipschitz set\, we study related analytical objec
 ts. In particular\, we construct the corresponding transition semigroup\, 
 and prove the exponential speed of convergence of the semigroup to a uniqu
 e stationary distribution over a long time. This is a joint work with Mark
 us Kunze.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Butkovsky (Technische Universität Berlin)
DTSTART:20230404T130000Z
DTEND:20230404T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/82/">Stochastic equations with singular drift driven by fractional B
 rownian motion</a>\nby Oleg Butkovsky (Technische Universität Berlin) as 
 part of Non-local operators\, probability and singularities\n\n\nAbstract\
 nJoint work with Khoa Le and Leonid Mytnik [1]. We consider stochastic dif
 ferential equation\n$$\nd X_t=b(X_t) dt +d W_t^H\,\n$$\nwhere the drift $b
 $ is either a measure or an integrable function\, and $W^H$ is a $d$-dimen
 sional fractional Brownian motion with Hurst parameter $H\\in(0\,1)$\, $d\
 \in\n$. For the case where $b\\in L_p(\\R^d)$\, $p\\in[1\,\\infty]$ we sho
 w weak existence of solutions to this equation under the   condition\n$$\n
 \\frac{d}p<\\frac1H-1\,\n$$\nwhich is an extension of the Krylov-Rockner c
 ondition (2005) to the fractional  case. We construct a counter-example sh
 owing optimality of this condition. If $b$ is a Radon measure\, particular
 ly the delta measure\, we prove weak existence of solutions to this equati
 on  under the optimal  condition $H<\\frac1{d+1}$. We also show strong wel
 l-posedness of solutions to this equation under certain conditions.\nTo es
 tablish these results\, we utilize the stochastic sewing technique and dev
 elop a new version of the stochastic sewing lemma.\n\n[1] Butkovsky\, O.\,
  Lê\, K.\, & Mytnik\, L. (2023). Stochastic equations with singular drift
  driven by fractional Brownian motion. arXiv preprint arXiv:2302.11937.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincenzo Ambrosio (Università Politecnica delle Marche)
DTSTART:20230627T130000Z
DTEND:20230627T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/83/">The nonlinear fractional relativistic Schrödinger equation</a>
 \nby Vincenzo Ambrosio (Università Politecnica delle Marche) as part of N
 on-local operators\, probability and singularities\n\n\nAbstract\nWe consi
 der the following class of fractional relativistic Schrödinger equations:
 \n\\[\n\\begin{cases}\n(-\\Delta+m^{2})^{s}u + V(\\varepsilon x) u= f(u)\,
 \\quad {\\rm in} \\quad \\mathbb{R}^{N}\,\\\\\nu \\in H^{s}(\\mathbb{R}^{N
 })\, \\quad u>0 \\quad {\\rm in} \\quad \\mathbb{R}^{N}\,\n\\end{cases}\n\
 \]\nwhere $\\varepsilon>0$ is a small parameter\, $s\\in (0\, 1)$\, $m>0$\
 , $N> 2s$\, $(-\\Delta+m^{2})^{s}$ is the fractional relativistic Schrödi
 nger operator\, $V:\\mathbb{R}^{N}\\rightarrow \\mathbb{R}$ is a  continuo
 us potential satisfying a local condition\, and $f:\\mathbb{R}\\rightarrow
  \\mathbb{R}$ is a continuous subcritical nonlinearity. We first show that
 \, for $\\varepsilon>0$ small enough\, the above problem has a weak soluti
 on $u_{\\varepsilon}$ (with exponential decay at infinity) which concentra
 tes around a local minimum point of $V$ as $\\varepsilon\\rightarrow 0$. W
 e also relate the number of positive solutions with the topology of the se
 t where the potential $V$ attains its minimum value.\n\nThe main results w
 ill be established by using a penalization technique\, the generalized Neh
 ari manifold method and Ljusternik-Schnirelman theory.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marvin Weidner (Universitat de Barcelona)
DTSTART:20230516T130000Z
DTEND:20230516T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/84/">The nonlocal Bernstein technique and the nonlocal obstacle prob
 lem</a>\nby Marvin Weidner (Universitat de Barcelona) as part of Non-local
  operators\, probability and singularities\n\n\nAbstract\nThe Bernstein te
 chnique is an elementary but powerful tool in the regularity theory for el
 liptic and parabolic equations. It is based on the insight that\, if deriv
 atives of a solution are also subsolutions to an equation\, then the maxim
 um principle can be used in order to obtain regularity estimates for these
  solutions.\nIn the first part of this talk\, we explain how the Bernstein
  technique can be extended to a large class of integro-differential equati
 ons driven by nonlocal operators that are comparable to the fractional Lap
 lacian. In the second part\, we discuss several applications of this techn
 ique to the regularity theory for the nonlocal obstacle problem in a bound
 ed domain.\nThis talk is based on a joint work with Xavier Ros-Oton and Da
 mià Torres-Latorre.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Krylov (University of Minnesota)
DTSTART:20230523T140000Z
DTEND:20230523T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/85
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/85/">On weak solutions of time inhomogeneous Ito's equations with VM
 O diffusion and Morrey drift</a>\nby Nikolay Krylov (University of Minneso
 ta) as part of Non-local operators\, probability and singularities\n\n\nAb
 stract\nWe prove the existence and weak uniqueness of weak solutions of It
 o's stochastic time dependent equations with irregular diffusion and drift
  terms of Morrey class with mixed norms.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kulik (Wrocław University of Science and Technology)
DTSTART:20230606T130000Z
DTEND:20230606T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/86/">Drift reduction and parametrix construction for stochastic diff
 erential equations driven by cylindrical Lévy noises.</a>\nby Alexei Kuli
 k (Wrocław University of Science and Technology) as part of Non-local ope
 rators\, probability and singularities\n\n\nAbstract\nIn the talk\, we wil
 l present an analytic construction for the unique weak solution \nof an SD
 E driven by a cylindrical Lévy noise which are spatially inhomogeneous in
  the sense that different coordinates of the driving Lévy process may hav
 e different  scaling properties. We will discuss how the classical paramet
 rix method for constructing fundamental solutions  to parabolic equations 
 should be adapted in order to handle numerous  difficulties which arise in
  this non-local setting\, including essential singularity\, lack of scalin
 g\, and presence of the drift (gradient) term which may be not order-domin
 ated by the noise.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guohuan Zhao (Chinese Academy of Sciences)
DTSTART:20230711T130000Z
DTEND:20230711T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/87
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/87/">Lévy-type operators with low singularity kernels: regularity e
 stimates and martingale problem</a>\nby Guohuan Zhao (Chinese Academy of S
 ciences) as part of Non-local operators\, probability and singularities\n\
 n\nAbstract\nThe main focus of this talk is on the linear non-local operat
 or $L$ defined by\n$$\nL u (x) = \\int_{\\mathbb{R}^d} (u(x+z)-u(x)) a(x\,
 z)J(z)~d z.\n$$\nHere $J$ is the jumping kernel of a L\\'evy process\, whi
 ch exhibits only a low-order singularity near the origin and does not perm
 it standard scaling. To analyze elliptic equations associated with $L$\, I
  will introduce generalized Orlicz-Besov spaces that are specifically tail
 ored for this purpose. Moreover\, I will establish certain regularity prop
 erties of the solutions to such equations in these spaces. Additionally\, 
 I intend to introduce the martingale problem associated with $L$. By explo
 iting analytic results\, we demonstrate the well-posedness of the martinga
