BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:William Riley Casper (CSUF) DTSTART:20210219T230000Z DTEND:20210220T000000Z DTSTAMP:20260404T111104Z UID:ags/1 DESCRIPTION:Title: Commuting differential and integral operators and the adelic Grassmanni an\nby William Riley Casper (CSUF) as part of Analysis and Geometry Se minar\n\n\nAbstract\nBeginning with the work of Landau\, Pollak and Slepia n in the 1960s on time-band limiting\, commuting pairs of integral and dif ferential operators have played a key role in signal processing\, random m atrix theory and integrable systems. In this talk\, we will describe a cl ose connection between commuting integral and differential operators and p oints in the adelic Grassmannian\, which provides a commuting pair for eac h self-adjoint point in the Grassmannian. Central to this relationship is the Fourier algebra\, a certain algebra of differential operators isomorp hic to the algebra of differential operators on a line bundle over a ratio nal curve.\n LOCATION:https://stable.researchseminars.org/talk/ags/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Volok (Kansas State University) DTSTART:20210305T230000Z DTEND:20210306T000000Z DTSTAMP:20260404T111104Z UID:ags/2 DESCRIPTION:Title: Zeros of discrete analytic polynomials\nby Dan Volok (Kansas State University) as part of Analysis and Geometry Seminar\n\n\nAbstract\nWe sha ll discuss some basic interpolation results for discrete analytic (in the sense of J. Ferrand and R.J. Duffin) functions on the integer lattice in t he complex plane.\n LOCATION:https://stable.researchseminars.org/talk/ags/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Mario Stipčić (University of Zagreb) DTSTART:20210312T230000Z DTEND:20210313T000000Z DTSTAMP:20260404T111104Z UID:ags/3 DESCRIPTION:Title: L^p estimates for dyadic singular integral forms associated with hyperg raphs and for ergodic-martingale paraproducts\nby Mario Stipčić (Uni versity of Zagreb) as part of Analysis and Geometry Seminar\n\n\nAbstract\ nWe will identify T(1)-type conditions and other characterizations of L^p boundedness of entangled multilinear singular integrals associated with hy pergraphs. After that\, we will examine the convergence of ergodic-marting ale paraproducts in the Lebesgue spaces with respect to the range of expon ents.\n LOCATION:https://stable.researchseminars.org/talk/ags/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Annina Iseli (UCLA) DTSTART:20210416T220000Z DTEND:20210416T230000Z DTSTAMP:20260404T111104Z UID:ags/5 DESCRIPTION:Title: Thurston maps with four postcritical points\nby Annina Iseli (UCLA) as part of Analysis and Geometry Seminar\n\n\nAbstract\nA Thurston map is a branched covering map of the 2-sphere which is not a homeomorphism and for which every critical point has a finite orbit under iteration of the m ap. Frequently\, a Thurston map admits a description in purely combinatori al-topological terms. In this context it is an interesting question whethe r a given map can (in a suitable sense) be realized by a rational map with the same combinatorics. This question was answered by Thurston in the 198 0's in his celebrated characterization of rational maps. Thurston's Theore m roughly says that a Thurston map is realized if and only if it does not admit a Thurston obstruction\, which is an invariant multicurve that satis fies a certain growth condition. However\, in practice it can be very hard to verify whether a given map has no Thurston obstruction\, because\, in principle\, one would need to check the growth condition for infinitely ma ny curves. \n \nIn this talk\, we will consider a specific family of Thurs ton maps with four postcritical points that arises from Schwarz reflection s on flapped pillows (a simple surgery of a polygonal sphere). Using a cou nting argument\, we establish a necessary and sufficient condition for a m ap in this family to be realized by a rational map. In the last part of th e talk\, we will discuss a generalization of this result which states that \, given an obstructed Thurston map with four postcritical points\, one ca n eliminate obstructions by applying a so-called blowing up operation. The se results are joint with M. Bonk and M. Hlushchanka.