BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jie Xiao (Memorial University of Newfoundland) DTSTART:20220913T010000Z DTEND:20220913T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/1 DESCRIPTION:Title: Mean Hoelder-Lipschitz Potentials in Curved Campanato-R adon Spaces\nby Jie Xiao (Memorial University of Newfoundland) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nThis talk will present L. Liu-J. Xiao's article: Math. Ann. 375(2019)1045-1077\, proving that f or $s \\in (0\,1)$\, $\\alpha \\in (0\,n)$\, $\\beta \\in (0\,n]$\, \n\\[\ n1\\leq \\min\\{p\, q\\}\\le\\max\\{p\,q\\}<\\beta p(n-\\alpha p)^{-1}<\\i nfty\n\\]\nand $\\lambda=q(np^{-1}-s-\\alpha)+n-\\beta$\, if $\\mu$ is a n onnegative Radon measure on $\\mathbb R^n$ with the $\\beta$-dimensional u pper curvature $|\\|\\mu|\\|_\\beta<\\infty$ then $I_\\alpha \\dot{\\varLa mbda}_s^{p\,\\infty}$ (the mean Hoelder-Lipschitz potential space on $\\ma thbb R^n$) embeds continuously into $\\mathcal{L}^{q\,\\lambda}_\\mu$ (the curved Campanato-Radon space on $\\mathbb R^n$)\; and yet its converse is still valid with $\\mu$ being admissible\, thereby discovering\nthe $\\ga mma$-Hoelder-Lipschitz continuity of any duality solution to the $\\alpha$ -th Laplace equation $(-\\varDelta)^{\\frac\\alpha 2}u=\\mu$\nor the $[1\, n/2)\\cap\\{1\,2...\,n\\}\\ni k$-th Hessian equation $F_k[u]=\\mu$ under a suitable curvature $|\\||\\mu|\\||_\\beta<\\infty$.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Volberg (Michigan State University) DTSTART:20220920T010000Z DTEND:20220920T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/2 DESCRIPTION:Title: Dyadic rectangles\nby Alexander Volberg (Michigan S tate University) as part of Nonlinear Analysis Seminar Series\n\nLecture h eld in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract \nWeighted Carleson embedding (weighted paraproduct estimates in another l anguage) lies in the core of various harmonic analysis and PDE results. N ot much is known about it in multi-parameter situation\, while one paramet er is completely understood. I will formulate several new results on weigh ted multi-parameter Carleson embedding on multi-trees and their corollarie s as embeddings of Hilbert spaces of analytic functions on poly-discs.\n\n I will also formulate corresponding Poincar\\'e inequalities on multi-tree s and poly-discs. Some of those results are final\, but even embedding of Hardy space on bi-disc is not completely described. My presentation is bas ed on joint works with N. Arcozzi\, I. Holmes\, P. Mozolyako\, P. Zorin-K ranich.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Lenka Slavikova (Charles University) DTSTART:20220927T070000Z DTEND:20220927T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/3 DESCRIPTION:Title: Classical multiplier theorems and their sharp variants< /a>\nby Lenka Slavikova (Charles University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathe matics Building.\n\nAbstract\nThe question of finding good sufficient cond itions on a bounded function $m$ guaranteeing the $L^p$-boundedness of the associated Fourier multiplier operator is a long-standing open problem in harmonic analysis. In this talk\, I will recall the classical multiplier theorems of H\\"ormander and Marcinkiewicz and present their sharp variant s in which the multiplier belongs to a certain fractional Sobolev space. T he talk is based in part on a joint work with L. Grafakos and M. Masty\\l o.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Maggi (UT Austin) DTSTART:20221004T010000Z DTEND:20221004T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/4 DESCRIPTION:by Francesco Maggi (UT Austin) as part of Nonlinear Analysis S eminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathema tics Building.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Jin-Cheng Jiang (National Tsing Hua University) DTSTART:20221018T070000Z DTEND:20221018T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/5 DESCRIPTION:Title: On the Cauchy problem for the cutoff Boltzmann equation with small initial data\nby Jin-Cheng Jiang (National Tsing Hua Unive rsity) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Roo m M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nWe prove the global existence of the non-negative unique mild\nsolution for the Ca uchy problem of the cutoff Boltzmann equation for\nsoft potential model −1<=γ<0 with the small initial data in three\ndimensional space. Thus o ur result fixes the gap for the case γ=−1 in\nthree dimensional space i n the authors' previous work where the estimate\nfor the loss term was imp roperly used. The other gap there for the case\nγ=0 in two dimensional sp ace is recently fixed by Chen\, Denlinger and\nPavlović. The initial data f0 is non-negative\, small in weighted\nL3_{x\,v} and finite in weighted L15/8_{x\,v}. We also show that the\nsolution scatters with respect to the kinetic transport operator. The\nnovel contribution of this work lies in the exploration of the symmetric\nproperty of the gain term in terms of we ighted estimate. It is the key\ningredient for solving the model −1<γ<0 when applying the Strichartz\nestimates.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Neal Bez (Saitama University) DTSTART:20221129T010000Z DTEND:20221129T033000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/6 DESCRIPTION:Title: An introduction to Strichartz estimates I\nby Neal Bez (Saitama University) as part of Nonlinear Analysis Seminar Series\n\nL ecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\n Abstract\nThe aim of these lectures is to give a gentle introduction to St richartz estimates\, with an emphasis on particular cases such as the line ar Schr\\"odinger and wave equations. The associated dispersive estimates play a highly important role in the theory of Strichartz estimates so I wi ll begin in Lecture 1 by proving the required dispersive estimates.\n\nNex t\, in Lecture 2\, I will prove the homogeneous Strichartz estimates in al l admissible cases\, including the so-called Keel--Tao endpoint case. Buil ding on the content of the first two lectures\, in Lecture 3\, I will disc uss the situation regarding inhomogeneous Strichartz estimates.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Neal Bez (Saitama University) DTSTART:20221206T010000Z DTEND:20221206T033000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/7 DESCRIPTION:Title: An introduction to Strichartz estimates II\nby Neal Bez (Saitama University) as part of Nonlinear Analysis Seminar Series\n\n Lecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\ nAbstract\nThe aim of these lectures is to give a gentle introduction to S trichartz estimates\, with an emphasis on particular cases such as the lin ear Schr\\"odinger and wave equations. The associated dispersive estimates play a highly important role in the theory of Strichartz estimates so I w ill begin in Lecture 1 by proving the required dispersive estimates.\n\nNe xt\, in Lecture 2\, I will prove the homogeneous Strichartz estimates in a ll admissible cases\, including the so-called Keel--Tao endpoint case. Bui lding on the content of the first two lectures\, in Lecture 3\, I will dis cuss the situation regarding inhomogeneous Strichartz estimates.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Neal Bez (Saitama University) DTSTART:20221213T010000Z DTEND:20221213T033000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/8 DESCRIPTION:Title: An introduction to Strichartz estimates III\nby Nea l Bez (Saitama University) as part of Nonlinear Analysis Seminar Series\n\ nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n \nAbstract\nThe aim of these lectures is to give a gentle introduction to Strichartz estimates\, with an emphasis on particular cases such as the li near Schr\\"odinger and wave equations. The associated dispersive estimate s play a highly important role in the theory of Strichartz estimates so I will begin in Lecture 1 by proving the required dispersive estimates.\n\nN ext\, in Lecture 2\, I will prove the homogeneous Strichartz estimates in all admissible cases\, including the so-called Keel--Tao endpoint case. Bu ilding on the content of the first two lectures\, in Lecture 3\, I will di scuss the situation regarding inhomogeneous Strichartz estimates.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Lubos Pick (Charles University) DTSTART:20221108T070000Z DTEND:20221108T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/9 DESCRIPTION:Title: Optimality problems in Orlicz spaces\nby Lubos Pick (Charles University) as part of Nonlinear Analysis Seminar Series\n\nLect ure held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbs tract\nWe prove a general principle\, called the principal alternative\, w hich yields an easily verifiable necessary and sufficient condition for th e existence or the non-existence of an optimal Orlicz space in a wide vari ety of specific tasks including boundedness of operators. We show that the key relation is the positioning of certain rearrangement-invariant space\ , characteristic for the task in question\, to its fundamental Orlicz spac e. The main motivation stems from the imbalance between the expressivity\, meaning the richness and versatility\, of certain class of function space s\, and its accessibility\, i.e.\, its complexity and technical difficulty . More precisely\, while an optimal rearrangement-invariant space in a giv en task often exists\, it might be too complicated or too implicit to be o f any practical value. Optimal Orlicz spaces\, on the other hand\, are sim pler and more manageable for applications\, but they tend not to exist at all. We apply the general abstract result to several specific tasks includ ing continuity of Sobolev embeddings or boundedness of integral operators such as the Hardy-Littlewood maximal operator and the Laplace transform. T he proof of the principal alternative is based on relations of endpoint Lo rentz spaces to unions or intersections of Orlicz spaces. This is a joint work with Vít Musil (Brno) and Jakub Takáč (Warwick).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tess Anderson (Carnegie Mellon University) DTSTART:20221025T010000Z DTEND:20221025T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/10 DESCRIPTION:Title: Analysis and number theory team up\nby Tess Anders on (Carnegie Mellon University) as part of Nonlinear Analysis Seminar Seri es\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Buildi ng.\n\nAbstract\nWe discuss two ways that analysis and number theory have recently teamed up\, using a back and forth interplay to make progress on two different types of counting problems. First we will count equilateral triangles in Euclidean space. Second we will determine how often a random polynomial fails to have "full" Galois group. Though easy to state\, these questions have generated a lot of interesting techniques through the year s\, which we will glimpse during this talk.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Carolin Kreisbeck (Katholischen Universität Eichstätt - Ingolsta dt) DTSTART:20221101T070000Z DTEND:20221101T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/11 DESCRIPTION:Title: Dealing with nonlocalities in variational functionals: Convexity notions\, lower semicontinuity\, and relaxation\nby Carolin Kreisbeck (Katholischen Universität Eichstätt - Ingolstadt) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gon gguan Campus Mathematics Building.