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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240328T163000
DTEND;TZID=America/Los_Angeles:20240328T173000
DTSTAMP:20260410T121417
CREATED:20240324T163045Z
LAST-MODIFIED:20240324T163045Z
UID:3413-1711643400-1711647000@colleges.claremont.edu
SUMMARY:Analysis seminar: Therese Basa Landry (UCSB)
DESCRIPTION:Title: Developments in Noncommutative Fractal Geometry\n\nAbstract:  As a noncommutative fractal geometer\, I look for new expressions of the geometry of a fractal through the lens of noncommutative geometry.  At the quantum scale\, the wave function of a particle\, but not its path in space\, can be studied.  Riemannian methods often rely on smooth paths to encode the geometry of a space.  Noncommutative geometry generalizes analysis on manifolds by replacing this requirement with operator algebraic data.  These same “point-free” techniques can also be used to study the geometry of classically pathological spaces like fractals.  The 2016 Nobel Prize in Physics was awarded for work on Hofstadter’s butterfly\, which is a fractal that describes for theoretical condensed matter physicists the allowed energy levels for electrons confined to a crystalline atomic lattice as a function of the magnetic field applied to the system.  By expanding the formalism of fractal geometry to include the mathematical language of quantum theory\, developments in noncommutative fractal geometry can give both mathematicians and physicists the tools to gain insights about quantum behaviors in solids and any new materials made possible by these phenomena.  Other directions in noncommutative fractal geometry will also be discussed.
URL:https://colleges.claremont.edu/ccms/event/analysis-seminar-therese-basa-landry-ucsb/
LOCATION:Estella 2131\, Pomona College\, 610 N College Ave\, Claremont\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231116T163000
DTEND;TZID=America/Los_Angeles:20231116T173000
DTSTAMP:20260410T121417
CREATED:20231113T045911Z
LAST-MODIFIED:20231113T045911Z
UID:3319-1700152200-1700155800@colleges.claremont.edu
SUMMARY:Continued fractions\, directed graphs\, and defining spectral triples on Effros-Shen AF algebras (Samantha Brooker\, Arizona State University)
DESCRIPTION:The Effros-Shen algebra corresponding to an irrational number $\theta$ can be described by an inductive sequence of direct sums of matrix algebras\, where the continued fraction expansion of $\theta$ encodes the dimensions of the summands\, and how the matrix algebras at the nth level fit into the summands at the (n+1)th level. In recent work\, Mitscher and Spielberg present an Effros-Shen algebra as the C*-algebra of a category of paths – a generalization of a directed graph – determined by the continued fraction expansion of \theta. With this approach\, the algebra is realized as the inductive limit of a sequence of infinite-dimensional\, rather than finite-dimensional\, subalgebras. Drawing on a construction by Christensen and Ivan\, we use this inductive limit structure to define a spectral triple\, trading the advantages of working with finite-dimensional approximants for the techniques provided by the category of paths\, pursuant to studying the algebras as quantum compact metric spaces. I will discuss categories of paths and their precursors\, graph C*-algebras\, the example of Mitscher and Spielberg\, and a bit about the spectral triple construction. This is joint work with Konrad Aguilar and Jack Spielberg.
URL:https://colleges.claremont.edu/ccms/event/continued-fractions-directed-graphs-and-defining-spectral-triples-on-effros-shen-af-algebras-samantha-brooker-arizona-state-university/
LOCATION:Estella 2141\, 610 N College Ave\, Claremont\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230406T163000
DTEND;TZID=America/Los_Angeles:20230406T173000
DTSTAMP:20260410T121417
CREATED:20230406T184956Z
LAST-MODIFIED:20230406T185011Z
UID:3120-1680798600-1680802200@colleges.claremont.edu
SUMMARY:Radial solutions to semilinear elliptic partial differential equations (Professor Alfonso Castro\, HMC)
DESCRIPTION:Using elementary methods from differential equations and analysis we will consider the existence and multiplicity of solutions to semilinear partial differential equations with boundary conditions.