\n LOCATION:https://stable.researchseminars.org/talk/ags/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Trang Thi Thien Nguyen (University of South Australia) DTSTART:20210514T220000Z DTEND:20210514T230000Z DTSTAMP:20260404T111104Z UID:ags/6 DESCRIPTION:Title: Non-homogeneous T(1) theorem for singular integrals on product quasimet ric spaces\nby Trang Thi Thien Nguyen (University of South Australia) as part of Analysis and Geometry Seminar\n\n\nAbstract\nIn the Calderón-Z ygmund Theory of singular integrals\, the T(1) theorem of David and Journ é is one of the most celebrated theorems. It gives easily-checked criteri a for a singular integral operator T to be bounded from L^2(R^n) to L^2(R^ n). Since then\, this classical result has been generalized to various set tings\, including replacing the underlying space R^n on which the operator s act. \nIn this talk\, I will present our work on generalizing the T(1) t heorem\, that brings together three attributes: 'product space'\, 'quasime tric' and 'non-doubling measure'. Specifically\, we prove a T(1) theorem t hat can be applied to operators acting on product spaces equipped with a q uasimetric and an upper doubling measure\, which only satisfies an upper c ontrol on the size of balls.\n LOCATION:https://stable.researchseminars.org/talk/ags/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Oumar Wone (U. of Dakar\, Senegal) DTSTART:20210507T220000Z DTEND:20210507T230000Z DTSTAMP:20260404T111104Z UID:ags/7 DESCRIPTION:Title: Frobenius determinants and Toric varieties\nby Oumar Wone (U. of Da kar\, Senegal) as part of Analysis and Geometry Seminar\n\n\nAbstract\nGiv en a finite group $G$ of order $n>1$ and variables $(X_g)_{g\\in G}$ the F robenius or group-determinant is by definition $\\Theta(G)((X_g)_{g\\in G} ):=\\det((X_{gh^{-1}})_{(g\,h)\\in G\\times G})$. We associate to every Fr obenius determinant of a finite abelian group of order $n\\geqslant3$ a to ric variety. We also study along the way its singular points and determine the number of its hyper-surfaces.\n LOCATION:https://stable.researchseminars.org/talk/ags/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kamal Diki (Chapman University) DTSTART:20210917T220000Z DTEND:20210917T230000Z DTSTAMP:20260404T111104Z UID:ags/8 DESCRIPTION:Title: An approach to the Gaussian RBF kernels via Fock spaces\nby Kamal D iki (Chapman University) as part of Analysis and Geometry Seminar\n\n\nAbs tract\nIn this talk we use methods from the Fock spaces theory in order to prove several results on the Gaussian RBF kernels in the complex case. Th e latter is one of the most used kernels in modern machine learning kernel methods\, and support vector machines (SVMs) classification algorithms. I t turns out that complex analysis techniques allow us to consider several notions linked to the RBF kernels like the feature space and the feature m ap\, using the so-called Segal-Bargmann transform. We show also that the R BF kernels can be related to some important operators in quantum mechanics and time frequency analysis\, specifically\, we prove different connectio ns of such kernels with creation\, annihilation\, Fourier\, translation\, modulation and Weyl operators. A semi-group property will be proved in the case of Weyl operators. This is a joint work with Daniel Alpay\, Fabrizio Colombo and Irene Sabadini.\n LOCATION:https://stable.researchseminars.org/talk/ags/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Paata Ivanisvili (UC Irvine) DTSTART:20211112T230000Z DTEND:20211113T000000Z DTSTAMP:20260404T111104Z UID:ags/9 DESCRIPTION:Title: Learning low degree functions in logarithmic number of random queries.< /a>\nby Paata Ivanisvili (UC Irvine) as part of Analysis and Geometry Semi nar\n\n\nAbstract\nPerhaps a very basic question one asks in learning theo ry is as follows: we have an unknown function $f$ on the hypercube $\\{-1\ ,1\\}^n$\, and we are allowed to query samples $(X\, f(X))$ where $X$ is u niformly distributed on $\\{-1\,1\\}^n$. After getting these samples $(X_1 \, f(X_1))\, ...