\n\nAbstract\nNonlocal variational probl ems arise in various applications\, such as continuum mechanics\, the theo ry of phase transitions\, or image processing. Naturally\, the presence of nonlocalities leads to new effects\, and the standard methods in the calc ulus of variations\, which tend to rely intrinsically on localization argu ments\, do not apply. In this talk\, we address questions arising from the existence theory for three different classes of variational functionals: integrals depending on Riesz fractional gradients\, double integrals\, and double supremals - and find qualitatively very different results. Regardi ng the characterization of weak lower semicontinuity\, it may be surprisin g that quasiconvexity\, which is well-known from the classical local setti ng\, also provides the correct convexity notion for the fractional integra ls. Our proof relies on a translation mechanism that allows switching betw een classical and fractional gradients. In the case of double supremals\, we show that the natural guess of separate level convexity fails in the ve ctorial case\, and introduce the new Cartesian level convexity. As for rel axation\, we discuss the central issue of why one cannot expect these nonl ocal functionals\, in contrast to their local counterparts\, to be structu re-preserving. This is based on joint work with Antonella Ritorto\, Hidde Schönberger (both KU Eichstätt-Ingolstadt)\, and Elvira Zappale (Sapienz a University of Rome).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Luz Roncal (Basque Center for Applied Mathematics) DTSTART:20221122T070000Z DTEND:20221122T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/12 DESCRIPTION:Title: Unique continuation for fractional discrete elliptic e quations\nby Luz Roncal (Basque Center for Applied Mathematics) as par t of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTN U Gongguan Campus Mathematics Building.\n\nAbstract\nIn this talk we will describe several qualitative and quantitative unique continuation properti es for the fractional discrete Laplacian. We will show that\, in contrast to the fractional continuous Laplacian\, global unique continuation fails to hold in general for fractional discrete elliptic equations.\n\nWe will also discuss quantitative versions of unique continuation which illustrate how the properties in the continuous setting may be recovered if exponent ially small (in terms of the lattice size) correction factors are added.\n \nJoint work with Aingeru Fernández-Bertolin and Angkana Rüland.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Serena Dipierro (University of Western Australia) DTSTART:20230411T070000Z DTEND:20230411T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/13 DESCRIPTION:Title: The Bernstein technique for integro-differential equat ions\nby Serena Dipierro (University of Western Australia) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gon gguan Campus Mathematics Building.\n\nAbstract\nIn this talk we discuss ho w to extend the classical Bernstein technique to the setting of integro-di fferential operators. As a consequence of this\, we are able to provide fi rst and one-sided second derivative estimates for solutions to fractional equations. Our method is robust enough to be applied to some Pucci-type ex tremal equations and to obstacle problems for fractional operators.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/13/ END:VEVENT BEGIN:VEVENT SUMMARY:María J. Carro (Universidad Complutense de Madrid) DTSTART:20230418T070000Z DTEND:20230418T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/14 DESCRIPTION:Title: Solving the Dirichlet and the Neumann problem at the e nd-point\nby María J. Carro (Universidad Complutense de Madrid) as pa rt of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NT NU Gongguan Campus Mathematics Building.\n\nAbstract\nIn 1980 C. Kenig pro ved that for every Lipschitz domain $\\Omega$ in the plane there exists $1 \\le p_0<2$ so that the Dirichlet problem has a solution for every $f\\in L^p(ds)$ and every $p\\in (p_0\, \\infty)$. Moreover\, if $p_0>1$\, the re sult is false for $p\\le p_0$. The goal of this talk is to analyze what ha ppen at the endpoint $p_0$\; that is\, we want to look for spaces $X\\subs et L^{p_0}$ so that the Dirichlet problem has a solution for every $f\\in X$. These spaces $X$ will be either a Lorentz space $L^{p_0\,1} (ds)$ or some Orlicz space of logarithmic type. Similar results will be presented f or the Neumann problem. This is a joint work with Virginia Naibo and Carme n Ortiz-Caraballo.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Campbell (Charles University) DTSTART:20230307T070000Z DTEND:20230307T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/15 DESCRIPTION:Title: Injectivity in second-gradient Nonlinear Elasticity\nby Daniel Campbell (Charles University) as part of Nonlinear Analysis S eminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathema tics Building.\n\nAbstract\nWe study injectivity for models of Nonlinear E lasticity that involve the second gradient. We assume that $\\Omega\\subse t\\mathbb{R}^n$ is a domain\, $f\\in W^{2\,q}(\\Omega\,\\mathbb{R}^n)$ sat isfies $|J_f|^{-a}\\in L^1$ and that $f$ equals a given homeomorphism on $ \\partial \\Omega$. Under suitable conditions on $q$ and $a$ we show that $f$ must be a homeomorphism. As a main new tool we find an optimal conditi on for $a$ and $q$ that imply that $\\mathcal{H}^{n-1}(\\{J_f=0\\})=0$ and hence $J_f$ cannot change sign. We further specify in dependence of $q$ a nd $a$ the maximal Hausdorff dimension $d$ of the critical set $\\{J_f=0\\ }$. The sharpness of our conditions for $d$ is demonstrated by constructin g respective counterexamples.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Keng Hao Ooi (National Central University) DTSTART:20230314T070000Z DTEND:20230314T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/16 DESCRIPTION:Title: Harmonic Analysis in Nonlinear Potential Theory\nb y Keng Hao Ooi (National Central University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathe matics Building.\n\nAbstract\nIn this talk I will introduce a type of Sobo lev multiplier which appears naturally in many super critical nonlinear PD Es. We will briefly study the preduals of the Sobolev multplier spaces an d the boundedness of Hardy-Littlewood maximal operators on such spaces. F urthermore\, the boundedness of maximal operators on the spaces of Choquet integrals associated with capacities will also be addressed. The main to ols in tackling these problems rely on classical harmonic analysis and non linear potential theory.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominic Breit (TU Clausthal) DTSTART:20230328T070000Z DTEND:20230328T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/17 DESCRIPTION:Title: Inclusion relations among fractional Orlicz-Sobolev sp aces and a Littlewood-Paley characterization\nby Dominic Breit (TU Cla usthal) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Ro om M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nOptimal embeddings among fractional Orlicz-Sobolev spaces with different smoothne ss are characterized. The equivalence of their Gagliardo-Slobodeckij norms to norms defined via Littlewood-Paley decompostions\, via oscillations\, or via Besov type difference quotients is also established. These equivale nces\, of independent interest\, are a key tool in the proof of the releva nt embeddings. \nThis is joint work with Andrea Cianchi\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Abhishek Ghosh (TIFR Centre For Applicable Mathematics) DTSTART:20230425T070000Z DTEND:20230425T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/18 DESCRIPTION:Title: On bilinear Stein-Weiss inequality\nby Abhishek Gh osh (TIFR Centre For Applicable Mathematics) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathe matics Building.\n\nAbstract\nIn this talk\, we discuss some bilinear frac tional integral operators introduced by Kenig and Stein. Also\, the Stein- Weiss inequality and its bilinear analogues will be addressed in Euclidean space and beyond. This is a joint work with Rajesh K. Singh.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Catalin Carstea (National Yang Ming Chiao Tung University) DTSTART:20230321T070000Z DTEND:20230321T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/19 DESCRIPTION:Title: An inverse problem for the porous medium equation\ nby Catalin Carstea (National Yang Ming Chiao Tung University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gon gguan Campus Mathematics Building.\n\nAbstract\nThe porous medium equation is a degenerate parabolic type quasilinear equation that models\, for exa mple\, the flow of a gas through a porous medium. In this talk I will pres ent recent results on uniqueness in the inverse boundary value problem fo r this equation. These are the first such results to be obtained for a deg enerate parabolic equation. The talk is based on work with T. Ghosh & G. N akamura and T. Ghosh & G. Uhlmann.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Kh. Balci (Universität Bielefeld) DTSTART:20230516T070000Z DTEND:20230516T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/20 DESCRIPTION:Title: Behind the regularity: variational problems with energ y gaps\nby Anna Kh. Balci (Universität Bielefeld) as part of Nonlinea r Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Ca mpus Mathematics Building.\n\nAbstract\nWe study different problems with energy gaps: local and nonlocal double potential\, variable exponent and w eights models. We design the general procedure to construct new examples o f energy gaps and present the numerical scheme that converges to the glob al minimiser of the problem. The talk is based on several joint projects with Lars Diening\, Michail Surnachev\, Johanness Srorn and Christoph Ortn er.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Qing Han (Notre Dame) DTSTART:20230607T060000Z DTEND:20230607T070000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/21 DESCRIPTION:Title: A Concise Boundary Regularity for the Uniformly Degene rate Elliptic Equations\nby Qing Han (Notre Dame) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Cam pus Mathematics Building.\n\nAbstract\nUniformly degenerate elliptic equat ions appear frequently in many geometric problems. Solutions may exhibit s ingular behaviors near the boundary where the degeneracy occurs. Usually\, behaviors of solutions near the boundary are described through expansions . In this talk\, we identify a precise singular term as an additional inde pendent self-variable and establish a concise boundary regularity.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Tien Nguyen (National Taiwan University) DTSTART:20230912T070000Z DTEND:20230912T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/22 DESCRIPTION:Title: Singularities in the Keller-Segel system\nby Tien Nguyen (National Taiwan University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Bu ilding.\n\nAbstract\nThe talk presents constructions of blowup solutions t o the Keller-Segel system in $\\mathbb{R}^d$.\n\n\n$d = 2$ ($L^1$-critical ): There exist finite time single blowup solutions that are of Type II wit h finite mass. Blowup rates are quantized according to a discrete spectrum of a linearized operator around the rescaled stationary solution in the s elf-similar setting. There is also \\textit{multiple collapsing blowup sol utions} formed by a collision of multiple single solutions with self-simil arity that provides a brand new mechanism of singularity formation.\n\n\n$ d \\geq 3$ ($L^1$-supercritical): For $d \\geq 3$\, there exist finite tim e blowup solutions having the form of collapsing-ring which consists of an imploding\, smoothed-out shock wave moving towards the origin to form a D irac mass at the singularity. For $d = 3\,4 $\, we found blowup solutions with infinite mass that are asymptotically self-similar with a log correct ion to their profile. \n\n\nThe constructions rely on a spectral approach for multiple-scale problems\, renormalization technique\, and refined ener gy estimates. The talk is based on a series of joint works with C. Collot (Paris Cergy)\, T. Ghoul (NYU Abu Dhabi)\, N. Nouaili (Paris Dauphine)\, N . Masmoudi (NYU) and H. Zaag (Paris Nord).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Cianchi (Universita' di Firenze) DTSTART:20231003T070000Z DTEND:20231003T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/24 DESCRIPTION:Title: Local boundedness of minimizers under unbalanced Orlic z growth conditions\nby Andrea Cianchi (Universita' di Firenze) as par t of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTN U Gongguan Campus Mathematics Building.