 le problem under mild conditions\, and establish a new Krylov-type estimat
 e for the corresponding Markov processes. This is based on joint work with
  Eryan Hu from Tianjin University.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phan Thành Nam (Ludwig-Maximilians-Universität München)
DTSTART:20231024T130000Z
DTEND:20231024T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/88/">Cwikel-Lieb-Rozenblum type estimates for Schrödinger operators
  with Hardy potential</a>\nby Phan Thành Nam (Ludwig-Maximilians-Universi
 tät München) as part of Non-local operators\, probability and singularit
 ies\n\n\nAbstract\nThe celebrated Cwikel-Lieb-Rozenblum (CLR) inequality s
 tates that the number of negative eigenvalues of the Schrödinger operator
  $-\\Delta-V(x)$ in $L^2(R^d)$ is bounded from above by the integration of
  |V|^{d/2}. Up to a universal constant factor\, this bound is optimal for 
 a wide range of fermionic systems\, from one-body systems where it is equi
 valent to the standard Sobolev inequality\, to large systems where it is c
 onsistent with Weyl's semiclassical approximation. I will discuss extensio
 ns of the CLR bound when $V(x)$ may be as singular as the Hardy potential 
 $(d/2-1)^2 |x|^{-2}$. The critical singularity requires a logarithmic corr
 ection which has been noticed for the one-body case but seems unknown for 
 the general case. The talk is based on joint work with Giao Ky Duong\, Thi
  Minh Thao Le\, and Phuoc Tai Nguyen.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nguyen H. Lam (Memorial University)
DTSTART:20231121T140000Z
DTEND:20231121T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/89
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/89/">Hardy-Rellich type inequalities: A new approach and symmetrizat
 ion principle</a>\nby Nguyen H. Lam (Memorial University) as part of Non-l
 ocal operators\, probability and singularities\n\n\nAbstract\nWe present a
  new way to use the notion of Bessel pair to establish the optimal Hardy-R
 ellich type inequalities. We also talk about necessary and sufficient cond
 itions on the weights for the Hardy-Rellich inequalities to hold. Symmetry
  properties of the Rellich type and Hardy-Rellich type inequalities will a
 lso be discussed. The talk is based on joint work with Anh Do\, Guozhen Lu
 \, and Lu Zhang.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Russo (ENSTA Paris)
DTSTART:20231205T140000Z
DTEND:20231205T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/90
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/90/">Weak Dirichlet processes with jumps and applications</a>\nby Fr
 ancesco Russo (ENSTA Paris) as part of Non-local operators\, probability a
 nd singularities\n\n\nAbstract\nIn this talk we will revisit the notion of
  weak Dirichlet process\nwhich is the natural extension of semimartingale 
 with jumps.\nIf $X$ is such a process\, then it is the sum of a local mart
 ingale $M$ and a\nmartingale ortogonal process $A$ in the sense\nthat $[A\
 ,N] = 0$ for every continuous local martingale $N$.\nWe remark that if $[A
 ] = 0$ then $X$ is a Dirichlet process.\nThe notion of Dirichlet process i
 s not very suitable in the\njump case since in this case $A$ is forced to 
 be continuous.\n\nThe talk will discuss the following points.\n\n- To prov
 ide a (unique) decomposition which\n  is also significant for semimartinga
 les with jumps.\n\n- To introduce the notion of characteristics\n  (simila
 rly to the case of semimartingales)\n  in equivalence with some It\\^o typ
 e chain rules.\n\n- To discuss various examples of such processes\n  arisi
 ng from path-dependent martingale problems.\n  This includes path-dependen
 t stochastic differential equations\n  with involving a distributional dri
 ft and with jumps.  \n\n\nThe talk is based on a joint paper with E. Bandi
 ni (Bologna).\n\nhttp://uma.ensta-paristech.fr/$\\sim$russo\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Issoglio (University of Torino)
DTSTART:20231003T130000Z
DTEND:20231003T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/91
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/91/">McKean SDEs with singular coefficients</a>\nby Elena Issoglio (
 University of Torino) as part of Non-local operators\, probability and sin
 gularities\n\n\nAbstract\nIn this talk we consider a class of SDEs with dr
 ift depending on the law density of the solution\, known as McKean SDEs. T
 he novelty here is that the drift is singular in the sense that it is `mul
 tiplied' by a generalised function (element of a negative fractional Sobol
 ev space). Those equations are interpreted in the sense of a suitable sing
 ular martingale problem\, thus a key tool is the study of the correspondin
 g singular Fokker-Planck equation. We define the notion of solution to the
  singular McKean equation and show its existence and uniqueness. This is b
 ased on a joint work with F. Russo (ENSTA).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhen-Qing Chen (University of Washington)
DTSTART:20231114T140000Z
DTEND:20231114T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/92
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/92/">Boundary Harnack principle for non-local operators</a>\nby Zhen
 -Qing Chen (University of Washington) as part of Non-local operators\, pro
 bability and singularities\n\n\nAbstract\nThe classical boundary Harnack p
 rinciple asserts that two positive harmonic\nfunctions that vanish on a po
 rtion of the boundary of a smooth domain decay\nat the same rate. It is we
 ll known that scale invariant boundary Harnack\ninequality holds for Lapla
 cian \\Delta on uniform domains and holds for\nfractional Laplacians \\Del
 ta^s on any open sets. It has been an open\nproblem whether the scale-inva
 riant boundary Harnack inequality holds on\nbounded Lipschitz domains for 
 Levy processes with Gaussian components such\nas the independent sum of a 
 Brownian motion and an isotropic stable process\n(which corresponds to \\D
 elta + \\Delta^s).\n \nIn this talk\, I will present a necessary and suffi
 cient\ncondition for the scale-invariant boundary Harnack inequality to ho
 ld for a\nclass of non-local operators on metric measure spaces through a\
 nprobabilistic consideration. This result will then be applied to give a\n
 sufficient geometric condition for the scale-invariant boundary Harnack\ni
 nequality to hold for subordinate Brownian motions having Gaussian compone
 nts \non bounded Lipschitz domains in Euclidean spaces. This condition is 
 almost optimal and  \na counterexample will be given showing that the scal
 e-invariant BHP may fail\non some bounded Lipschitz domains with large Lip
 schitz constants.\n\nBased on joint work with Jieming Wang.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Flandoli (Scuola Normale Superiore di Pisa)
DTSTART:20240305T140000Z
DTEND:20240305T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/93
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/93/">Stochasticity into fluids</a>\nby Franco Flandoli (Scuola Norma
 le Superiore di Pisa) as part of Non-local operators\, probability and sin
 gularities\n\n\nAbstract\nFrom the beginning of the advent of Stochastic P
 artial Differential Equations (SPDEs)\, classes of equations related to fl
 uid dynamics were considered. Even earlier\, Landau and Lischitz wrote a N
 avier-Stokes equation perturbed by additive noise\, in their volume on flu
 id mechanics. However\, deciding the form of stochasticity realistic or in
 teresting for fluid dynamics remains one of the most important questions s
 till debated and stochastic analysis helps a lot to address this problem. 