URL:https://colleges.claremont.edu/ccms/event/radial-solutions-to-semilinear-elliptic-partial-differential-equationsprofessor-alfonso-castro-hmc/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230323T163000
DTEND;TZID=America/Los_Angeles:20230323T173000
DTSTAMP:20260410T121417
CREATED:20230323T212318Z
LAST-MODIFIED:20230323T212318Z
UID:3108-1679589000-1679592600@colleges.claremont.edu
SUMMARY:The Hilbert space approach in the theory of differential equations (Adolfo Rumbos\, Pomona College)
DESCRIPTION:In this talk we discuss the Hilbert space approach\, or the variational approach\, in the study of questions of existence and multiplicity for some two-point boundary-value problems for nonlinear\, second order\, ordinary differential equations (ODEs).  We illustrate the use of the Hilbert space approach in obtaining some old existence results for periodic solutions of a semilinear ODE\, and some recent multiplicity results for a related problem. The talk is based on joint work with Noah Benjamin (Pomona College ’23) and Leandro Recôva (Cal Poly Pomona).
URL:https://colleges.claremont.edu/ccms/event/the-hilbert-space-approach-in-the-theory-of-differential-equations-adolfo-rumbos-pomona-college/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230309T163000
DTEND;TZID=America/Los_Angeles:20230309T173000
DTSTAMP:20260410T121417
CREATED:20230306T061639Z
LAST-MODIFIED:20230306T061639Z
UID:3094-1678379400-1678383000@colleges.claremont.edu
SUMMARY:Existence and uniqueness of minimizers in variational problems (Wilfrid Gangbo\, UCLA)
DESCRIPTION:We comment on the main steps to take when studying some variational problems. This includes optimization problems arising in geometry\, machine learning\, non linear elasticity\, fluid mechanics\, etc… For the sake of illustration\, in this talk\, we keep our focus on a minimization problem obtained after a time-discretization of the incompressible Navier-Stokes equations. Elementary geometric intuitions are used to uniquely characterize equilibria which are minimizers.
URL:https://colleges.claremont.edu/ccms/event/existence-and-uniqueness-of-minimizers-in-variational-problems-wilfrid-gangbo-ucla/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230302T163000
DTEND;TZID=America/Los_Angeles:20230302T173000
DTSTAMP:20260410T121417
CREATED:20230302T165631Z
LAST-MODIFIED:20230302T165631Z
UID:3090-1677774600-1677778200@colleges.claremont.edu
SUMMARY:The Fell topology and the modular Gromov-Hausdorff propinquity (Jiahui Yu\, Pomona College)
DESCRIPTION:Given a unital AF (approximately finite-dimensional) algebra A equipped with a faithful tracial state\, we equip each (norm-closed two-sided) ideal of A with a metrized quantum vector bundle structure\, when canonically viewed as a module over A\, in the sense of Latrémolière using previous work of Aguilar and Latrémolière. Moreover\, we show that convergence of ideals in the Fell topology implies convergence of the associated metrized quantum vector bundles in the modular Gromov-Hausdorff propinquity of Latrémolière. In a similar vein but requiring a different approach\, given a compact metric space (X\,d)\, we equip each ideal of C(X) with a metrized quantum vector bundle structure\, and show that convergence in the Fell topology implies convergence in the modular Gromov-Hausdorff propinquity. (This is joint work with Konrad Aguilar).