\, (X_N\, f(X_N))$ we would like to construct a function $ h$ which approximates f up to an error epsilon (say in $L^2$). Of course $ h$ is a random function as it involves i.i.d. random variables $X_1\, ... \, X_N$ in its construction. Therefore\, we want to construct such $h$ whi ch approximates $f$ with probability at least ($1-\\delta$). So given para meters epsilon\, $\\delta$ in $(0\,1)$ the goal is to minimize the number of random queries $N$. I will show that around $\\log(n)$ random queries are sufficient to learn bounded "low-complexity" functions. Based on joint work with Alexandros Eskenazis.\n LOCATION:https://stable.researchseminars.org/talk/ags/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Izchak Lewkowicz (Ben-Gurion University of the Negev\, Israel) DTSTART:20211008T220000Z DTEND:20211008T230000Z DTSTAMP:20260404T111104Z UID:ags/10 DESCRIPTION:Title: Passive Linear Time-invariant Systems - Characterization through Struc ture\nby Izchak Lewkowicz (Ben-Gurion University of the Negev\, Israel ) as part of Analysis and Geometry Seminar\n\n\nAbstract\nPassivity is a b asic physical property. We here show that the family linear time-invariant passive systems may be characterized by the structure of the whole set. A refined description of strict dissipativity will be presented as well.\n LOCATION:https://stable.researchseminars.org/talk/ags/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Alain Yger (Université Bordeaux) DTSTART:20211117T200000Z DTEND:20211117T210000Z DTSTAMP:20260404T111104Z UID:ags/12 DESCRIPTION:Title: Revisiting syzygies\, hence division or interpolation problems\, in te rms of residue and principal value currents\nby Alain Yger (Universit é Bordeaux) as part of Analysis and Geometry Seminar\n\n\nAbstract\nA joi nt paper I wrote together with M. Passare and August Tsikh in 2000 (ideas there coming from my unfortunately last joint paper with Carlos Berenste in in 1998) inspired since then the construction of what reveals to be a v ery powerful method to attack interpolation or division problems in Cn or Pn(C) (also on Stein manifolds) by solving them through explicit closed fo rmulae. The beautiful idea which was introduced by Mats Andersson since 20 04 consists in the following: attach to any generically exact complex of h ermitian bundles over a complex analytic space both a Principal Value curr ent and a residue current\, the last one precisely encoding the lack of ex actness of the complex of holomorphic bundles one started with. Time has n ow come\, despite the technicity inherent to such construction\, to popula rize such tool facing general questions such as Hilbert’s nullstellensat z\, the surprising (and curiously not so-well known) Brian ̧con-Skoda the orem (even in the polynomial setting)\, Euler-Ehrenpreis- Palamodov Fundam ental Principle\, or spectral synthesis problem in (ad hoc) weighted algeb ras of entire functions. I will try to explain this in general terms\, avo iding as far as I can technicity by cheating a little\, and will illustrat e with few concrete examples the novelty and efficiency of such approach.\ n LOCATION:https://stable.researchseminars.org/talk/ags/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Ahmed Sebbar (Chapman University) DTSTART:20220218T223000Z DTEND:20220218T233000Z DTSTAMP:20260404T111104Z UID:ags/13 DESCRIPTION:Title: On a question of J. P. Serre\nby Ahmed Sebbar (Chapman University) as part of Analysis and Geometry Seminar\n\n\nAbstract\nIn his Bourbaki t alk "{\\em Distribution asymptotique des valeurs propres des endomorphisme s de Frobenius (d'après Abel\, Chebyshev\, Robinson\,$\\cdots)$}" of 03/3 1/2018\, J.P. Serre raised the following question: \n\nLet $K\\subset \\BC $ be a compact (infinite) set\, stable under complex conjugation and havi ng a capacity greater than one. Let $U$ be an open set containing $K$. The n there exists a sequence of monic polynomials $P_n(X)\\in \\BZ[X]$\, ${\\ rm deg} P_n= n\,\\\; P_n^{-1}(0)\\subset U$ and \n\n\\[\\displaystyle \\li m_{n\\to \\infty} \\frac{1}{n} \\sum_{P_n(z)=0} \\delta_z= \\mu\n\\]\n whe re $\\mu$ is the equilibrium measure of $K$ and $\\delta_z$ is the Dirac m easure at $z$. \\\\ I will present some results on this question\, obtain ed with Th\\'er\\`ese Falliero(University of Avignon).