 I will try to review part of the present understanding of this modeling is
 sue and its consequences.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Luis Pérez Garmendia (CIMAT)
DTSTART:20231219T140000Z
DTEND:20231219T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/94
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/94/">Multi-armed Lévy bandits with periodic decision opportunities<
 /a>\nby José Luis Pérez Garmendia (CIMAT) as part of Non-local operators
 \, probability and singularities\n\n\nAbstract\nWe consider a version of t
 he continuous-time multi-armed bandit problem where decision\nopportunitie
 s arrive at Poisson arrival times and study its Gittins index policy. When
  driven by a Lévy process\, we will show that the Gittins index can be ex
 pressed in terms of a Wiener-Hopf factorization of the Lévy process obser
 ved at the arrival times of an independent Poisson process.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassili Kolokoltsov (Moscow State University\, Higher School of Ec
 onomics and the University of Warwick)
DTSTART:20240123T140000Z
DTEND:20240123T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/95
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/95/">Convergence rates for functional central limit theorems with st
 able laws and domains of quasi-attraction</a>\nby Vassili Kolokoltsov (Mos
 cow State University\, Higher School of Economics and the University of Wa
 rwick) as part of Non-local operators\, probability and singularities\n\n\
 nAbstract\nThe talk will be devoted to the three new directions of researc
 h:\n\n1) Rates of convergence in the functional CLT with stable limits\; 2
 ) Domains of quasi-attraction\n\nas distributions\, whose normalised sums 
 of $n$ i.i.d terms approach stable laws for large\,\n\nbut not too large $
 n$ (full quantitative and qualitative description of this effect in a func
 tional setting)\;\n\n3) Rates of convergence of CTRWs (continuous time\n\n
 random walks) to fractional evolutions. The ideas of the talk are taken fr
 om the recent author's papers\n\n(1) The Rates of Convergence for Function
 al Limit Theorems with\n\nStable Subordinators and for CTRW Approximations
  to\n\nFractional Evolutions. Fractal Fract. (2023)\, 7\, 335.\n\nhttps://
 doi.org/10.3390/fractalfract7040335\n\n(2) Domains of Quasi Attraction: Wh
 y Stable Processes Are Observed in Reality?\n\nFractal Fract. (2023)\, 7\,
  752.\n\nhttps://doi.org/10.3390/fractalfract7100752\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krzysztof Burdzy (University of Washington)
DTSTART:20240416T150000Z
DTEND:20240416T160000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/96
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/96/">Simple nonlinear PDEs inspired by billiards</a>\nby Krzysztof B
 urdzy (University of Washington) as part of Non-local operators\, probabil
 ity and singularities\n\n\nAbstract\nHow many times can $n$ billiard balls
  collide\nin the open $d$-dimensional space? I will provide some\nestimate
 s. I will explain how the above question leads\nto a ``pinned billiard bal
 ls'' model. On a large scale\,\nthe model seems to have a hydrodynamic lim
 it.\nThe parameters of the conjectured limit should satisfy\nsimple nonlin
 ear PDEs. While the existence and properties\nof the conjectured hydrodyna
 mic limit are open questions\,\nI will provide a quite complete analysis o
 f the conjectured PDEs.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Saldaña (National Autonomous University of Mexico)
DTSTART:20240319T140000Z
DTEND:20240319T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/97
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/97/">The logarithmic Laplacian: a new tool in the analysis of PDEs w
 ith fractional diffusions</a>\nby Alberto Saldaña (National Autonomous Un
 iversity of Mexico) as part of Non-local operators\, probability and singu
 larities\n\n\nAbstract\nIn this talk\, I will give an introduction to the 
 logarithmic Laplacian\, which is a relatively new pseudodifferential opera
 tor that has shown to be a powerful tool in the study of linear and nonlin
 ear fractional PDEs.  I will describe some of its main properties\, applic
 ations\, and some recent regularity results.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Simonov (Sorbonne Université)
DTSTART:20240409T130000Z
DTEND:20240409T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/98
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/98/">Fast diffusion equations\, tails and convergence rates</a>\nby 
 Nikita Simonov (Sorbonne Université) as part of Non-local operators\, pro
 bability and singularities\n\n\nAbstract\nUnderstanding the intermediate a
 symptotic and computing convergence rates towards equilibria are among the
  major problems in the study of parabolic equations. Convergence rates dep
 end on the tail behaviour of solutions. This observation raised the follow
 ing question: how can we understand the tail behaviour of solutions from t
 he tail behaviour of the initial datum?\n\nIn this talk\, I will discuss t
 he asymptotic behaviour of solutions to the fast diffusion equation. It is
  well known that non-negative solutions behave for large times as the Bare
 nblatt (or fundamental) solution\, which has an explicit expression. In th
 is setting\, I will introduce the Global Harnack Principle (GHP)\, precise
  global pointwise upper and lower estimates of non-negative solutions in t
 erms of the Barenblatt profile. I will characterize the maximal (hence opt
 imal) class of initial data such that the GHP holds by means of an integra
 l tail condition. As a consequence\, I will provide rates of convergence t
 owards the Barenblatt profile in entropy and in stronger norms such as the
  uniform relative error.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:René Schilling (Technische Universität Dresden)
DTSTART:20240507T130000Z
DTEND:20240507T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/99/">The Liouville Theorem for Lévy Generators (and beyond) and the
  Unique Continuation Property</a>\nby René Schilling (Technische Universi
 tät Dresden) as part of Non-local operators\, probability and singulariti
 es\n\n\nAbstract\nWe discuss necessary and sufficient criteria for certain
  Fourier\nmultiplication operators to satisfy the Liouville property (boun
 ded\nharmonic functions are a.s.\\ constant) and the local continuation\np
 roperty (bounded functions\, that are harmonic and identically zero on a\n
 domain\, are a.s. zero on the whole space). Since the operators generate\n
 stochastic processes\, there is also a probabilistic interpretation of\nth
 ese findings.\n\nThis is a joint work with David Berger (TU Dresden)\,\nEu
 gene Shargorodsky (King's College\, London) and Teo Sharia (Royal\nHollowa
 y\, London).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zimo Hao (Universität Bielefeld)
DTSTART:20240312T140000Z
DTEND:20240312T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/100/">SDEs with supercritical distributional drifts</a>\nby Zimo Hao
  (Universität Bielefeld) as part of Non-local operators\, probability and
  singularities\n\n\nAbstract\nLet $d\\geq 2$.  In this talk\, we investiga
 te the following  stochastic\ndifferential equation (SDE) in ${\\mathbb R}
 ^d$ driven by Brownian motion\n$$\n{\\rm d} X_t=b(t\,X_t){\\rm d} t+\\sqrt