URL:https://colleges.claremont.edu/ccms/event/the-fell-topology-and-the-modular-gromov-hausdorff-propinquity-jiahui-yu-pomona-college/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230216T163000
DTEND;TZID=America/Los_Angeles:20230216T173000
DTSTAMP:20260410T121417
CREATED:20230208T194019Z
LAST-MODIFIED:20230208T194019Z
UID:3074-1676565000-1676568600@colleges.claremont.edu
SUMMARY:structural aspects of von Neumann algebras arising as graph products (Rolando de Santiago\, Purdue University)
DESCRIPTION:Graph products of groups were introduced in E. Green’s thesis in the 90’s as generalizations of Right-Angled Artin Groups. These have become objects of intense study due to their key roles in topology and group theory.  Recently\, Caspers and Fima introduced graph products of von Neumann algebras. Since their inception\, several structural aspects such as absence of Cartan subalgebras\, and classification of tensor products have been established for graph products arising from groups.  Here we describe new progress in this direction\, emphasizing characterization of diffuseness\, factoriality\, and if time\, strong 1-boundedness for graph products of a large class of von Neumann algebras. \nThis is joint work with Ian Charlesworth\, Srivatsav Kunnawalkam-Ellayavali\,  Ben Hayes\, David Jekel\, and Brent Nelson.
URL:https://colleges.claremont.edu/ccms/event/structural-aspects-of-von-neumann-algebras-arising-as-graph-products-rolando-de-santiago-purdue-university/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230209T163000
DTEND;TZID=America/Los_Angeles:20230209T173000
DTSTAMP:20260410T121417
CREATED:20230208T193627Z
LAST-MODIFIED:20230213T200028Z
UID:3073-1675960200-1675963800@colleges.claremont.edu
SUMMARY:Linear Multifractional Stable Sheets in the Broad Sense: Existence and Joint Continuity of Local Times (Qidi Peng\, Institute of Mathematical Sciences\, CGU)
DESCRIPTION:We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) to include both linear multifractional Brownian sheets and linear multifractional stable sheets. The purpose of the framework is to study the existence and joint continuity of the local times of LMSS\, and also the local Holder condition of the local times in the set variable. As the main results\, (1) we provide a sufficient and necessary condition for the existence of local times of LMSS; (2) we show a sufficient condition for the joint continuity of local times; and (3) we prove a sharp local Holder condition for the local times in the set variable. All these theorems improve significantly the existing results for the local times of multifractional Brownian sheets and linear multifractional stable sheets in the literature.
URL:https://colleges.claremont.edu/ccms/event/linear-multifractional-stable-sheets-in-the-broad-sense-existence-and-joint-continuity-of-local-times-qidi-peng-institute-of-mathematical-sciences-cgu/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221201T160000
DTEND;TZID=America/Los_Angeles:20221201T170000
DTSTAMP:20260410T121417
CREATED:20221128T163157Z
LAST-MODIFIED:20221128T163157Z
UID:3003-1669910400-1669914000@colleges.claremont.edu
SUMMARY:On discrete subgroups of Euclidean spaces (Lenny Fukshansky\, CMC)
DESCRIPTION:Let x_1\,…\,x_n be an overdetermined spanning set for the Euclidean space R^k\, where n > k. Let L be the integer span of these vectors. Then L is an additive subgroup of R^n. When is it discrete in R^n? Naturally\, this depends on the choice of the spanning set\, but in which way? We will review some classical results leading up to this question and then will discuss some more recent developments.
URL:https://colleges.claremont.edu/ccms/event/on-discrete-subgroups-of-euclidean-spaces-lenny-fukshansky-cmc/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221110T160000
DTEND;TZID=America/Los_Angeles:20221110T170000
DTSTAMP:20260410T121417
CREATED:20221110T225833Z
LAST-MODIFIED:20221110T230507Z
UID:2991-1668096000-1668099600@colleges.claremont.edu
SUMMARY:Norms on self-adjoint symmetric tensor power of linear operators on Hilbert spaces (Yunied Puig de Dios\, CMC)
DESCRIPTION:We introduce a family of norms on the space of self-adjoint trace class symmetric tensor power of linear operators acting on an infinite-dimensional Hilbert space. Our technique is to extend to infinite dimension an original and nice idea of a very recent result by K. Aguilar\,  Á. Chávez\, S. R. Garcia and J. Volčič\, in which the authors introduce a family of norms on the space of n x n  complex matrices induced by complete homogeneous symmetric polynomials. This is a work in progress paper\, so it goes without saying that it will be very much appreciated any comment or/and suggestion coming from the audience. This is joint work with K. Aguilar\, Á. Chávez and S. R. Garcia.
