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Norms on self-adjoint symmetric tensor power of linear operators on Hilbert spaces (Yunied Puig de Dios, CMC)

Roberts North 105, CMC 320 E. 9th St., Claremont, CA, United States

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 […]

On discrete subgroups of Euclidean spaces (Lenny Fukshansky, CMC)

Roberts North 105, CMC 320 E. 9th St., Claremont, CA, United States

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 […]

Linear Multifractional Stable Sheets in the Broad Sense: Existence and Joint Continuity of Local Times (Qidi Peng, Institute of Mathematical Sciences, CGU)

Roberts North 105, CMC 320 E. 9th St., Claremont, CA, United States

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 […]

structural aspects of von Neumann algebras arising as graph products (Rolando de Santiago, Purdue University)

Roberts North 105, CMC 320 E. 9th St., Claremont, CA, United States

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 […]

The Fell topology and the modular Gromov-Hausdorff propinquity (Jiahui Yu, Pomona College)

Roberts North 105, CMC 320 E. 9th St., Claremont, CA, United States

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 […]

Existence and uniqueness of minimizers in variational problems (Wilfrid Gangbo, UCLA)

Roberts North 105, CMC 320 E. 9th St., Claremont, CA, United States

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 […]

The Hilbert space approach in the theory of differential equations (Adolfo Rumbos, Pomona College)

Roberts North 105, CMC 320 E. 9th St., Claremont, CA, United States

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 […]

Continued fractions, directed graphs, and defining spectral triples on Effros-Shen AF algebras (Samantha Brooker, Arizona State University)

Estella 2141 610 N College Ave, Claremont, United States

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, […]

Analysis seminar: Therese Basa Landry (UCSB)

Estella 2131 610 N College Ave, Claremont, United States

Title: Developments in Noncommutative Fractal Geometry Abstract:  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 […]

Analysis seminar: Shanna Dobson (UCR)

Estella 2131 610 N College Ave, Claremont, United States

Title: The Chronicles of Fractal Geometry: Fractal Strings, and Functorial Harps Abstract: In this talk, we explore the colorful analytical world of fractal geometry. We introduce fractal strings in the sense of Lapidus, both intuitively and by way of rigorous constructions. We examine rich illustrations of higher dimensional fractals and p-adic fractal strings. Then, we […]

Analysis seminar: Reginald Anderson (CMC)

Estella 2131 610 N College Ave, Claremont, United States

Title: Review of differential geometry Abstract: 1. Given the embedding of a sphere of radius rho centered at the origin of \R^3 from spherical coordinates, what is the pullback of the flat metric in \R^3? i.e., what is the "round metric" on the 2-sphere of radius rho? 2. If we impose a complex structure on S^2 via […]