 {2}{\\rm d} W_t\,\n$$\nwhere $b$ belongs to the space ${\\mathbb L}_T^q \\
 mathbf{H}_p^\\alpha$\nwith $\\alpha \\in [-1\, 0]$ and $p\,q\\in[2\, \\inf
 ty]$\, which is a\ndistribution-valued and divergence-free vector field.\n
 In the subcritical case $\\frac dp+\\frac 2q<1+\\alpha$\, we establish the
 \nexistence and uniqueness of a weak solution to the integral equation:\n$
 $\nX_t=X_0+\\lim_{n\\to\\infty}\\int^t_0b_n(s\,X_s){\\rm d} s+\\sqrt{2} W_
 t.\n$$\nHere\, $b_n:=b*\\phi_n$ represents the mollifying approximation\, 
 and the\nlimit is taken in the $L^2$-sense.\nIn the critical and supercrit
 ical case $1+\\alpha\\leq\\frac dp+\\frac\n2q<2+\\alpha$\, assuming the in
 itial distribution has an $L^2$-density\, we\nshow the existence of weak s
 olutions and associated Markov processes.\nMoreover\, under the additional
  assumption that $b=b_1+b_2+\\div a$\, where\n$b_1\\in {\\mathbb L}^\\inft
 y_T{\\mathbf B}^{-1}_{\\infty\,2}$\, $b_2\\in\n{\\mathbb L}^2_TL^2$\,\nand
  $a$ is a bounded antisymmetric matrix-valued function\, we establish\nthe
  convergence of mollifying approximation solutions without the need\nto su
 btract a subsequence.\nTo illustrate our results\, we provide examples of 
 Gaussian random fields\nand singular interacting particle systems\, includ
 ing the two-dimensional\nvortex models.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milica Tomasevic (École polytechnique)
DTSTART:20240528T130000Z
DTEND:20240528T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/101
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/101/">Particle approximation of the doubly parabolic Keller-Segel eq
 uation in the plane</a>\nby Milica Tomasevic (École polytechnique) as par
 t of Non-local operators\, probability and singularities\n\n\nAbstract\nIn
  this talk\, we study a stochastic system of $N$ particles associated with
  the parabolic-parabolic Keller-Segel system in the plane. This particle s
 ystem is singular and non Markovian in that its drift term depends on the 
 past of the particles. When the sensitivity parameter is sufficiently smal
 l\, we show that this particle system indeed exists for any $N \\geq 2$\, 
 we show tightness in $N$ of its empirical measure\, and that any weak limi
 t point of this empirical measure\, as $N\\to \\infty$\, solves some nonli
 near martingale problem\, which in particular implies that its family of t
 ime-marginals solves the parabolic-parabolic Keller-Segel system in some w
 eak sense. The main argument of the proof consists of a Markovianization o
 f the interaction kernel: We show that\, in some loose sense\, the two-by-
 two path-dependant interaction can be controlled by a two-by-two Coulomb i
 nteraction\, as in the parabolic-elliptic case. This is a joint work with 
 N. Fournier (Sorbonne Université).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huyuan Chen (Jiangxi Normal University)
DTSTART:20240521T130000Z
DTEND:20240521T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/102
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/102/">The Cauchy problem associated to the logarithmic Laplacian</a>
 \nby Huyuan Chen (Jiangxi Normal University) as part of Non-local operator
 s\, probability and singularities\n\n\nAbstract\nIn this talk\,  we study 
 the Cauchy problem \n$$\\partial_tu+ \\mathcal{L}_{\\Delta} u=0 \\ \\  {\\
 rm in}\\ \\\,  (0\,\\frac N2) \\times \\R^N\,\\quad\\quad  u(0\,\\cdot)=0\
 \ \\ {\\rm in}\\  \\\, \\R^N\\setminus \\{0\\}.$$\nwhere $L_\\Delta$ is th
 e logarithmic Laplacian operator\,  a singular integral operator with symb
 ol $2\\log |\\zeta|$. We apply our results to give a classification of the
  solutions of\n$$\n\\begin{cases}\n \\partial_t u+\\mathcal{L}_{\\Delta} u
 =0 \\quad \\  &{\\rm in}\\ \\   (0\,T)\\times \\R^N \\\\\n \\phantom{  \\ 
 \\\,   }\n\\displaystyle   u(0\,\\cdot)=f\\quad \\ &{\\rm{in}}\\  \\   \\R
 ^N\n\\end{cases}\n$$\nand obtain an expression of  the fundamental solutio
 n of the associated stationary equation in $\\R^N$\,\nand of the fundament
 al solution in a bounded domain\, i.e.\n$$\\mathcal{L}_{\\Delta}  u=k\\del
 ta_0\\quad {\\rm in}\\ \\ \\mathcal{D}'(\\Omega)\\quad  {\\rm such\\ that 
 \n }\\quad u=0\\quad {\\rm in}\\ \\ \\R^N\\setminus\\Omega. $$\n\nThis is 
 a joint work with Laurent Véron.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Biočić (University of Zagreb)
DTSTART:20240618T130000Z
DTEND:20240618T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/103
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/103/">Semilinear equations for subordinate spectral Laplacian: moder
 ate and large solutions</a>\nby Ivan Biočić (University of Zagreb) as pa
 rt of Non-local operators\, probability and singularities\n\n\nAbstract\nI
 n this talk\, we solve semilinear problems in bounded $C^{1\,1}$ domains f
 or non-local operators with a non-homogeneous Dirichlet boundary condition
 \, based on the work [1] and a joint work in progress with Vanja Wagner. T
 he operators cover and extend the case of the spectral fractional Laplacia
 n\, and are modelled using the process called subordinate killed Brownian 
 motion. Our focus will be on the potential-probabilistic approach to these
  problems with an emphasis on methods\, intuition\, and calculations. This
  approach is a consequence of recent developments in [2\,3].\n\nWe present
  an integral representation of harmonic functions for such non-local opera
 tors and give sharp boundary behaviour of Green and Poisson potentials. H\
 \"older regularity of distributional solutions is given as well as a versi
 on of Kato's inequality. We explore moderate (i.e. harmonically bounded) s
 olutions and large (i.e. harmonically unbounded) solutions to the semiline
 ar problem. Large solutions are obtained by using a Keller-Osserman-type c
 ondition\, by an approximation method.\n\n\n[1] I. Biočić\, Semilinear D
 irichlet problem for subordinate spectral Laplacian\, Communications on Pu
 re and Applied Analysis\,  22 (2023)\, 851-898.\n\n[2] I. Biočić\, Z. Vo
 ndraček\, V. Wagner\, Semilinear equations for non-local operators: Beyon
 d the fractional Laplacian\, Nonlinear Analysis\, 207 (2021)\, 112303.\n\n
 [3] P. Kim\, R. Song\, Z. Vondraček\, Potential theory of subordinate kil
 led Brownian motion\, Transactions of the American mathematical society\, 
 371 (2019)\, 3917-3969.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandar Mijatović (University of Warwick)
DTSTART:20240702T130000Z
DTEND:20240702T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/105
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/105/">Subexponential lower bounds for $f$-ergodic Markov processes</
 a>\nby Aleksandar Mijatović (University of Warwick) as part of Non-local 
 operators\, probability and singularities\n\n\nAbstract\nIn this talk I wi
 ll describe a  criterion for establishing lower bounds on the rate of conv
 ergence in $f$-variation of a continuous-time ergodic Markov process to it
 s invariant measure. The criterion consists of novel super- and submarting
 ale conditions for certain functionals of the Markov process. It provides 
 a general approach for proving lower bounds on the tails of the invariant 
 measure and the rate of convergence in $f$-variation of a Markov process\,
  analogous to the widely used  Lyapunov drift conditions for upper bounds.