\n LOCATION:https://stable.researchseminars.org/talk/ags/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Michel Balazard (Institut de Mathématiques de Marseille) DTSTART:20220225T223000Z DTEND:20220225T233000Z DTSTAMP:20260404T111104Z UID:ags/14 DESCRIPTION:Title: The criteria of Nyman and Baez-Duarte for the Riemann hypothesis\n by Michel Balazard (Institut de Mathématiques de Marseille) as part of An alysis and Geometry Seminar\n\n\nAbstract\nIn his doctoral dissertation\, Nyman gave in 1950 a necessary and sufficient criterion for the validity o f the Riemann hypothesis\, in terms of the density of some subspace in L^2 (0\,1). In 2003\, Baez-Duarte gave a modified form of this criterion. The talk will present these two criteria\, as well as related results and ques tions.\n LOCATION:https://stable.researchseminars.org/talk/ags/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Alpay (Chapman University) DTSTART:20220311T223000Z DTEND:20220311T233000Z DTSTAMP:20260404T111104Z UID:ags/15 DESCRIPTION:Title: Discrete analytic functions and Schur analysis\nby Daniel Alpay (C hapman University) as part of Analysis and Geometry Seminar\n\n\nAbstract\ nWe introduce the Schur class of functions\, discrete analytic on the inte ger lattice in the complex plane. As a special case\, we derive the explic it form of discrete analytic Blaschke factors and solve the related basic interpolation problem. We define and study rational discrete analytic func tions and prove the existence of a coisometric realization for discrete an alytic Schur multipliers. The talk is based on collaborations with F. Colo mbo\, K. Diki\, I. Sabadini and D. Volok.\n LOCATION:https://stable.researchseminars.org/talk/ags/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Brett Wick (Washington University in St. Louis) DTSTART:20220318T213000Z DTEND:20220318T223000Z DTSTAMP:20260404T111104Z UID:ags/16 DESCRIPTION:Title: Commutators of Calder\\'on-Zygmund Operators and Bounded Mean Oscillat ion (or Factorization and Hardy Spaces)\nby Brett Wick (Washington Uni versity in St. Louis) as part of Analysis and Geometry Seminar\n\n\nAbstra ct\nCalder\\'on-Zygmund operators play an important role in partial differ ential equations and complex analysis. Some problems in analysis benefit from an understanding of the commutation between certain operators or the factorization of functions from natural function spaces. These topics all interact when studying the commutators of Calder\\'on-Zygmund operators a nd multiplication operators. In this talk\, we will discuss some recent r esults about commutators of certain Calderon-Zygmund operators and BMO spa ces and how these generate bounded operators on Lebesgue spaces. Motivati ons and connections to operator theory and partial differential equations will be provided. Versions of these results on the Heisenberg group\, pse udoconvex domains with $C^2$ boundary\, and other examples will be explain ed to show how the general theory carries over to many other settings. Th is talk is based on joint collaborative work.\n LOCATION:https://stable.researchseminars.org/talk/ags/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Ahmed Sebbar (Chapman University) DTSTART:20220304T223000Z DTEND:20220304T233000Z DTSTAMP:20260404T111104Z UID:ags/17 DESCRIPTION:Title: On a question of J. P. Serre II\nby Ahmed Sebbar (Chapman Universi ty) as part of Analysis and Geometry Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/ags/17/ END:VEVENT BEGIN:VEVENT SUMMARY:José Ramón Madrid Padilla (UCLA) DTSTART:20220429T210000Z DTEND:20220429T220000Z DTSTAMP:20260404T111104Z UID:ags/18 DESCRIPTION:Title: On classical inequalities for autocorrelations and autoconvolutions\nby José Ramón Madrid Padilla (UCLA) as part of Analysis and Geometry Seminar\n\n\nAbstract\nWe will discuss some convolution inequalities on th e real line\, the study of these problems is motivated by a classical prob lem in additive combinatorics about estimating the size of Sidon sets. We will also discuss many related open problems. This talk will be accessible for a broad audience.\n LOCATION:https://stable.researchseminars.org/talk/ags/18/ END:VEVENT END:VCALENDAR