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## September 2022

### Factorization theorems of Backward Shifts and Nuclear Maps (Asuman Aksoy, CMC)

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

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 $c_0$ . This factorization theorem has a number of important connections and consequences analogous to how the ideals of continuous linear operators factoring […]

### Frobenius-Rieffel norms on matrix algebras (Konrad Aguilar, Pomona)

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

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 […]

## October 2022

### On Schauder’s Theorem and $s$-numbers (Daniel Akech Thiong, CGU)

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

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 […]

### Quantum metrics on the natural numbers (Katrine von Bornemann Hjelmborg, University of Southern Denmark)

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

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 […]

## November 2022

### 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

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 […]

## December 2022

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

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

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 […]

## February 2023

### 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

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

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 […]

## March 2023

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

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

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

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

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 […]