\n\nAbstract\nLocal minimizers of i ntegral functionals of the calculus of variations are analyzed under growt h conditions dictated by different lower and upper bounds for the integran d. Growths \n of non-necessarily power-type are allowed. The local bounde dness of the relevant minimizers is established under a suitable balance b etween the lower and the upper bounds. Classical minimizers\, as well as q uasi-minimizers are included in our discussion. Functionals subject to so- called $p\,q$-growth conditions are embraced as special cases and the corr esponding sharp results available in the literature are recovered.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Manfredi (University of Pittsburgh) DTSTART:20231017T010000Z DTEND:20231017T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/25 DESCRIPTION:Title: On Viscosity Solutions to the Non-Homogeneous Infinite Laplace Equation\nby Juan Manfredi (University of Pittsburgh) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nWe will revisit the Th eorem on Sums and use it to study viscosity solutions of non-homogeneous equations involving the infinite Laplacian in Euclidean Space\, Riemannian manifolds\, and Carnot Groups.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Zdeněk Mihula (Czech Technical University in Prague) DTSTART:20230919T070000Z DTEND:20230919T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/26 DESCRIPTION:Title: Optimal Sobolev inequalities in the hyperbolic space\nby Zdeněk Mihula (Czech Technical University in Prague) as part of No nlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongg uan Campus Mathematics Building.\n\nAbstract\nIn this talk\, we consider a (higher order) Sobolev inequality for the Laplace--Beltrami operator in t he ball model of the hyperbolic space $\\mathbb{H}^n$\, and we look for fu nction spaces that are in a sense optimal in the inequality. The inequalit y in question is\n$$\\|u\\|_{Y(\\mathbb{H}^n)} \\leq C \\|\\nabla_g^m u\\| _{X(\\mathbb{H}^n)} \\quad \\text{for every $u\\in V_0^m X(\\mathbb{H}^n)$ }\;$$\nhere $$\\nabla_g^m = \n\\begin{cases}\n\\Delta_g^{\\frac{m}{2}} \\q uad &\\text{if $m$ is even}\,\\\\\n\\nabla_g\\Delta_g^{\\lfloor \\frac{m}{ 2} \\rfloor} \\quad &\\text{if $m$ is odd}\,\n\\end{cases}\n$$\nwhere $\\D elta_g$ is the Laplace--Beltrami operator and $\\nabla_g$ is the hyperboli c gradient\; $X(\\mathbb{H}^n)$ and $Y(\\mathbb{H}^n)$ are rearrangement-i nvariant spaces\, and $V_0^m X(\\mathbb{H}^n)$ is a suitable $m$th order S obolev space. For a given rearrangement-invariant space $X(\\mathbb{H}^n)$ \, we will describe the optimal (i.e.\, with the strongest norm) rearrange ment-invariant space $Y(\\mathbb{H}^n)$ on the left-hand side.\n\nWe first discuss the general description(s) of the optimal space. Then we turn our attention to some concrete examples. Namely\, when $X$ is $L^1$\, $L^\\fr ac{n}{m}$\, or an exponential Orlicz space ``near $L^\\infty$''. Even in t hese simple cases\, the inequalities that we obtain seems to be missing in the literature (especially\, when $m\\geq3$).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Rami Ayoush (Universitreiy of Warsaw) DTSTART:20231128T070000Z DTEND:20231128T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/27 DESCRIPTION:Title: On finite configurations in the spectra of singular me asures\nby Rami Ayoush (Universitreiy of Warsaw) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Camp us Mathematics Building.\n\nAbstract\nDuring the talk I will discuss appli cations of elementary additive combinatorics to dimensional estimates of P DE- and Fourier-constrained measures. My main tool will be a simple certai nty principle of the following form: a set $S ⊂ \\mathbb{R}^N$ contains a given finite linear pattern if $S$ is a spectrum of a sufficiently singu lar measure.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Cody Stockdale (Clemson University) DTSTART:20230926T010000Z DTEND:20230926T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/28 DESCRIPTION:Title: A different approach to endpoint weak-type estimates f or Calderón-Zygmund operators\nby Cody Stockdale (Clemson University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nThe weak-type $(1\,1)$ estimate for Calderón-Zygmund operators is fundamental in harmon ic analysis. We investigate weak-type inequalities for Calderón-Zygmund s ingular integral operators using the Calderón-Zygmund decomposition and i deas inspired by Nazarov\, Treil\, and Volberg. We discuss applications of these techniques in the Euclidean setting\, in weighted settings\, for mu ltilinear operators\, for operators with weakened smoothness assumptions\, and in studying the dimensional dependence of the Riesz transforms.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Armin Schikorra (University of Pittsburgh) DTSTART:20231114T010000Z DTEND:20231114T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/29 DESCRIPTION:Title: On s-Stability of W^{s\,n/s}-minimizing maps between s pheres in homotopy classes\nby Armin Schikorra (University of Pittsbur gh) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M 210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nWe consider maps between spheres S^n to S^\\ell that minimize the\nSobolev-space ener gy W^{s\,n/s} for some s \\in (0\,1) in given homotopy\nclass.\nThe basic question is: in which homotopy class does a minimizer exist?\nThis is a no ntrivial question since the energy under consideration is\nconformally inv ariant and bubbles can form.\nSacks-Uhlenbeck theory tells us that minimiz ers exist in a set of\nhomotopy classes that generates the whole homotopy group\n\\pi_{n}(\\S^\\ell). In some situations explicit examples are known if\nn/s = 2 or s=1.\n\nIn our talk we are interested in the stability of the above question\nin dependence of s. We can show that as s varies local ly\, the set of\nhomotopy classes in which minimizers exists can be chosen stable. We\nalso discuss that the minimum W^{s\,n/s}-energy in homotopy c lasses is\ncontinuously depending on s.\n\nJoint work with K. Mazowiecka ( U Warsaw)\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Felipe Hernandez (MIT) DTSTART:20231024T010000Z DTEND:20231024T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/30 DESCRIPTION:Title: Uncertainty principles for Wigner functions\nby Fe lipe Hernandez (MIT) as part of Nonlinear Analysis Seminar Series\n\nLectu re held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbst ract\nThe Wigner function of a quantum state is a way of describing the ph ase space distribution of a quantum particle. The uncertainty principle f rom Fourier analysis places some restriction on the allowable decay of a W igner function. In this talk I will give an introduction to the Wigner fu nction and show that rapidly decaying Wigner functions must also be Schwar tz\, which can also be interpreted as a type of uncertainty principle. Th is is based on joint work with Jess Riedel.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Angela Alberico (CNR - IAC) DTSTART:20231121T070000Z DTEND:20231121T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/31 DESCRIPTION:Title: Optimal embeddings for fractional Orlicz-Sobolev space s\nby Angela Alberico (CNR - IAC) as part of Nonlinear Analysis Semina r Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nThe optimal target space is exhibited for embedding s of fractional-order Orlicz-Sobolev spaces.\nBoth the subcritical and the supercritical regimes are considered.\nIn the former case\, the smallest possible Orlicz target space is detected. In the latter\,\n the relevant O rlicz-Sobolev spaces are shown to be embedded into the space of bounded\nc ontinuous functions in $\\mathbb R^n$. Moreover\, their\n optimal modulus of continuity is exhibited.\nThese results are the subject of a series of joint papers with Andrea Cianchi\, Lubos Pick and Lenka\nSlavikova.\n\n\nA .Alberico\, A.Cianchi\, L.Pick and L.Slavikova\,\nFractional Orlicz-Sobol ev embeddings\,\n J. de Mathematiqués Pures et Appliquées\, 149 (2021).\n\n\nA.Alberico\, A.Cianchi\, L.Pick and L.Slavikova\,\n Boundedness of functions in fractional Orlicz-Sobolev spaces\,\n Nonlinear Analysis\, 230 (2023).\n\n\n A.Alberico\, A.Cianchi \, L.Pick and L.Slavikova\,\nOn the Modulus of Continuity of fractional Or licz-Sobolev functions\,\n in progress.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Hajłasz (University of Pittsburgh) DTSTART:20231205T010000Z DTEND:20231205T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/32 DESCRIPTION:Title: Approximation of mappings with derivatives of low rank \nby Piotr Hajłasz (University of Pittsburgh) as part of Nonlinear An alysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nMy talk is based on two recent joint p apers with Paweł Goldstein.\n\n\nJacek Gałęski in 2017\, in the context of his research in geometric measure theory\, formulated the following co njecture:\n\nConjecture.\nLet $1\\leq m< n$ be integers and let $\\Omega\\ subset\\mathbb{R}^n$ be open. If $f\\in C^1(\\Omega\,\\mathbb{R}^n)$ satis fies $\\operatorname{rank} Df\\leq m$ everywhere in $\\Omega$\, then $f$ c an be uniformly approximated by smooth mappings $g\\in C^\\infty(\\Omega\, \\mathbb{R}^n)$ such that $\\operatorname{rank} Dg\\leq m$ everywhere in $ \\Omega$.\n\nOne can also modify the conjecture and ask about a local appr oximation: smooth approximation in a neighborhood of any point.\nThese are very natural problems with possible applications to PDEs and Calculus of Variations. However\, the problems are difficult\, because standard approx imation techniques like the one based on convolution do not preserve the r ank of the derivative. It is a highly nonlinear constraint\, difficult to deal with.\n\nIn 2018 Goldstein and Hajłasz obtained infinitely many coun terexamples to this conjecture. Here is one:\n\nExample.\nThere is $f\\in C^1(\\mathbb{R}^5\,\\mathbb{R}^5)$ with $\\operatorname{rank} Df\\leq 3$ t hat cannot be locally and uniformly approximated by mappings\n$g\\in C^2(\ \mathbb{R}^5\,\\mathbb{R}^5)$ satisfying $\\operatorname{rank} Dg\\leq 3$. \n\nThis example is a special case of a much more general result and the c onstruction heavily depends on algebraic topology including the homotopy g roups of spheres and the Freudenthal suspension theorem.\n\nMore recently Goldstein and Hajłasz proved the conjecture in the positive in the case w hen $m=1$. The proof is based this time on methods of analysis on metric s paces and in particular on factorization of a mapping through metric trees .\n\nThe method of factorization through metric trees used in the proof of the conjecture when $m=1$ is very different and completely unrelated to t he methods of algebraic topology used in the construction of counterexampl es. However\, quite surprisingly\, both techniques have originally been us ed by Wenger and Young as tools for study of Lipschitz homotopy groups of the Heisenberg group\, a problem that seems completely unrelated to proble ms discussed in this talk.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Bogdan Raita (Georgetown University) DTSTART:20231107T010000Z DTEND:20231107T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/33 DESCRIPTION:Title: Limiting linear $L^1$ estimates near the boundary\ nby Bogdan Raita (Georgetown University) as part of Nonlinear Analysis Sem inar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathemati cs Building.\n\nAbstract\nWe identify necessary and sufficient conditions on $k$th order linear differential operators $\\mathbb{A}$ in terms of a f ixed halfspace $H\\subset\\mathbb{R}^n$ such that the Gagliardo--Nirenberg --Sobolev inequality\n $$\n \\|D^{k-1}u\\|_{\\mathrm{L}^{\\frac{n}{n-1}} (H)}\\leq c\\|\\mathbb{A} u\\|_{\\mathrm{L}^1(H)}\\quad\\text{for }u\\in\\ mathrm{C}^\\infty_c (\\mathbb{R}^{n}\,V)\n $$\n holds. This comes as a c onsequence of sharp trace theorems on $\\partial H$. Strong estimates on l ower order derivatives are the best possible due to the failure of Calder\ \'on--Zygmund theory in $L^1$.