  Our key innovation\, which will be discussed in the talk\, produces lower
  bounds on the tails of the heights and durations of the excursions from b
 ounded sets of a continuous-time Markov process using path-wise arguments.
   \n\nI will present applications of our theory to elliptic diffusions and
   Levy-driven stochastic differential equations with known polynomial/stre
 tched exponential upper bounds on their rates of convergence. Our lower bo
 unds match asymptotically the known upper bounds for these classes of mode
 ls\, thus establishing their rate of convergence to stationarity. The gene
 rality of our approach suggests that\, analogous to the Lyapunov drift con
 ditions for upper bounds\, our methods can be expected to find  applicatio
 ns in many other settings. This is joint work with Miha Brešar at Warwick
 . The paper is available on https://arxiv.org/abs/2403.14826\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Andraus (Tsukuba Gakuin University)
DTSTART:20240924T130000Z
DTEND:20240924T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/106
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/106/">Collision times of multivariate Bessel processes with their We
 yl chambers' boundaries and their Hausdorff dimension</a>\nby Sergio Andra
 us (Tsukuba Gakuin University) as part of Non-local operators\, probabilit
 y and singularities\n\n\nAbstract\nIn this talk\, I consider multivariate 
 Bessel processes\, which are\nmultivariate generalizations of the well-kno
 wn Bessel processes and\nwhich depend on a choice of root system. These pr
 ocesses are confined\nto a subset of N-dimensional space\, the Weyl chambe
 r\, which depends on\nthis root system\, and they are an active topic of r
 esearch in\nmathematical physics as well as probability theory. Their conf
 inement\nto the Weyl chamber is a consequence of repulsive drifts that dri
 ve\nthe processes away from the boundaries\, and the strength of these\ndr
 ifts depends on a set of parameters\, called multiplicities.\n\nGiven the 
 root system $R$\, the multiplicities $k(\\alpha)>0\,\\ \\alpha\\in\nR$\, a
 nd a standard\, $N$-dimensional Brownian motion\n$\\{B(t)\\}_{t\\geq0}$\, 
 the multivariate Bessel process' evolution\,\n$\\{X(t)\\}_{t\\geq0}$\, is 
 given by the SDE\n\\[\n\\textrm{d}X(t)=\\textrm{d}B(t)+\\sum_{\\alpha\\in\
 nR}\\frac{k(\\alpha)}2\\frac{\\alpha}{\\langle\\alpha\,X(t)\\rangle}\\\,\\
 textrm{d}\nt\,\\ X(0)=x_0.\n\\]\nDemni showed that in spite of the singula
 r drift\, $X(t)$ hits the Weyl\nchamber's boundary in finite time almost s
 urely whenever a\nmultiplicity is less than $1/2$. The main objective of t
 he talk is to\nshow that the set of hitting times at the Weyl chamber's bo
 undary has\na fractal structure given by the following result: the Hausdor
 ff\ndimension of collision times with the boundary is given by\n\\[\n\\dim
 [X^{-1}(\\partial W)]=\\max\\Big\\{0\,\\frac12-\\min_{\\alpha\\in R}k(\\al
 pha)\\Big\\}.\n\\]\n\nI start by giving a quick overview of one particular
  case\, namely\nDyson's Brownian motion\, for which one can perform a dire
 ct\ncalculation of the Hausdorff dimension based on the transition density
 \nof the process and an asymptotic formula by Graczyk and Sawyer. Then\,\n
 I move on to the general case where the root system is reduced and\ngive a
 n outline of the proof of our result based on an observation by\nJ. Małec
 ki: a particular polynomial of the process given by the\nalternating polyn
 omial defined by the root system has an SDE which is\nnothing but a time-c
 hanged squared Bessel process SDE.\n\nThis is joint work with N. Hufnagel 
 at Düsseldorf\, and the paper can\nbe found here: https://arxiv.org/abs/2
 312.05420\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Komorowski (IMPAN - Institute of Mathematics Polish Academy
  of Sciences)
DTSTART:20241029T140000Z
DTEND:20241029T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/107
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/107/">Diffusive and superdiffusive limits for a kinetic equation wit
 h a transmitting-reflecting-absorbing  boundary condition</a>\nby Tomasz K
 omorowski (IMPAN - Institute of Mathematics Polish Academy of Sciences) as
  part of Non-local operators\, probability and singularities\n\n\nAbstract
 \nWe consider the limit of  a linear  kinetic equation with a degenerate s
 cattering kernel and a reflection-transmission-absorption condition at an 
 interface. An equation of this type arises from  the kinetic limit of a mi
 croscopic harmonic chain of oscillators whose dynamics is perturbed by a s
 tochastic term\, conserving energy and momentum.  The chain  is in contact
 \, via one oscillator\, with a heat bath\, which\, in the limit\, generate
 s the boundary condition at the interface.    \n\nIt is known that in the 
 absence of the interface\, the solution of the kinetic equation  exhibits 
 either\n\nsuperdiffusive\, or diffusive behavior\, in the proper long time
  - large scale limit\, depending on the dispersion relation of the harmoni
 c chain.  We discuss how the presence of the interface influences the boun
 dary condition for the limiting diffusion\, or anomalous diffusion. \n\nTh
 e presented results have been obtained in collaboration with G. Basile (Un
 iv. Roma I)\, \n\nA. Bobrowski (Lublin Univ. of Techn.)\, K. Bogdan (Wroc
 ław Univ. of Sci. and Techn.)\, L. Arino (Ensta\, Paris)\, S. Olla (Univ.