URL:https://colleges.claremont.edu/ccms/event/norms-on-self-adjoint-symmetric-tensor-power-of-linear-operators-on-hilbert-spaces/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221013T160000
DTEND;TZID=America/Los_Angeles:20221013T170000
DTSTAMP:20260410T121417
CREATED:20221010T130525Z
LAST-MODIFIED:20221010T130525Z
UID:2956-1665676800-1665680400@colleges.claremont.edu
SUMMARY:Quantum metrics on the natural numbers (Katrine von Bornemann Hjelmborg\, University of Southern Denmark)
DESCRIPTION:Quantum metrics in the sense of Rieffel were introduced to prove some statements arising in the high-energy physics literature. Since then\, the area of quantum metric geometry has been used to answer questions stemming from within mathematics as well. To prove such results\, it is often the case that certain properties of a quantum metric are sufficient enough\, and explicit calculations of the quantum metric are rare. Thus\, in this talk\, we focus on certain quantum metrics introduced by Aguilar and Latrémolière on $c$\, the space of complex-valued convergent sequences (which is isomorphic to the space of complex-valued continuous functions on the Alexandroff compactification of the natural numbers)\, and calculate exactly the metrics on the natural numbers that these quantum metrics induce. Moreover\, we compare the quantum metrics of Aguilar and Latrémolière with a classical quantum metric on $c$ induced by the Lipschitz seminorm. (This is joint work with Konrad Aguilar).
URL:https://colleges.claremont.edu/ccms/event/quantum-metrics-on-the-natural-numbers-katrine-von-bornemann-hjelmborg-university-of-southern-denmark/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221006T160000
DTEND;TZID=America/Los_Angeles:20221006T170000
DTSTAMP:20260410T121417
CREATED:20221002T165522Z
LAST-MODIFIED:20230816T042942Z
UID:2946-1665072000-1665075600@colleges.claremont.edu
SUMMARY:On Schauder's Theorem and $s$-numbers (Daniel Akech Thiong\, CGU)
DESCRIPTION:Let \(\mathcal{L}(X\,Y)\) denote the normed vector space of all continuous operators from \(X\) to \(Y\)\, \(X^*\) be the dual space of \(X\)\, and \(\mathcal{K}(X\,Y)\) denote the collection of all compact operators from \(X\) to \(Y\). Denote by \(T^{*} \in \mathcal{L}(Y^{*}\, X^{*} )\) the adjoint operator of \(T\in \mathcal{L} (X\, Y)\). The well known theorem of Schauder states that \(T \in \mathcal{K}(X\,Y) \iff T^{*} \in \mathcal{K}(Y^{*}\,X^{*})\). When an operator fails to be compact\, it is sometimes useful to be able to quantify the degree to which it fails to be compact\, which has led to the introduction of certain approximation quantities\, usually called \(s\)-numbers\, and are closely related to singular values. Specifically\, the concept of \(s\)-numbers\, \(s_n(T)\)\, arises from the need to assign to every operator \(T: X \to Y\) a certain sequence of numbers \(\{s_n(T)\}\) such that \[s_1(T) \geq s_2(T) \geq \dots \geq 0\] which characterizes the degree of compactness/non-compactness of \(T\). The main examples of \(s\)-numbers include approximation numbers and Kolmogorov numbers. Motivated by Schauder’s theorem\, in this talk I will present the relationship between various \(s\)-numbers of an operator \(T\) and its adjoint \(T^*\) between Banach spaces. Joint work with Asuman G. Aksoy. \n1. A. G. Aksoy\, On a theorem of Terzioğlu\, Turk J Math\, 43\, (2019)\, 258-267.2. A. G. Aksoy and M. Nakamura\, The approximation numbers \(\gamma_n(T)\) and Q–compactness\, Math. Japon. 31 (1986)\, no. 6\, 827-840.3. K. Astala\, On measures of non-compactness and ideal variations in Banachspaces\, Ann. Acad. Sci. Fenn. Ser. AI Math. Dissertations 29\, (1980)\, 1-42.4. B. Carl and I. Stephani\, Entropy\, compactness and the approximation of oper-ators\, Cambridge University Press\, 1990.5. C. V. Hutton\, On approximation numbers and its adjoint. Math. Ann. 210(1974)\, 277-280.6. Oja\, Eve\, and Silja Veidenberg. ”Principle of local reflexivity respecting nestsof subspaces and the nest approximation properties.” Journal of FunctionalAnalysis 273.9 (2017): 2916-2938.7. A.Pietsch\, Operator ideals\, North-Holland\, Amsterdam\, 1980.