\n\nJoint work with Franz Gmeineder and Jean Van Schaftingen.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/33/ END:VEVENT BEGIN:VEVENT SUMMARY:David Cruz-Uribe (University of Alabama) DTSTART:20231212T070000Z DTEND:20231212T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/34 DESCRIPTION:Title: Weighted norm inequalities for multiplier weak-type in equalities\nby David Cruz-Uribe (University of Alabama) as part of Non linear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gonggu an Campus Mathematics Building.\n\nAbstract\nIn this talk we will consider a version of weak-type inequalities we\nrefer to as {\\em multiplier weak -type inequalities}. Given a weight\n$w$ and $1\\leq p<\\infty$\, the $( p\,p)$ multiplier weak-type inequality\nfor an operator $T$ is of the form \n\\[ |\\{ x\\in {\\mathbb{R}^n} : |w^{\\frac{1}{p}}(x)T(w^{-\\frac{1}{p}} f)(x)|> t\\}|\n \\leq \\frac{C}{t^p} \\int_{\\mathbb{R}^n} |f(x)|^p\\\,dx . \\]\nThese inequalities follow from the a strong $(p\,p)$ inequality of the\nform\n\\[ \\int_{\\mathbb{R}^n} |Tf(x)|^pw(x)\\\,dx \\leq C \\int_{\ \mathbb{R}^n} |f(x)|^pw(x)\\\,dx \\]\nby mapping $f\\mapsto w^{-\\frac{1}{ p}}f$ and applying Chebyshev's\ninequality. These inequalities were first considered by Muckenhoupt\nand Wheeden (1977) for the maximal operator an d the Hilbert transform\non the real line. They showed that such inequali ties hold if $w$ is a\nMuckenhoupt $A_p$ weight\, but gave examples to sho w that the class of\nweights is strictly larger for these operators. Thei r $A_p$ results\nwere extended to all dimensions and all Calder\\'on-Zygmu nd integral\noperators by myself\, Martell\, and Perez (2005). They have attracted\nrenewed attention since they were shown to be the right way of\ ngeneralizing weak-type inequalities to the setting of matrix weights\n(DC U\, Isralowitz\, Moen\, Pott\, Rivera-Rios\, 2020).\n\nIn this talk\, we w ill consider the problem of quantitative estimates\,\nin terms of the $A_p $ characteristic\, for maximal operators and\nsingular integrals. Our res ults extend those gotten in 2020 in the\ncase $p=1$ to all $1\\leq p<\\inf ty$. We also show that our proofs can\nbe adapted to prove quantitative estimates for matrix weighted\ninequalities. Finally\, we prove the analo gous results for the\nfractional integral/Riesz potential in both the scal ar and matrix\nweighted cases. These results are completely new\, as even qualitative\nresults for fractional integrals were not known.\n\n\\bigski p\n\nThis talk is joint work with Brandon Sweeting\, the University of Ala bama.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Anastasia Molchanova (University of Vienna) DTSTART:20240319T070000Z DTEND:20240319T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/35 DESCRIPTION:Title: Limits of Sobolev Homeomorphisms in Nonlinear Elastici ty\nby Dr. Anastasia Molchanova (University of Vienna) as part of Nonl inear Analysis Seminar Series\n\nLecture held in Room 509\, Cosmology Buil ding\, National Taiwan University.\n\nAbstract\nLimits of Sobolev homeomor phisms naturally appear in geometric function theory\, calculus of variati ons\, and continuum mechanics. In this talk\, we discuss essential propert ies of mappings essential for elastic deformations\, focusing on aspects s uch as continuity\, injectivity\, and differentiability\, as well as Lusin 's $(N)$- and $(N^{-1})$-conditions.\nWe consider variational problems of nonlinear elasticity\, where admissible deformations are given by limits o f Sobolev homeomorphisms\, and prove the existence of minimizers.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. MingQing Xiao (Southern Illinois University) DTSTART:20240312T010000Z DTEND:20240312T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/36 DESCRIPTION:Title: Low Rank Approximation of Multi-Dimensional Data Set f or Completion\nby Dr. MingQing Xiao (Southern Illinois University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nLarge datasets oft en manifest naturally as multi-dimensional arrays\, commonly referred to a s tensors. These tensors may represent diverse phenomena\, from sensor mea surements in scientific experiments to user behavior in recommendation sys tems. However\, real-world data is rarely perfect\, and incomplete entries are common due to various reasons such as sensor failures\, missing obser vations\, or privacy constraints. In this talk\, we introduce a new noncon vex regularization approach\, which can better capture the low-rank charac teristics than the convex approach for data completion. A minimization alg orithm\, associated with the augmented Lagrangian multipliers and the nonc onvex regularizer\, will be presented.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Fulton Gonzalez (Tufts University) DTSTART:20240326T073000Z DTEND:20240326T083000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/37 DESCRIPTION:Title: The Snapshot Problem for the Wave Equation\nby Dr. Fulton Gonzalez (Tufts University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Bu ilding.\n\nAbstract\nBy definition\, a wave is a $C^\\infty$ solution $u(x \,t)$ of the wave equation on $\\mathbb{R}^n$\, and a snapshot of the wave $u$ at time $t$ is the function $u_t$ on $\\mathbb{R}^n$ given by $u_t(x )=u(x\,t)$. We show that there are infinitely many waves with given $C^\\ infty$ snapshots $f_0$ and $f_1$ at times $t=0$ and $t=1$ respectively\, b ut that all such waves have the same snapshots at integer times. We prese nt necessary and sufficient conditions for the existence and uniqueness of a wave $u$ to have three given snapshots at three different times\, and w e show how this leads to problems in Diophantine approximations and "small denominators"\, which dates back to the early study of the $n$-body probl em in $\\mathbb{R}^3$. We consider generalizations to the Euler-Poisson-Da rboux equation and to modified wave equations on spheres and symmetric spa ces\, as well as some open questions. \n\n \nJoint with J. Christensen (Co lgate)\, J. Wang (N. China Inst. of Science & Technology)\, and T. Kakehi (Tsukuba).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Oscar Dominguez Bonilla (Cunef Universidad) DTSTART:20240402T070000Z DTEND:20240402T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/38 DESCRIPTION:Title: Affine fractional Moser-Trudinger and Morrey inequalit ies\nby Dr. Oscar Dominguez Bonilla (Cunef Universidad) as part of Non linear Analysis Seminar Series\n\nLecture held in Room 509\, Cosmology Bui lding\, National Taiwan University.\n\nAbstract\nIn this talk we establish affine versions of fractional Moser-Trudinger and Morrey inequalities. Th ese new inequalities are stronger than the affine Moser-Trudinger and Morr ey inequalities due to Cianchi-Lutwak-Yang-Zhang and complement the affine fractional Sobolev inequalities of Haddad-Ludwig. This is a joint work wi th Y. Li\, S. Tikhonov\, D. Yang\, and W. Yuan.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Prasun Roychowdhury (National Center for Theoretical Sciences Taiwan) DTSTART:20240416T070000Z DTEND:20240416T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/40 DESCRIPTION:Title: Classification of radial solutions to $-\\Delta_g u = e^u$ on Riemannian models\nby Dr. Prasun Roychowdhury (National Center for Theoretical Sciences Taiwan) as part of Nonlinear Analysis Seminar Se ries\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Buil ding.\n\nAbstract\nThe talk is devoted to the complete classification with respect to asymptotic behaviour\, stability\, and intersections propertie s of radial smooth solutions to the equation $-\\Delta_g u=e^u$ on Riemann ian model manifolds $(M\,g)$ in dimension $N\\ge 2$. Our assumptions inclu de Riemannian manifolds with sectional curvatures bounded or unbounded fro m below. Intersection and stability properties of radial solutions are inf luenced by the dimension $N$ in the sense that two different kinds of beha viour occur when $2\\le N\\le 9$ or $N\\ge 10$\, respectively. The crucial role of these dimensions in classifying solutions is well-known in Euclid ean space\; here the analysis highlights new properties of solutions that cannot be observed in the flat case. This is based on a joint work with El vise Berchio\, Alberto Ferrero\, and Debdip Ganguly.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Robin Neumayer (Carnegie Mellon University) DTSTART:20240611T010000Z DTEND:20240611T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/41 DESCRIPTION:Title: The Saint-Venant inequality and quantitative resolvent estimates for the Dirichlet Laplacian\nby Dr. Robin Neumayer (Carnegi e Mellon University) as part of Nonlinear Analysis Seminar Series\n\nLectu re held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbst ract\nAmong all cylindrical beams of a given cross-sectional area\, those with circular cross sections are the most resistant to twisting forces. Th e general dimensional analogue of this fact is the Saint-Venant inequality \, which says that balls have the largest torsional rigidity among subsets of Euclidean space with a fixed volume. We discuss recent results showing that for a given set $E$\, the gap in the Saint-Venant inequality quantit atively controls the $L^2$ difference between solutions of the Poisson equ ation on $E$ and on the nearest ball\, for any Holder continuous right-han d side. We additionally prove quantitative closeness of all eigenfunctions of the Dirichlet Laplacian. This talk is based on joint work with Mark Al len and Dennis Kriventsov.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Cody Stockdale (Clemson University) DTSTART:20240528T070000Z DTEND:20240528T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/42 DESCRIPTION:Title: On the theory of compact Calderón-Zygmund operators\nby Dr. Cody Stockdale (Clemson University) as part of Nonlinear Analys is Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mat hematics Building.\n\nAbstract\nWe present new developments in the theory of compact Calderón-Zygmund operators. In particular\, we give a new form ulation of the $T1$ theorem for compactness of CZ operators\, which\, comp ared to existing compactness criteria\, more closely resembles David and J ourné’s classical $T1$ theorem for boundedness and follows from a simpl er argument. Our methods generalize to treat a class of "localized" operat ors on a Hilbert space -- we apply this abstraction to characterize the co mpact pseudodifferential operators on $L^2(\\mathbb{R}^n)$. Additionally\, we discuss the extension of compact CZ theory to weighted Lebesgue spaces via sparse domination methods. \n\nThis talk is based on joint works with Mishko Mitkovski\, Paco Villarroya\, Cody Waters\, and Brett Wick.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Ji Li (Macquarie University) DTSTART:20240423T073000Z DTEND:20240423T083000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/44 DESCRIPTION:Title: Schatten Properties of Calderon–Zygmund Singular Int egral Commutator on stratified Lie groups\nby Prof. Ji Li (Macquarie U niversity) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room 515 in NCTS in NTU.