  Paris-Dauphine and GSSI\, L’Aquila)\, L. Ryzhik (Stanford Univ.)\, H. S
 pohn (TU\, Munich).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aníbal Rodríguez Bernal (Universidad Complutense de Madrid)
DTSTART:20241008T130000Z
DTEND:20241008T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/108
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/108/">Homogeneous spaces\, operators and semigroups: optimal estimat
 es and selfsimilarity</a>\nby Aníbal Rodríguez Bernal (Universidad Compl
 utense de Madrid) as part of Non-local operators\, probability and singula
 rities\n\n\nAbstract\nWe present some results on evolution problems govern
 ed by homogeneous\noperators. We show that many relevant features of these
  problems do\nnot really depend from specifics of the equations but stem f
 rom\nhomogeneity. These include sharp estimates for solutions in\nhomogene
 ous spaces and several selfsimilarity results. These\nproperties hold in p
 articular for higer order equations and fractional\ndiffusion ones.\n\nThi
 s is a joint work with J. Cholewa (U. Silesia)\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Bobrowski (Lublin University of Technology)
DTSTART:20241112T140000Z
DTEND:20241112T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/109
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/109/">A couple of recent approximations of skew Brownian motion</a>\
 nby Adam Bobrowski (Lublin University of Technology) as part of Non-local 
 operators\, probability and singularities\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katarzyna Pietruska-Pałuba (University of Warsaw)
DTSTART:20241203T140000Z
DTEND:20241203T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/110
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/110/">Functional identities  related to nonlocal Levy processes: Dou
 glas\, Hardy-Stein</a>\nby Katarzyna Pietruska-Pałuba (University of Wars
 aw) as part of Non-local operators\, probability and singularities\n\n\nAb
 stract\nWe will present developments concerned with a class of\nfunctional
  inequalities related to nonlocal Levy processes and their\ngenerators. Th
 e identities considered are of Douglas and Hardy-Stein type.\nThey have be
 en obtained in collaboration with Krzysztof Bogdan\, Tomasz\nGrzywny\, Mic
 hal Gutowski and Artur Rutkowski.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoan Tardy (École polytechnique)
DTSTART:20250107T140000Z
DTEND:20250107T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/111
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/111/">Collisions of the supercritical Keller-Segel particle system</
 a>\nby Yoan Tardy (École polytechnique) as part of Non-local operators\, 
 probability and singularities\n\n\nAbstract\nWe study a particle system na
 turally associated to the 2-dimensional Keller-Segel equation. It consists
  of N Brownian particles in the plane\, interacting through a binary attra
 ction in θ/(Nr)\, where r stands for the distance between two particles. 
 When the intensity θ of this attraction is greater than 2\, this particle
  system explodes in finite time. We assume that N>3θ and study in details
  what happens near explosion. There are two slightly different scenarios\,
  depending on the values of N and θ\, here is one: at explosion\, a clust
 er consisting of precisely k0 particles emerges\, for some deterministic k
 0≥7 depending on N and θ. Just before explosion\, there are infinitely 
 many (k0−1)-ary collisions. There are also infinitely many (k0−2)-ary 
 collisions before each (k0−1)-ary collision. And there are infinitely ma
 ny binary collisions before each (k0−2)-ary collision. Finally\, collisi
 ons of subsets of 3\,…\,k0−3 particles never occur. The other scenario
  is similar except that there are no (k0−2)-ary collisions.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Metafune (Università del Salento)
DTSTART:20250211T140000Z
DTEND:20250211T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/112
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/112/">The spectrum of the Ornstein-Uhlenbeck operator</a>\nby Giorgi
 o Metafune (Università del Salento) as part of Non-local operators\, prob
 ability and singularities\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Valdinoci (The University of Western Australia)
DTSTART:20241217T120000Z
DTEND:20241217T130000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/113
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/113/">Nonlocal minimal surfaces: a tricky question about the strict 
 maximum principle</a>\nby Enrico Valdinoci (The University of Western Aust
 ralia) as part of Non-local operators\, probability and singularities\n\n\
 nAbstract\nSuppose that two nonlocal minimal surfaces are included one int
 o the other and touch at a point. Then\, they must coincide. But this is p
 erhaps less obvious than what it seems at first glance.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Bernardin (Higher School of Economics)
DTSTART:20250422T130000Z
DTEND:20250422T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/114
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/114/">Microscopic Fluctuations Theory for systems with long-range in
 teractions</a>\nby Cédric Bernardin (Higher School of Economics) as part 
 of Non-local operators\, probability and singularities\n\n\nAbstract\nMicr
 oscopic Fluctuations Theory is the cornerstone of modern  non-equilibrium 
 statistical mechanics. Developed for bounary driven diffusive sytems durin
 g the last 25 years\, it remains mainly limited to interacting particles s
 ystems with short range interactions. In this talk we will explain how to 
 generalise this theory for microscopic models with long range interactions
  which are macrocopically described by fractional diffusion equation.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federica Gregorio (Università di Salerno)
DTSTART:20250311T140000Z
DTEND:20250311T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/115
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/115/">Fourth-order operators with polynomially growing  coefficients
 </a>\nby Federica Gregorio (Università di Salerno) as part of Non-local o
 perators\, probability and singularities\n\n\nAbstract\nIn this talk we wi
 ll prove generation results in $L^p$ spaces as well as domain characteriza
 tion for some fourth-order operators with polynomially growing coefficient
 s under suitable growth conditions on the coefficients.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haojie Hou\, Xicheng Zhang (School of Mathematics and Statistics\,
  Beijing)
DTSTART:20250121T140000Z
DTEND:20250121T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/116
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/116/">Heat kernel estimates for nonlocal kinetic operators</a>\nby H
 aojie Hou\, Xicheng Zhang (School of Mathematics and Statistics\, Beijing)
  as part of Non-local operators\, probability and singularities\n\n\nAbstr
 act\nIn this paper\, we employ probabilistic techniques to derive sharp\, 
 explicit two-sided estimates for the heat kernel of the nonlocal kinetic o
 perator\n  $$\n  \\Delta^{\\alpha/2}_v + v \\cdot \\nabla_x\, \\quad \\alp
 ha \\in (0\, 2)\,\\ (x\,v)\\in{\\mathbb R}^{d}\\times{\\mathbb R}^d\,\n  $
 $\nwhere $ \\Delta^{\\alpha/2}_v $ represents the fractional Laplacian act
 ing on the velocity variable $ v $. Additionally\, we establish logarithmi
 c gradient estimates with respect to both the spatial ariable $ x $ and th
 e velocity variable $v$. In fact\, the estimates are developed for more ge
 neral non-symmetric stable-like operators\, demonstrating explicit depende
 nce on the lower and upper bounds of the kernel functions.  These results\
 , in particular\, provide a solution to a fundamental problem in the study
  of nonlocal kinetic operators. This is a joint work with Haojie Hou.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eryan Hu (Tianjin University)
DTSTART:20250218T140000Z
DTEND:20250218T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/117
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/117/">Dirichlet heat kernel estimates for rectilinear stable process