URL:https://colleges.claremont.edu/ccms/event/on-schauders-theorem-and-s-numbers-daniel-akech-thiong-cgu/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220922T160000
DTEND;TZID=America/Los_Angeles:20220922T170000
DTSTAMP:20260410T121417
CREATED:20220918T041430Z
LAST-MODIFIED:20220918T041430Z
UID:2930-1663862400-1663866000@colleges.claremont.edu
SUMMARY:Frobenius-Rieffel norms on matrix algebras (Konrad Aguilar\, Pomona)
DESCRIPTION:Noncommutative metric geometry is the study of certain noncommuative algebras in the context of metric geometry. For instance\, the Lipschitz constant (which measures the maximum slope obtained by a real-valued continuous function on a metric space (allowed to be infinite)) is a vital tool in metric geometry\, and a main feature of noncommutative metric geometry is the introduction of a noncommutative notion of the Lipschitz constant\, called an L-seminorm\, due to M.A. Rieffel. The purpose of our work is to introduce suitable L-seminorms on matrix algebras. To accomplish this\, we used norms introduced by Rieffel on certain unital C*-algebras built from conditional expectations onto unital C*-subalgebras. We begin by showing that these norms generalize the Frobenius norm on matrix algebras\, and we provide explicit formulas for certain conditional expectations onto unital C*-subalgebras of finite-dimensional C*-algebras. This allows us to compare these norms to the unique C*-norm (the operator 2-norm)\, by finding explicit equivalence constants. (This is joint work with Stephan R. Garcia and Elena Kim (’21)\, arxiv: 2112.13164).
URL:https://colleges.claremont.edu/ccms/event/frobenius-rieffel-norms-on-matrix-algebras-konrad-aguilar-pomona/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220908T160000
DTEND;TZID=America/Los_Angeles:20220908T170000
DTSTAMP:20260410T121417
CREATED:20220905T060933Z
LAST-MODIFIED:20230816T041748Z
UID:2824-1662652800-1662656400@colleges.claremont.edu
SUMMARY:Factorization theorems of Backward Shifts and Nuclear Maps (Asuman Aksoy\, CMC)
DESCRIPTION:The theory of compact linear operators between Banach spaces has a classical core and is familiar to many. Perhaps lesser known is the factorization of compact maps through a closed subspace of \(c_0\) [2]. This factorization theorem has a number of important connections and consequences analogous to how the ideals of continuous linear operators factoring compactly through \(\ell^p\)-spaces \((1\leq p < \infty)\) (see [1] and the references therein). In this talk\, even though hypercyclic operators are not compact\, we consider operator ideals generated by hypercyclic backward weighted shifts and examine their factorization properties. (Joint work with Yunied Puig)\n\n\n\nFourie\, Jan H. Injective and surjective hulls of classical \(p\)-compact operators with application to unconditionally \(p\)-compact operators. Studia Math.  240  (2018)\, no. 2\, 147–159. MR3720927\nTerzioğlu\, T. A characterization of compact linear mappings. Arch. Math. (Basel) 22 (1971)\, 76–78. MR0291865
URL:https://colleges.claremont.edu/ccms/event/factorization-theorems-of-backward-shifts-and-nuclear-maps-asuman-aksoy-cmc/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
END:VEVENT
END:VCALENDAR