\n\nAbstract\nSchatten class estimates of the com mutator of Riesz transform in $\\mathbb R^n$ link to the quantised derivat ive of A. Connes. A general setting for quantised calculus is a spectral t riple $(\\mathcal A\,\\mathcal H\,D)$\, which consists of a Hilbert space $\\mathcal H$\, a pre-$C^*$-algebra $\\mathcal A $\, represented faithfull y on $\\mathcal H$ and a self-adjoint operator $D$ acting on $\\mathcal H$ such that every $a\\in A$ maps the domain of $D$ into itself and the comm utator $[D\,a] = Da-aD$ extends from the domain of $D$ to a bounded linear endomorphism of $\\mathcal H$. Here\, the quantised differential $\\qd a$ of $a \\in \\mathcal A$ is defined to be the bounded operator ${\\rm i} [ {\\rm sgn}(D)\,a]$\, ${\\rm i}^2=-1$. \n\nWe provide full characterisation of the Schatten properties of $[M_b\,T]$\, the commutator of Calder\\'{o }n--Zygmund singular integral $T$ with symbol $b$ $(M_bf(x):=b(x)f(x))$ on stratified Lie groups $\\mathcal G$. We show that\, when $p$ is larger th an the homogeneous dimension $\\mathbb Q$ of $\\mathcal G$\, the Schatten $\\mathcal L_p$ norm of the commutator is equivalent to the Besov semi-nor m $B_{p}^{\\mathbb Q/p}$ of the function $b$\; but when $p\\leq \\mathbb Q $\, the commutator belongs to $\\mathcal L_p$ if and only if $b$ is a cons tant. For the endpoint case at the critical index $p=\\mathbb Q$\, we furt her show that the Schatten $\\mathcal L_{\\mathbb Q\,\\infty}$ norm of the commutator is equivalent to the Sobolev norm $\\dot{W}^{1\,\\mathbb Q}$ o f $b$. Our method at the endpoint case differs from existing methods of Fo urier transforms or trace formula for Euclidean spaces or Heisenberg group s\, respectively.\n\nThis talk is based on my recent work joint with Xiao Xiong and Fulin Yang.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. You Wei-Chen (National Taiwan University) DTSTART:20240430T070000Z DTEND:20240430T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/45 DESCRIPTION:Title: A self-improving property of Riesz potentials in BMO\nby Dr. You Wei-Chen (National Taiwan University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Camp us Mathematics Building.\n\nAbstract\nIn this talk\, we introduce the conc ept of beta-dimensional BMO space \$ BMO^\\beta \$ and the associated Jo hn-Nirenberg inequality. We will discuss the mapping properties of Riesz p otentials within \$BMO^\\beta\$ spaces\, focusing specifically on the Mo rrey spaces and weak Lebesgue spaces \$L^{n/ \\alpha\,\\infty} (\\mathbb{ R}^n)\$. Additionally\, we present that \$ I_\\alpha f \\in BMO^{n-\\al pha + \\epsilon} \$ is actually a necessary and sufficient condition for \$ I_\\alpha f \\in BMO \$ when \$ f \$ is a non-negative function.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Bogdan Raita (Georgetown University) DTSTART:20240618T073000Z DTEND:20240618T083000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/46 DESCRIPTION:Title: Self improving size estimates in compensated compactne ss\nby Dr. Bogdan Raita (Georgetown University) as part of Nonlinear A nalysis Seminar Series\n\nLecture held in Room 509\, Cosmology Building\, National Taiwan University.\n\nAbstract\nWe review some recent results in compensated compactness\, concerning primarily concentration effects of pd e constrained sequences. We show that Müller's $L\\log L$ bound \n $$\n \\Phi(Du)\\geq 0\,\\\,Du\\in L^q(\\mathbb{R}^n)\\implies \\Phi(Du)\\in L\\log L_{loc}\n$$\n for $\\Phi =\\det$ and $q=n$ holds for quasiconcav e $\\Phi$ which are homogeneous of degree $q>1$. This contrasts similar Ha rdy bounds which hold only for null Lagrangians.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. José Carlos Bellido (Universidad de Castilla-La Mancha) DTSTART:20240507T070000Z DTEND:20240507T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/47 DESCRIPTION:Title: Nonlocal gradients and applications to Continuum Mecha nics\nby Dr. José Carlos Bellido (Universidad de Castilla-La Mancha) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nThis presentati on collects joint work with C. Mora-Corral\, J. Cueto\, H. Schönberger\, P. Radu and M. Foss. \n\nInterest in nonlocal gradients has increased in t he last decades due to development of nonlocal modeling in a variety of fi elds\, including mechanics and materials science. We start by defining non local gradients in a general context\, where their calculation depends on a general kernel. Our goal is to explore the structural properties of spac es associated with these gradients. From a functional analysis perspective \, we seek kernels that make these spaces useful for studying variational problems and\, consequently\, applicable to physical models. Beyond the th eoretical groundwork\, we delve into the mathematical intricacies of these new functional spaces. These spaces are essential for understanding nonlo cal phenomena and capturing behavior that local models might miss. Nonloca l gradients find practical applications in solid mechanics\, particularly in finite elasticity. Additionally\, we establish connections between non local models derived from nonlinearly elastic models and the well-known Er ingen’s nonlocal model of linear elasticity. Remarkably\, these solid me chanics models can be seen as a special case of state-based peridynamics\, a continuum theory designed to address material failure where classical e lasticity theories fall short.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Riju Basak (National Taiwan Normal University) DTSTART:20240514T073000Z DTEND:20240514T083000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/48 DESCRIPTION:Title: Wave equation on Hardy spaces\nby Dr. Riju Basak ( National Taiwan Normal University) as part of Nonlinear Analysis Seminar S eries\n\nLecture held in Room 509\, Cosmology Building\, National Taiwan U niversity.\n\nAbstract\nThe sharp fixed-time estimates for the solution of the Cauchy problem associated with the standard Euclidean Laplacian on Le besgue and Hardy spaces were first studied independently by A. Miyachi and J.C. Peral in 1980. However\, the sharp fixed-time estimate is still not available for many operators\, especially on Hardy spaces for $0< p <1 $. \n\nIn this talk\, we shall discuss fixed-time estimates for the solution of the wave equation associated with the twisted Laplacian. This talk is b ased on a joint work with K. Jotsaroop.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Diego Cordoba (ICMAT) DTSTART:20241008T073000Z DTEND:20241008T083000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/50 DESCRIPTION:Title: Finite time blow-up for the hypodissipative Navier Sto kes equations\nby Prof. Diego Cordoba (ICMAT) as part of Nonlinear Ana lysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nIn this talk we establish the formation of singularities of classical solutions with finite energy of the forced fractional Navier Stokes equations where the dissipative term is given by $|\\nabla|^{\\alpha}$ for any $\\alpha\\in [0\, \\alpha_0)$ ($\\alpha_0 = 0.09\\cdots$).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Yoshihiro Sawano (Chuo University) DTSTART:20240910T010000Z DTEND:20240910T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/51 DESCRIPTION:Title: A norm close to the $L^1$-norm\nby Prof. Yoshihiro Sawano (Chuo University) as part of Nonlinear Analysis Seminar Series\n\n Lecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\ nAbstract\nAround 10 years ago\, Armin Schikorra\, Daniel Spector\, Jean V an Schaftingen pointed out that there exists a variant of the boundedness of the Riesz potential $I_\\alpha$ which maps $L^1$ to weak $L^{\\frac{n}{ n-\\alpha}}$. The goal of this talk is to extend it to Morrey spaces. Some variants as well as the proof will be discussed. This is a joint work wit h Denny Ivanal Hakim and Mei Dita Kumala at Bandung Institute Technology.\ n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Blake Temple (UC Davis) DTSTART:20241015T010000Z DTEND:20241015T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/52 DESCRIPTION:Title: On the Essential Regularity of Singular Connections in Geometry\nby Prof. Blake Temple (UC Davis) as part of Nonlinear Analy sis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Ma thematics Building.\n\nAbstract\nAuthor together with collaborator Moritz Reintjes recently introduced the Regularity Transformation Equations (RT-e quations)\, an elliptic\, non-invariant system of equations which determin e the Jacobians of coordinate transformations which (locally) lift the reg ularity of a connection to one derivative above the regularity of its Riem ann curvature tensor. Our existence theory for the RT-equations generali ze celebrated results of Kazden-DeTurck\, valid for Riemannian metrics\, t o arbitrary non-Riemannian connections\, including the metrics and connect ions of General Relativity. Authors have found applications of the RT-eq uations\, including extending Uhlenbeck compactness from Riemannian to non -Riemannian connections on vector bundles\, extending existence and unique ness of ODEs one derivative below the threshold for Picard's method\, and an application to the Strong Cosmic Censorship Conjecture (Reintjes). In this talk I discuss our forthcoming paper in which we use the theory of t he RT-equations to give a necessary and sufficient condition for determini ng when a singularity appearing in a connection or metric in geometry can be regularized by coordinate transformation\; we establish the consistency of the $\\textit{essential}$\, highest possible regularity to which a sin gular connection can be regularized by coordinate transformation\; and we describe an explicit procedure (based in the RT-equations) for constructin g the coordinate transformations which lift a singular connection to its e ssential regularity. Results apply both locally and globally\, and we sho w that there always exists a maximal $C^\\infty$ atlas on a manifold which globally preserves the essential regularity of any connection. Our neces sary and sufficient condition relies on our existence theory for the RT-eq uations which we currently require connection regularity in $L^p$\, $p>n$\ , sufficient to address shock wave singularities in GR\, but not yet black hole singularities. Extending our existence theory to the case $p\\verb+ <+n$ is an important topic of authors' current research.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Simon Bortz (University of Alabama) DTSTART:20241022T010000Z DTEND:20241022T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/53 DESCRIPTION:Title: Regularity of Co-normal Derivatives and Weights\nb y Prof. Simon Bortz (University of Alabama) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathem atics Building.\n\nAbstract\nThis talk is concerned with the properties of the co-normal derivative of (adjoint) solutions to elliptic and parabolic PDEs in divergence form\, that is\, $Lu = -div A \\nabla u = 0$ or $L = - \\partial_t u - div A \\nabla u = 0$ in some domain $\\Omega$. Specificall y\, the properties of co-normal derivative on a subset of the boundary wh ere the solution $u$ vanishes. A prototypical situation is when $\\Omega$ is the upper half space ($\\{(x\,\\lambda) : x \\in \\mathbb{R}^n\, \\lamb da > 0\\}$ or $\\{(t\,x\,\\lambda) : t\\in \\mathbb{R}\, x \\in \\mathbb{R }^n\, \\lambda > 0\\}$) and $u$ is the Green function of $L$ with pole at infinity and\, in that case\, the co-normal derivative is the elliptic/par abolic measure. \n\nIn this talk\, I will introduce the co-normal derivati ve and discuss some sufficient conditions on the coefficients $A$ for the co-normal derivative to be quantitatively absolutely continuous with respe ct to surface measure or even have a density that is $\\dot{C}^\\alpha_{lo c}$ (locally H\\"older continuous) on the boundary. The method will unify these regimes\, by refining the work of David\, Li and Mayboroda and combi ning it with some of my recent work with Toro and Zhao\, and Egert and Saa ri. For simplicity\, in the talk $\\Omega$ will be assumed to be the upper half space\, but more exotic domains can be considered.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Reinaldo Resende (Carnegie Mellon University) DTSTART:20241001T010000Z DTEND:20241001T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/55 DESCRIPTION:Title: Regularity results for area minimizing currents\nb y Dr. Reinaldo Resende (Carnegie Mellon University) as part of Nonlinear A nalysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campu s Mathematics Building.