 es</a>\nby Eryan Hu (Tianjin University) as part of Non-local operators\, 
 probability and singularities\n\n\nAbstract\nLet $d \\ge 2$\, $\\alpha \\i
 n (0\,2)$\, and $X$ be the rectilinear $\\alpha$-stable process on $\\math
 bb{R}^d$. We first present a geometric characterization of open subset $D\
 \subset \\mathbb{R}^d$ so that the part process $X^D$ of $X$ in $D$ is ir
 reducible. We then study the properties of the transition density function
 s of $X^D$\, including the strict positivity property as well as their sha
 rp two-sided bounds in $C^{1\,1}$ domains in $\\mathbb{R}^d$. Our bounds a
 re shown to be sharp for a class of $C^{1\,1}$ domains.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucio Galeati (University of L'Aquila)
DTSTART:20250408T130000Z
DTEND:20250408T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/118
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/118/">Regularity of the conditional densities for singular fractiona
 l SDEs</a>\nby Lucio Galeati (University of L'Aquila) as part of Non-local
  operators\, probability and singularities\n\n\nAbstract\nWe consider mult
 idimensional SDEs with singular drift\, driven by additive fractional Brow
 nian motion (fBm). Under appropriate regularity assumptions\, such equatio
 ns are known to be solvable in a strong sense\, thanks to modern tools lik
 e the Stochastic Sewing Lemma (SSL). However\, due to the singularity of t
 he drift and the non-Markovian nature of the noise\, many standard methods
  to estimate the density of the law of the solution are not available anym
 ore\; conditional estimates are even harder to attain. In this talk I will
  present several results in this direction\, based on a combination of dua
 lity arguments\, sewing techniques\, Romito's lemma and Girsanov transform
 . As a consequence\, we provide novel existence and uniqueness results for
  McKean-Vlasov equations driven by fBm with convolutional drift\, thanks t
 o a regularity bootstrapping procedure.\n\nBased on an ongoing joint work 
 with Lukas Anzeletti\, Alexandre Richard and Etienne Tanré.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Veretennikov (Moscow State University)
DTSTART:20250513T130000Z
DTEND:20250513T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/119
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/119/">On some recent news about SDEs and McKean - Vlasov equations w
 ith irregular drift</a>\nby Alexandre Veretennikov (Moscow State Universit
 y) as part of Non-local operators\, probability and singularities\n\n\nAbs
 tract\nSome recent news about MV SDEs concern solutions\nwith irregular dr
 ift\, in particular\, for degenerate SDEs\,\nas well as some moment condit
 ions on the initial\ndistributions. For Ito SDEs there is a new variation 
 of\none of Yamada - Watanabe theorems on pathwise uniqueness.\nPartly\, th
 e results in both branches are obtained jointly\nwith some my colleagues a
 nd some my students.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Perkowski (Freie Universität Berlin)
DTSTART:20250401T130000Z
DTEND:20250401T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/120
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/120/">Energy solutions of singular SPDEs on Hilbert spaces</a>\nby N
 icolas Perkowski (Freie Universität Berlin) as part of Non-local operator
 s\, probability and singularities\n\n\nAbstract\nI will discuss a unified 
 setting for well-posedness of a class of nonlinear stochastic (partial) di
 fferential equations with singular noise\, such as the KPZ/Burgers equatio
 n\, stochastic Navier-Stokes equations or finite-dimensional diffusions wi
 th distributional drift. Under structural assumptions we develop a probabi
 listic theory\, in duality with potentially infinite-dimensional partial d
 ifferential equations\, which allows to easily include boundary conditions
  in SPDEs. This is motivated by the goal of deriving (weakly) universal fl
 uctuations of interacting particle systems with boundary effects. The talk
  is based on joint work with Lukas Gräfner\, Shyam Popat and partly on on
 going work with Adrian Martini.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Krylov (University of Minnesota)
DTSTART:20250520T140000Z
DTEND:20250520T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/121
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/121/">Morrey-Sobolev spaces and second-order elliptic and parabolic 
 PDEs with singular first-order coefficients</a>\nby Nicolai Krylov (Univer
 sity of Minnesota) as part of Non-local operators\, probability and singul
 arities\n\n\nAbstract\nIn recent years we witness growing interest\nin usi
 ng   Real Analysis methods and results\nin the theory of nondivergence for
 m partial differential equations (PDEs)\nand the goal of this lecture is t
 o give a brief  account of \napplications of several results in Real Analy
 sis to the theory of\nelliptic and parabolic equations in Sobolev and Sobo
 lev-Morrey spaces.\nIn particular\, we concentrate on some results\nobtain
 ed by using Hardy-Littlewood maximal function\ntheorem\, Fefferman-Stein t
 heorem\,\ntheory of Muckenhoupt weights\, and Rubio de Francia\nextrapolat
 ion theorem and their role in Sobolev or Morrey-Sobolev space\ntheory of p
 arabolic equations with mixed norms.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikolaj Sierzega (University of Warsaw & George Mason University)
DTSTART:20251104T140000Z
DTEND:20251104T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/122
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/122/">Differential Harnack bounds for fractional heat equations</a>\
 nby Mikolaj Sierzega (University of Warsaw & George Mason University) as p
 art of Non-local operators\, probability and singularities\n\n\nAbstract\n
 Harnack-type estimates lie at the very heart of the regularity theory for 
 partial differential equations. One way to obtain such bounds is by integr
 ating differential Harnack inequalities\; for instance\, in the case of th
 e standard heat equation\, integrating the remarkable Li–Yau inequality 
 yields the classical Gaussian bound\, also known as the Hadamard–Pini in
 equality. In this talk\, I will describe how a seemingly straightforward a
 ttempt to extend this framework to fractional heat flows requires recastin
 g the Li–Yau technique to accommodate a broader class of equations and 
 leads to an interesting reformulation of classical Harnack bounds.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu-Ting Chen (University of Victoria)
DTSTART:20251014T140000Z
DTEND:20251014T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/123
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/123/">Stochastic path integrals in the two-dimensional stochastic he
 at equation</a>\nby Yu-Ting Chen (University of Victoria) as part of Non-l
 ocal operators\, probability and singularities\n\n\nAbstract\nThe two-dime
 nsional stochastic heat equation (SHE) at criticality was\nintroduced arou
 nd the end of the ’90s. It arises from problems of statistical physics v
 ia\nseveral stochastic models of surface growth dynamics and from the diso
 rdered system\nof a directed polymer in a random medium. The delta-Bose ga
 s in quantum physics is\nalso involved. This talk will introduce stochasti
 c path integrals in the two-dimensional\nSHE at criticality and emphasize 
 those at the level of annealed expectations. These\nemphasized stochastic 
 path integrals have the interesting feature of being governed by\nSDEs wit
 h supercritical singular drift and taking a special “sum form” that co
 ntrasts\nthe known “product form” in the one-dimensional case\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rohan Sarkar (Binghamton University SUNY)
DTSTART:20251007T130000Z
DTEND:20251007T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/124
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/124/">Spectrum of Lévy-Ornstein-Uhlenbeck semigroups on R^d</a>\nby
  Rohan Sarkar (Binghamton University SUNY) as part of Non-local operators\