\n\nAbstract\nWe will explore exciting new results on the interior and boundary regularity of currents $T$ solving the orient ed Plateau’s problem\, with a special focus on higher codimensions. We w ill extend well-known estimates concerning the Hausdorff dimension of the interior singular set of $T$ to a broader context\, and also share results from an upcoming work that optimally resolves several long-standing open questions on boundary regularity. Additionally\, we’ll discuss recent ad vancements in the rectifiability of the singular set and\, if time permits \, review the general proof strategy for these regularity results using mu ltivalued functions and the frequency function.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Willie Wong (Michigan State University) DTSTART:20241126T010000Z DTEND:20241126T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/56 DESCRIPTION:Title: Some Big Bangs are Unstable\nby Prof. Willie Wong (Michigan State University) as part of Nonlinear Analysis Seminar Series\n \nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\ n\nAbstract\nOur understanding of cosmological processes\, like many other predictions of physical theories\, are based on studying regimes where th e equations of motion reduce to a finite dimensional dynamical system. An example of a conclusion derived from such reductions is the idea of a big bang cosmology in general relativity. Such reductions are physically justi fied by the working assumption that when viewed from the largest scales\, the inhomogeneities average out and the matter content can be approximated by a homogeneous compressible fluid. Jointly with Shih-Fang Yeh\, we prob e whether this working assumption is justified mathematically. Our results show that on the cosmological timescale\, some big bang solutions are sus ceptible to instabilities generated through nonlinear self-interactions of the constituent matter when inhomogeneities are present. The goal of this talk is to present the mathematical context of this result and briefly de scribe the mechanism driving the instability\, focusing on the relevance o f the conformal (or causal) geometry of the big bang solutions. (No prior familiarity with mathematical relativity is assumed.)\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Thomas Hou (Caltech) DTSTART:20241105T010000Z DTEND:20241105T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/57 DESCRIPTION:Title: A computer assisted proof of finite time singularity o f 3D Euler equations with smooth data\nby Prof. Thomas Hou (Caltech) a s part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 i n NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nWhether the 3D i ncompressible Euler equations can develop a finite time singularity from s mooth initial data is one of the most challenging problems in nonlinear PD Es. In this talk\, I will present a recent result with Dr. Jiajie Chen in which we prove finite time blowup of the 2D Boussinesq and 3D Euler equati ons with smooth initial data and boundary. There are several essential dif ficulties in establishing such blowup result. We use the dynamic rescaling formulation and turn the problem of proving finite time singularity into a problem of proving stability of an approximate self-similar profile. A c rucial step is to establish linear stability of the approximate self-simil ar profile. We decompose the solution operator into a leading order operat or with the desired stability property plus a finite rank perturbation ope rator that can be estimated with computer assistance. This enables us to e stablish nonlinear stability of the approximate self-similar profile and p rove stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler e quations.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Luis Silvestre (University of Chicago) DTSTART:20241029T010000Z DTEND:20241029T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/58 DESCRIPTION:Title: The Landau equation does not blow up\nby Prof. Lui s Silvestre (University of Chicago) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Bu ilding.\n\nAbstract\nThe Landau equation is one of the main equations in k inetic theory. It models the evolution of the density of particles when th ey are assumed to repel each other by Coulomb potentials. It is a limit ca se of the Boltzmann equation with very soft potentials. In the space-homog eneous case\, we show that the Fisher information is monotone decreasing i n time. As a consequence\, we deduce that for any initial data the solutio ns stay smooth and never blow up\, closing a well-known open problem in th e area.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Thomas Schmidt (University of Hamburg) DTSTART:20241112T073000Z DTEND:20241112T083000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/59 DESCRIPTION:Title: Isoperimetric conditions and lower semicontinuity for functionals with measures\nby Prof. Thomas Schmidt (University of Hamb urg) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nThe talk d eals with functionals in the calculus of variations which are the sum of a perimeter or total variation term and a $\\mu$-volume term. Here\, $\\mu$ is a possibly lower-dimensional signed measure which has the role of a gi ven right-hand side in corresponding Euler equations. Lower semicontinuity and existence results will be shown to depend crucially on certain (small -volume) isoperimetric conditions for $\\mu$. These conditions admit a wid e class of measures up to the critical case of area measures on hypersurfa ces and are partially optimal and interesting in themselves. The general t heory will be illustrated with examples. Some of the results have been obt ained in a joint work with E. Ficola (Hamburg).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Franz Gmeineder (University of Konstanz) DTSTART:20241203T073000Z DTEND:20241203T083000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/60 DESCRIPTION:Title: Extensions and differential constraints\nby Prof. Franz Gmeineder (University of Konstanz) as part of Nonlinear Analysis Sem inar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathemati cs Building.\n\nAbstract\nExtension operators are at the core of studying function spaces\, allowing us to reduce numerous problems on domains to th ose on full space. While this theme has witnessed a huge number of contrib utions over the past century\, very little is known on extension operators that preserve certain differential constraints. In this talk\, we will gi ve a rather complete picture for divergence-type constraints\, where we pu t a special focus on the borderline case $p=1$ and thereby answer a border line case left open by Kato\, Mitrea\, Ponce & Taylor. This is joint work with Stefan Schiffer (MPI MIS Leipzig).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Eitan Tadmor (University of Maryland\, College Park) DTSTART:20241210T010000Z DTEND:20241210T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/61 DESCRIPTION:Title: Hierarchical construction of images and the problem of Bourgain-Brezis\nby Prof. Eitan Tadmor (University of Maryland\, Coll ege Park) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nEdges are noticeable features in images which can be extracted from noisy data using different variational models. The analysis of such models leads to t he question of expressing general $L^2$-data\, $f$\, as the divergence of uniformly bounded vector fields\, $div(U)$. \nWe present a multi-scale app roach to construct uniformly bounded solutions of $div(U)=f$ for general $ f$’s in the critical regularity space $L^d(T^d)$. The study of this equa tion and related problems was motivated by results of Bourgain & Brezis. T he intriguing critical aspect here is that although the problems are linea r\, construction of their solution is not. These constructions are special cases of a rather general framework for solving linear equations\, formul ated as inverse problems in critical regularity spaces. The solutions are realized in terms of nonlinear hierarchical representations $U=\\sum_j u_j $ which we introduced earlier in the context of image processing\, and yi eld a multi-scale decomposition of “objects” U.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Polona Durcik (Chapman University) DTSTART:20250506T010000Z DTEND:20250506T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/62 DESCRIPTION:Title: On trilinear singular Brascamp-Lieb forms\nby Dr. Polona Durcik (Chapman University) as part of Nonlinear Analysis Seminar S eries\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Bui lding.\n\nAbstract\nBrascamp-Lieb forms are multilinear integral forms act ing on functions on Euclidean spaces. A necessary and sufficient condition for their boundedness on Lebesgue spaces is known. Singular Brascamp-Lieb forms arise when one of the functions in a classical Brascamp-Lieb form i s replaced by a singular integral kernel. Examples include Coifman-Meyer m ultipliers and multilinear Hilbert transforms. A general necessary and suf ficient condition for the boundedness of singular Brascamp-Lieb forms rema ins unknown\, and their theory continues to be developed on a case-by-case basis. In this talk\, we classify all trilinear singular Brascamp-Lieb fo rms and establish bounds for a specific class of forms that naturally emer ge from this classification. Additionally\, we provide a survey of the lit erature and briefly discuss conditional bounds for forms associated with m utually related representations. This talk is based on joint work with Lar s Becker and Fred Yu-Hsiang Lin.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Bochen Liu (Southern University of Science and Technology) DTSTART:20251028T010000Z DTEND:20251028T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/63 DESCRIPTION:Title: Fourier frames on measures with Fourier decay\nby Dr. Bochen Liu (Southern University of Science and Technology) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gon gguan Campus Mathematics Building.\n\nAbstract\nIn this talk we shall disc uss the (non)existence of Fourier frames on measures with Fourier decay. I n dimension 2 and higher we only focus on surfaces with nonvanishing Gauss ian curvature\, while in the unit interval we consider all existing constr uctions of Salem measures in the literature.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Zane Li (North Carolina State University) DTSTART:20250401T010000Z DTEND:20250401T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/64 DESCRIPTION:Title: Mixed norm decoupling for paraboloids\nby Dr. Zane Li (North Carolina State University) as part of Nonlinear Analysis Semina r Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nIn this talk we discuss mixed norm decoupling estim ates for the paraboloid. One motivation of considering such an estimate is a conjectured mixed norm Strichartz estimate on the torus which essential ly is an estimate about exponential sums. This is joint work with Shival D asu\, Hongki Jung\, and José Madrid.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Alan Chang (Washington University in St. Louis) DTSTART:20250408T010000Z DTEND:20250408T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/65 DESCRIPTION:Title: Venetian blinds\, digital sundials\, and efficient cov erings\nby Dr. Alan Chang (Washington University in St. Louis) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nDavies's efficient cov ering theorem states that we can cover any measurable set in the plane by lines without increasing the total measure. This result has a dual formula tion\, known as Falconer's digital sundial theorem\, which states that we can construct a set in the plane to have any desired projections\, up to n ull sets. The argument relies on a Venetian blind construction\, a classic al method in geometric measure theory. In joint work with Alex McDonald an d Krystal Taylor\, we study a variant of Davies's efficient covering theor em in which we replace lines with curves. This has a dual formulation in t erms of nonlinear projections.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Myles Workman (National Taiwan Normal University) DTSTART:20250325T010000Z DTEND:20250325T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/66 DESCRIPTION:Title: Minimal hypersurfaces: bubble convergence and index\nby Dr. Myles Workman (National Taiwan Normal University) as part of Non linear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gonggu an Campus Mathematics Building.\n\nAbstract\nThe regularity theories of Sc hoen--Simon--Yau and Schoen--Simon for stable minimal hypersurfaces are fo undational in geometric analysis. Using this regularity theory\, in low di mensions\, Chodosh--Ketover--Maximo\, and Buzano--Sharp\, studied singular ity formation along sequences of minimal hypersurfaces through a bubble an alysis.\n\nI will review this background\, before talking about my recent work in this bubble analysis theory. In particular I will show how to obta in upper semicontinuity of index plus nullity along a bubble converging se quence of minimal hypersurfaces.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Hiroki Saito (Nihon University) DTSTART:20250513T020000Z DTEND:20250513T030000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/67 DESCRIPTION:Title: Infinitesimal $L^{p}\\to L^{q}$ relative bounds for $( -\\Delta)^{\\alpha/2}+v$\nby Dr. Hiroki Saito (Nihon University) as pa rt of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NT NU Gongguan Campus Mathematics Building.\n\nAbstract\nBy analyzing the tra ce inequality for Bessel potentials\,\nsome Morrey-type sufficient conditi ons are given \nfor which $L^p\\to L^q$\, $1{<}p\,q<\\infty$\,\ninfinitesi mal relative boundedness of \nthe Schr\\"{o}dinger operators \n$(-\\Delta) ^{\\alpha/2}+v$ holds.\nThese results provide new aspects of Morrey spaces and \na nice application of weight theory.\nThis is a joint work with Pro f. N. Hatano\, R. Kawasumi and H. Tanaka.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Hitoshi Tanaka (Tsukuba University of Technology) DTSTART:20250513T010000Z DTEND:20250513T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/68 DESCRIPTION:Title: Multilinear embedding theorem for fractional sparse op erators\nby Dr. Hitoshi Tanaka (Tsukuba University of Technology) as p art of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in N TNU Gongguan Campus Mathematics Building.\n\nAbstract\nUnder $A_p$ conditi on for weights\,\nwe show some simple sufficient conditions for which\nthe multilinear emmbedding theorem holds for fractional sparse operators.\nCh ecking this simple sufficient condition\,\nwe demonstrate that theorem for power weights.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Nicolau S. Aiex (National Taiwan Normal University) DTSTART:20250318T010000Z DTEND:20250318T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/69 DESCRIPTION:Title: Quantitative estimates on singularities of minimal hyp ersurfaces\nby Dr. Nicolau S. Aiex (National Taiwan Normal University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nWe will discus s the occasionally unavoidable presence of singularities\non minimal hyper surfaces in high dimensional ambient spaces and\nestimates on its size.\nT his is seemingly an analysis problem but the variational notion of\nminima l hypersurfaces plays a much more important role than its defining\nPDE.\n The proof relies simply on coverings arguments by suitable open sets and\n we will go over the main ideas and consequences.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Luca Gennaioli (University of Warwick) DTSTART:20250429T070000Z DTEND:20250429T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/70 DESCRIPTION:Title: On the Fourier transform of BV functions\nby Dr. L uca Gennaioli (University of Warwick) as part of Nonlinear Analysis Semina r Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nThe plan is to introduce BV functions and the Fouri er transform and study how this two objects interact. We will prove asympt otic formulae for the Fourier transform of BV functions and (as a corollar y) for characteristic functions of sets of finite perimeter. Then we will show how\, using techniques of geometric measure theory\, it is possible t o sharpen some results of Herz\, concerning convergence properties of the Fourier transform of sets. Time permitting\, we will provide some applicat ions to the isoperimetric inequality and some open problems.\nThis talk is based on a joint work with Thomas Beretti (SISSA\, Trieste).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Alexander Tyulenev (Steklov Mathematical Institute) DTSTART:20251104T070000Z DTEND:20251104T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/71 DESCRIPTION:Title: Traces of weighted Sobolev spaces in the limiting case \nby Dr. Alexander Tyulenev (Steklov Mathematical Institute) as part o f Nonlinear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU G ongguan Campus Mathematics Building.\n\nAbstract\nA complete description o f traces on $\\mathbb{R}^{n}$ of functions from the weighted Sobolev spa ce\n$W^{l}_{1}(\\mathbb{R}^{n+1}\,\\gamma)$\, $l \\in \\mathbb{N}$\, with weight $\\gamma \\in A^{\\rm loc}_{1}(\\mathbb{R}^{n+1})$ will be present ed.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Jaemin Park (Yonsei University) DTSTART:20251014T070000Z DTEND:20251014T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/72 DESCRIPTION:Title: No anomalous dissipation in two dimensional fluids \nby Dr. Jaemin Park (Yonsei University) as part of Nonlinear Analysis Sem inar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathemati cs Building.\n\nAbstract\nIn this talk\, we will discuss Leray-Hopf soluti ons to the incompressible Navier-Stokes equations with vanishing viscosity . We explore important features of turbulence\, focusing around the anomal ous energy dissipation phenomenon. As a related result\, I will present a recent result proving that for two-dimensional fluids\, assuming that the initial vorticity is merely a Radon measure with nonnegative singular par t\, there is no anomalous energy dissipation. Our proof draws on several k ey observations from the work of J. Delort (1991) on constructing global w eak solutions to the Euler equation. We will also discuss possible extensi ons to the viscous SQG equation in the context of Hamiltonian conservation and existence of weak solutions for a rough initial data. This is a joint work with Mikael Latocca (Univ. Evry) and Luigi De Rosa (GSSI).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Sung-Jin Oh (University of California\, Berkeley) DTSTART:20250909T010000Z DTEND:20250909T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/73 DESCRIPTION:Title: Integral formulas for under/overdetermined differentia l operators via recovery on curves and the finite-dimensional cokernel con dition\nby Dr. Sung-Jin Oh (University of California\, Berkeley) as pa rt of Nonlinear Analysis Seminar Series\n\nLecture held in Room M212 in NT NU Gongguan Campus Mathematics Building.\n\nAbstract\nUnderdetermined diff erential operators arise naturally in diverse areas of physics and geometr y\, including the divergence-free condition for incompressible fluids\, th e linearized scalar curvature operator in Riemannian geometry\, and the co nstraint equations in general relativity. The duals of underdetermined ope rators\, which are overdetermined\, also play a significant role. In this talk\, I will present recent joint work with Philip Isett (Caltech)\, Yuch en Mao (UC Berkeley)\, and Zhongkai Tao (IHÉS) that introduces a novel ap proach - called recovery on curves - to constructing integral solution/rep resentation formulas (i.e.\, right-/left-inverses) for a broad class of un der/overdetermined operators via solving ODEs on curves. They are optimall y regularizing and have prescribed support properties (e.g.\, produce comp actly supported solutions for compactly supported forcing terms). A key fe ature of our approach is a simple algebraic condition on the principal sym bol - called the finite-dimensional cokernel (FC) condition - that implies the applicability of our method. This condition simplifies and unifies va rious treatments of related problems in the literature. If time permits\, I will discuss applications to studying the flexibility of initial data se ts in general relativity.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Elia Brué (Università Bocconi) DTSTART:20250923T070000Z DTEND:20250923T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/74 DESCRIPTION:Title: Non-Uniqueness and Flexibility in Two-Dimensional Eule r Equations\nby Dr. Elia Brué (Università Bocconi) as part of Nonlin ear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nIn 1962\, Yudovich established t he well-posedness of the two-dimensional incompressible Euler equations fo r solutions with bounded vorticity. However\, uniqueness within the broade r class of solutions with L^p vorticity remains a key unresolved question. In this talk\, I will survey recent advances on this problem and present new nonuniqueness results\, obtained via the convex integration method. Th is work is in collaboration with Colombo and Kumar.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Surjeet Choudhary (National Center for Theoretical Sciences\, Taiwan) DTSTART:20251021T070000Z DTEND:20251021T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/75 DESCRIPTION:Title: Twisted bilinear spherical maximal functions\nby D r. Surjeet Choudhary (National Center for Theoretical Sciences\, Taiwan) a s part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 i n NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nIn this talk\, w e will discuss $L^p−$estimates for the full and lacunary maximal functio ns associated with the twisted bilinear spherical averages given by\n\\[\\ mathfrak{A}_t(f_1\,f_2)(x\,y)=\\int_{\\mathbb S^{2d-1}}f_1(x+tz_1\,y)f_2(x \,y+tz_2)\\\;d\\sigma(z_1\,z_2)\,\\\;t>0\,\\]\nfor all dimensions $d\\geq1 $.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Alexander Nabutovsky (University of Toronto) DTSTART:20251111T010000Z DTEND:20251111T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/76 DESCRIPTION:Title: Boxing inequalities\, widths\, and systolic geometry\nby Dr. Alexander Nabutovsky (University of Toronto) as part of Nonlin ear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nWe will present generalizations of the classical boxing inequality:\nFor a bounded domain $\\Omega\\subset \\mathbb{R}^{n+1}$ and a positive $m\\in (0\,n]$ ${\\rm HC}_m(\\Omega)\\l eq c(m){\\rm HC}_m(\\partial\\Omega)$\, where ${\\rm HC}_m$ denotes the $m $-dimensional Hausdorff content. Recall that ${\\rm HC}_m(X)$ is defined a s the infimum of $\\Sigma_i r_i^m$ over all coverings of $X$ by metric bal ls\, where $r_i$ denote the radii of these balls.\nThe case $m=n$ here is the classical boxing inequality that is stronger than the isoperimetric in equality. \n\nYet this result is only a particular case of our boxing ineq uality valid also in higher codimensions: For each Banach space $B$ and co mpact $M\\subset B$ there is a ``filling" of $M$ by $W$ so that\n$W$ is at the distance at most $c(m){\\rm HC}^{1\\over m}_m(M)$ from $M$ and ${\\rm HC}_m(W)\\leq const(m){\\rm HC}_m(M)$. This result can be further general ized to the case where the ambient space $B$ is a metric space with a line ar contractibility function.\n\nThis result generalizes the high-codimensi on isoperimetric inequality for Hausdorff contents proven by B. Lishak\, Y . Liokumovich\, R. Rotman and the speaker originally motivated by applicat ions to systolic geometry.\n\nThe applications to systolic geometry involv e inequalities that provide upper bounds\nfor the widths of $M\\subset B$ in terms of volume or Hausdorff contents of $M$. The widths $W_m^B(M)$ mea sure how far $M$ is from a $m$-dimensional simplicial complex in $B$. In t he second part of the talk we will explain the new inequality $W_{m-1}^{l^ \\infty}(M)\\leq {\\rm const} \\sqrt{m}\\ vol(M^m)^{1\\over m}$ for closed manifolds $M^m\\subset{\\mathbb R}^N$ and its implications to systolic ge ometry. Here\, the width is measured with respect to the $l^\\infty$ dista nce in the ambient Euclidean space.