 , probability and singularities\n\n\nAbstract\nWe investigate spectral pro
 perties of Markov semigroups associated with Ornstein-Uhlenbeck (OU) proce
 sses driven by Lévy processes. These semigroups are generated by non-loca
 l\, non-self-adjoint operators. In the special case where the driving Lév
 y process is Brownian motion\, one recovers the classical diffusion OU sem
 igroup\, whose spectral properties have been extensively studied over past
  few decades. Our main results show that\, under suitable conditions on th
 e Lévy process\, the spectrum of the Lévy-OU semigroup in the $L^p$-spac
 e weighted with the invariant distribution coincides with that of the diff
 usion OU semigroup. Furthermore\, when the drift matrix $B$ is diagonaliza
 ble with real eigenvalues\, we derive explicit formulas for eigenfunctions
  and co-eigenfunctions. A key ingredient in our approach is intertwining r
 elationship: we prove that every Lévy-OU semigroup is intertwined with a 
 diffusion OU semigroup\, thereby preserving the spectral properties.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerald Trutnau (Seoul National University)
DTSTART:20251125T140000Z
DTEND:20251125T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/125
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/125/">Existence and uniqueness of (infinitesimally) invariant measur
 es for second order partial differential operators on Euclidean space</a>\
 nby Gerald Trutnau (Seoul National University) as part of Non-local operat
 ors\, probability and singularities\n\n\nAbstract\nWe consider a locally u
 niformly strictly elliptic second order partial differential operator in E
 uclidean space with dimension greater or equal to two\, with low regularit
 y assumptions on its coefficients\, as well as an associated Hunt process 
 and semigroup. The Hunt process is known to solve a corresponding stochast
 ic differential equation that is pathwise unique. In this situation\, we s
 tudy the relation of invariance\, infinitesimal invariance\, recurrence\, 
 transience\, conservativeness and L^r-uniqueness. Our main result is that 
 recurrence implies uniqueness of infinitesimally invariant measures\, as w
 ell as existence and uniqueness of invariant measures. We can hence make i
 n particular use of various explicit analytic criteria for recurrence that
  have been previously developed in the context of (generalized) Dirichlet 
 forms and present diverse examples and counterexamples for uniqueness of i
 nfinitesimally invariant\, as well as invariant measures and an example wh
 ere L^1-uniqueness fails although pathwise uniqueness holds. This is joint
  work with Haesung Lee.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soobin Cho (University of Illinois Urbana-Champaign)
DTSTART:20251202T140000Z
DTEND:20251202T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/126
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/126/">Approximate factorizations for non-symmetric jump processes</a
 >\nby Soobin Cho (University of Illinois Urbana-Champaign) as part of Non-
 local operators\, probability and singularities\n\n\nAbstract\nIn this tal
 k\, we first discuss approximate factorizations of heat kernels and Green 
 functions for purely discontinuous Markov processes\, and their equivalenc
 e. In the second part\, we present applications of these factorizations to
  obtain two-sided heat kernel estimates for two classes of processes: stab
 le-like processes with critical killing in $C^{1\,Dini}$ open sets\, and n
 on-symmetric stable processes in $C^{1\,2-Dini}$ open sets. In particular\
 , we derive sharp\, explicit two-sided estimates for killed and censored s
 table processes in $C^{1\,Dini}$ open sets. We also discuss the optimality
  of the $C^{1\,Dini}$ condition for heat kernel estimates of killed stable
  processes. This talk is based on joint work with Professor Renming Song (
 UIUC).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Bertoin (University of Zurich)
DTSTART:20260113T140000Z
DTEND:20260113T150000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/127
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/127/">On the elephant random walk and its zeros</a>\nby Jean Bertoin
  (University of Zurich) as part of Non-local operators\, probability and s
 ingularities\n\n\nAbstract\nThe so-called elephant random walk is a simple
  random process with\nmemory on $\\Z$. After recalling some well-known res
 ults about its asymptotic behavior\,\nwe shall turn our interest to its ze
 ro-set. I will notably present recent results obtained by Zheng Fang in hi
 s (ongoing) PhD about the following related questions:\n- For how long has
  to be trained the elephant  ?\n- For how long does the elephant remember 
 ?\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takashi Kumagai (Waseda University)
DTSTART:20260210T130000Z
DTEND:20260210T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/128
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/128/">Quantitative homogenization on time-dependent random conductan
 ce models with stable-like jumps</a>\nby Takashi Kumagai (Waseda Universit
 y) as part of Non-local operators\, probability and singularities\n\n\nAbs
 tract\nIn this talk\, I will present quantitative homogenization results f
 or stable-like long range random walks in time-dependent random conductanc
 e models\, where the conductances are bounded from above\, but may be dege
 nerate.\n\nThis talk is based on joint work with X. Chen (Shanghai)\, Z.-Q
 . Chen (Seattle) and J. Wang (Fuzhou).\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raffaella Servadei (Università degli Studi di Urbino Carlo Bo)
DTSTART:20260505T130000Z
DTEND:20260505T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/129
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NonLocalOper
 ators/129/">On some local and nonlocal problems with lack of compactness</
 a>\nby Raffaella Servadei (Università degli Studi di Urbino Carlo Bo) as 
 part of Non-local operators\, probability and singularities\n\nInteractive
  livestream: https://ulaval.zoom.us/j/69592078369?pwd=8v4uUabn7JmyX7zyQBYp
 34LVuQh9Yb.1\n\nAbstract\nIn this talk\, we address some critical growth p
 roblems\, both local and nonlocal\, even in the presence of jumping nonlin
 earities. Using variational and topological methods\, we prove the existen
 ce of a nontrivial solution to the problem at hand. These existence result
 s can be viewed as the nonlocal counterpart of those obtained in the conte
 xt of Laplace equations. In the nonlocal context\, the arguments used in t
 he classical framework must be refined. Indeed\, the presence of the fract
 ional Laplace operator introduces additional difficulties\, which we overc
 ome by proving new regularity results for weak solutions of nonlocal probl
 ems\, which are of independent interest.\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/129/
URL:https://ulaval.zoom.us/j/69592078369?pwd=8v4uUabn7JmyX7zyQBYp34LVuQh9Y
 b.1
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naian Liao (Universität Salzburg)
DTSTART:20260519T130000Z
DTEND:20260519T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/130
DESCRIPTION:by Naian Liao (Universität Salzburg) as part of Non-local ope
 rators\, probability and singularities\n\nInteractive livestream: https://
 ulaval.zoom.us/j/69592078369?pwd=8v4uUabn7JmyX7zyQBYp34LVuQh9Yb.1\nAbstrac
 t: TBA\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/130/
URL:https://ulaval.zoom.us/j/69592078369?pwd=8v4uUabn7JmyX7zyQBYp34LVuQh9Y
 b.1
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Cannizzaro (University of Warwick)
DTSTART:20260609T130000Z
DTEND:20260609T140000Z
DTSTAMP:20260421T120712Z
UID:NonLocalOperators/131
DESCRIPTION:by Giuseppe Cannizzaro (University of Warwick) as part of Non-
 local operators\, probability and singularities\n\nInteractive livestream:
  https://ulaval.zoom.us/j/69592078369?pwd=8v4uUabn7JmyX7zyQBYp34LVuQh9Yb.1
 \nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NonLocalOperators/131/
URL:https://ulaval.zoom.us/j/69592078369?pwd=8v4uUabn7JmyX7zyQBYp34LVuQh9Y
 b.1
END:VEVENT
END:VCALENDAR