\n\nJoint work with Sergey Avvakumov.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Dr. Paz Hashash (Ben Gurion University of the Negev) DTSTART:20251118T070000Z DTEND:20251118T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/77 DESCRIPTION:Title: The refined area formula for Sobolev mappings\nby Dr. Paz Hashash (Ben Gurion University of the Negev) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Camp us Mathematics Building.\n\nAbstract\nWe present a refined area formula fo r Sobolev mappings \n$\\varphi : \\Omega \\to \\mathbb{R}^n$.\nThe classic al identity\n\\[\n\\int_\\Omega f(x)\\\,|J\\varphi(x)|\\\,dx\n = \\int_{\ \mathbb{R}^n} \\sum_{x\\in\\varphi^{-1}\\{y\\}} f(x)\\\,dy\n\\]\ndoes not hold in general\, since Sobolev mappings are not differentiable on large s ets.\nWe show that the formula is valid once we remove an exceptional set of vanishing Riesz capacity.\nThe argument uses Lipschitz approximation of Sobolev mappings on subsets where the capacity is large.\nOn these subset s we apply the usual area formula\, and then pass to the limit.\nThis give s an extension of the change of variables formula beyond the Lipschitz cas e.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Long Huang (Guangzhou University) DTSTART:20260303T070000Z DTEND:20260303T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/78 DESCRIPTION:Title: Capacitary Muckenhoupt weights\nby Long Huang (Gua ngzhou University) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstra ct\nIn this talk\, we mainly introduce a new class of capacitary Muckenhou pt weights denoted by A_{p\,\\delta}. It is proved to be a proper subset of standard Muckenhoupt's A_p weight. By proposing a new approach\, we the n show Muckenhoupt's theorem\, reverse Holder's inequality\, self-improvin g property\, and Jones' factorization theorem within this capacitary Mucke nhoupt weight framework. Finally\, we will reveal the deep connections bet ween A_{p\,\\delta} with BMO and BLO spaces with respect to Hausdorff cont ents.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriele Cassese (Oxford University) DTSTART:20260310T070000Z DTEND:20260310T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/79 DESCRIPTION:Title: Martingales\, laminates and Korn-type inequalities \nby Gabriele Cassese (Oxford University) as part of Nonlinear Analysis Se minar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathemat ics Building.\n\nAbstract\nKorn-type inequalities quantify a fundamental r igidity principle in linear elasticity: the size of the full gradient of a displacement can be controlled by a reduced set of “strain-like” quan tities. Motivated by a question of Chipot\, one can ask for a minimal vers ion of this principle: how many scalar linear measurements of the gradient does one need to control the whole gradient? I will present a reformulati on of this problem in terms of rank-one convexity and quasiconvexity\, lea ding to sharp bounds. A central new ingredient is a systematic connection between laminates and martingales\, which produces explicit families reali sing the extremal behaviour. The same construction gives a streamlined\, q uantitative route to Ornstein-type non-inequalities for broad classes of f irst-order homogeneous operators. If time permits\, I will discuss additio nal applications of this method to calculus of variations\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Paolo Bonicatto (University of Trento) DTSTART:20260428T070000Z DTEND:20260428T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/80 DESCRIPTION:Title: Geometric Transport Equation for currents: recent deve lopments\nby Paolo Bonicatto (University of Trento) as part of Nonline ar Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan C ampus Mathematics Building.\n\nAbstract\nI will report on recent results c oncerning the Geometric Transport Equation for $k$-dimensional currents in $\\mathbb R^n$. This equation generalises the classical continuity and tr ansport equations to model the motion of geometric objects such as lines a nd surfaces. I will discuss well-posedness results for Lipschitz velocity fields\, highlighting a deep connection with the notion of decomposability bundle of a measure (introduced by Alberti and Marchese). This theory fur ther extends to the time-dependent setting with minimal regularity in time of the vector field\, thus offering a unified framework for the evolution of geometric data under non-smooth flows. If time allows\, I will also ou tline a recent approach to the classical Frobenius’ theorem via the tran sport of currents. The vanishing bracket condition is recast into transpor t identities that remain meaningful even when one of the vector fields is a normal 1-current and this perspective sheds light on some Alfvén-type s tatements in magnetohydrodynamics.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Yohei Tsutsui (Kyoto University) DTSTART:20260317T010000Z DTEND:20260317T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/81 DESCRIPTION:Title: Another proof of Alvino's embedding via medians\nb y Yohei Tsutsui (Kyoto University) as part of Nonlinear Analysis Seminar S eries\n\nLecture held in 台灣大學次震宇宙館509研討室+ Zoom.\n\ nAbstract\nThe median of a function on Euclidean space was introduced by F . John in 1965\, and can be regarded as a type of average. Unlike the inte gral average\, even for non-integrable functions\, a median always exists. However\, the median is not unique\, in general. In fact\, it is well-kno wn that the set of all medians for a function is a closed interval. With t he aid of a result due to Poelhuis and Torchinsky (2012)\, we can see that the endpoints of the closed interval are two distinct rearrangements. We introduce a fractional version of medians and give a similar expression fo r the set of all fractional medians. We introduce the maximal operator def ined via medians instead of integral averages\, and establish smoothing pr operties for the fractional maximal operator. Finally\, we give a short pr oof of Alvino's embedding\, $L^{n/(n-1)\,1} \\to BV$ by using properties o f medians and the coarea formula. Our estimate is covered by a result by S pector (2020).\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiroki Ohyama (Kyoto University) DTSTART:20260317T020000Z DTEND:20260317T030000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/82 DESCRIPTION:Title: Long-time solvability and asymptotics for the 3D rotat ing MHD equations\nby Hiroki Ohyama (Kyoto University) as part of Nonl inear Analysis Seminar Series\n\nLecture held in 台灣大學次震宇宙館509研討室+ Zoom.\n\nAbstract\nWe consider the initial value problem for the 3D incompressible rotating MHD equations around a constant magneti c field. We prove the long-time existence and uniqueness of solutions for small viscosity coefficient and high rotating speed. Moreover\, we investi gate the asymptotic behavior of solutions in the limit of vanishing viscos ity and fast rotation\, and show that the velocity and magnetic field conv erge to the zero vector and the solution to the linear heat equation\, res pectively. We also derive the rates of these convergences in some space-ti me norm.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Caroccia (University of Firenze) DTSTART:20260324T070000Z DTEND:20260324T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/83 DESCRIPTION:Title: On the contact surface of Cheeger sets\nby Marco C aroccia (University of Firenze) as part of Nonlinear Analysis Seminar Seri es\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathematics Buildi ng.\n\nAbstract\nGeometrical properties of Cheeger sets have been deeply s tudied by many authors since their introduction\, as a way of bounding fro m below the first Dirichlet p-Laplacian eigenvalue. They represent\, in so me sense\, the first eigenfunction of the Dirichlet 1-Laplacian of a domai n. In this talk we will introduce a property\, studied in collaboration wi th Simone Ciani\, concerning their contact surface with the ambient space. In particular\, we will show that the contact surface cannot be too small \, with a lower bound on the (Hausdorff) dimension strictly related to the regularity of the ambient space. The talk will focus on the introduction of the problem and on the proof of the dimensional bounds. Functional to t he whole argument is the notion of removable singularity\, as a tool for e xtending solutions of PDEs under some regularity constraint. Finally\, exa mples providing the sharpness of the bounds in the planar case are briefly treated.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Wenqi Zhang (The Australian National University) DTSTART:20260414T010000Z DTEND:20260414T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/84 DESCRIPTION:Title: Stein-Weiss and power weight Sobolev inequalities in $ L^1$\nby Wenqi Zhang (The Australian National University) as part of N onlinear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gong guan Campus Mathematics Building.\n\nAbstract\nIt is known that $L^1$ Sobo lev and Stein-Weiss inequalities follow a slightly different pattern to th eir $L^p$ counterparts. For instance\, they serve as weaker replacement in equalities for the failure of $L^1$ inequalities between differential oper ators. Recent work by P. De Napoli and T. Picon has shown that the canceli ng/cocanceling framework introduced by J. Van Schaftingen can be used to e xtend the $L^1$ Stein-Weiss inequalities beyond their expected range. Insp ired by these ideas\, we investigate if the cocanceling constraint can be weakened in a subcritical setting\, and we also explore how one may furthe r extend these inequalities to a critical case.\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Quoc-Hung Nguyen (Academy of Mathematics and Systems Science) DTSTART:20260331T070000Z DTEND:20260331T080000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/85 DESCRIPTION:Title: The 3D Inhomogeneous Incompressible Navier–Stokes Sy stem with ( \\mathbf{BMO}^{-1} ) Data\nby Quoc-Hung Nguyen (Academy of Mathematics and Systems Science) as part of Nonlinear Analysis Seminar Se ries\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathematics Buil ding.\n\nAbstract\nWe study the three-dimensional inhomogeneous incompress ible Navier–Stokes equations with rough initial velocity data. We first establish the local existence of strong solutions when the initial density is smooth and the velocity belongs to\n( L^2 \\cap \\mathbf{VMO}^{-1} ). Moreover\, under a smallness condition on the (\\mathbf{BMO}^{-1} -norm of the initial velocity\, we prove global existence of solutions.\nThe proof relies on a new estimate for the transport equation\, which provides regu larity of the density\, together with a freezing-coefficient method for th e velocity equation\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Josh Kline (University of Cincinnati) DTSTART:20260505T010000Z DTEND:20260505T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/86 DESCRIPTION:by Josh Kline (University of Cincinnati) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Camp us Mathematics Building.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Albert Wood (Chinese University Hong Kong) DTSTART:20260505T023000Z DTEND:20260505T033000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/87 DESCRIPTION:by Albert Wood (Chinese University Hong Kong) as part of Nonli near Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathematics Building.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Oscar Dominguez (CUNEF Universidad) DTSTART:20260519T010000Z DTEND:20260519T020000Z DTSTAMP:20260422T225656Z UID:Nonlinear_Analysis_Seminar/88 DESCRIPTION:by Oscar Dominguez (CUNEF Universidad) as part of Nonlinear An alysis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Mathematics Building.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/88/ END:VEVENT END:VCALENDAR