Department of Mathematics

# Functional Analysis and Mathematical Physics Interdepartmental Research Group (FAMP)

## Upcoming Colloquia

TBA

### Recent Colloquia

**Date and Time: **Friday, November 12, 2021, at 10:00 AM

**Location:** Via Zoom on the FAMP Zoom link

**Speaker: J**oey Contreras (Research Advisors: Drs. Douglas Singleton and Michael Bishop, Departments
of Physics and Mathematics, California State University, Fresno)

**Title: ***Modified Commutators vs. Modified Operators in a Quantum Gravity Minimal Length Scale*

**Abstract: **Generic theories of quantum gravity often postulate that at some high energy/momentum
scale there will be a fixed, minimal length. Such a minimal length can be phenomenologically
investigated by modifying the standard Heisenberg Uncertainty relationship. This is
often done by modifying the position-momentum commutator, which in turn means modifying
the position and momentum operators. However, modifications which change the uncertainty
relationships lead to conflicts with observational data (e.g., gamma ray bursts).
These observations seem to imply that there is no minimal length scale. Meanwhile,
modifying the operators, such that the standard uncertainty relation retains the same
form, leads to no such conflict with observational data. We show that it is this modification
of the position and momentum operators that is the key determining factor in the existence
(or not) of a minimal length scale.

**Date and Time: **Friday, October 29, 2021, at 10:00 AM

**Location**: Via Zoom on the FAMP Zoom link

**Speaker:** Douglas Singleton, Ph.D. (California State University, Fresno)

**Title:** *What is Spin?*

**Abstract: **All electrons have the following properties: charge, mass and spin. Spin is an intrinsic
angular momentum but in almost all standard quantum mechanics texts the student is
warned that spin cannot be described as the rotating of anything; that spin is purely
a quantum property of the electron that cannot be thought of in terms of any classical
rotation. In this talk, we follow the arguments of an American Journal of Physics
article to show that this point of view is just wrong. We also discuss some other
interesting and unusual properties of the electron that arise due to its

spin.

**Date and Time:** Friday, October 15, 2021, at 11:00 AM

**Location:** Via Zoom on the FAMP Zoom link

**Speaker:** Michael Maroun , Ph.D. Development (Global Vice President of Research and TeXDyn
Industries Corporate Laboratories Austin, TX)

**Title:** *Singular Perturbations of Schrödinger Operators in Generalized Distributional Quantum
Theory*

**Abstract: **

**Date and Time:** Friday, October 8, 2021, at 11:00 AM

**Location: **Via Zoom on the FAMP Zoom link

**Speaker:** Olivia Soghomonian, Student

**Title: ***On a Characterization of Convergence in Banach Spaces with a Schauder Basis *

**Abstract: **We extend the well-known characterizations of convergence in the spaces *l _{p} *(1 \le

*p*< \infty) of

*p*-summable sequence and

*c*of vanishing sequences to a general characterization of convergence in a Banach space with a Schauder basis and obtain as instant corollaries characterizations of convergence in an infinite-dimensional separable Hilbert space and the space of

_{0}*c*convergent sequences.

## The Functional Analysis, Mathematical Physics, and Dynamical Systems (FAMPDS) Joint American-Ukrainian Virtual Colloquium Series

### Upcoming Colloquia

**Date and Time: **Friday, December 10, 2021, at 10 AM

**Location:** Zoom on the FAMP Zoom link

**Speaker: **Igor V. Nikolaev (St. John's University, New York City)

**Title: ***Langlands Reciprocity for C*-Algebras*

**Abstract:**

### Recent Colloquia

**Date and Time: **Friday, November 5, 2021, at 10 AM

**Location:** Zoom on the FAMP Zoom link

**Speaker:** Marat V. Markin (California State University, Fresno)

**Title:** *On Spectral Inclusion and Mapping Theorems and Asymptotics for C _{0}-Semigroups*

**Abstract:** We establish *spectral inclusion* and *mapping theorems* for scalar type spectral operators, generalizing their counterparts for normal operators.
Thereby, we extend a precise weak spectral mapping theorem along with the *spectral bound equal growth bound condition and a generalized Lyapunov stability theorem*, known to hold for *C _{0}*-semigroups of normal operators on complex Hilbert spaces, to the more general case
of

*C*-semigroups of scalar type spectral operators on complex Banach spaces. The finer spectrum structure is given itemized consideration. We also obtain exponential estimates with the best stability constants for such semigroups and extend to a Banach space setting a celebrated characterization of uniform exponential stability for

_{0}*C*-semigroups on complex Hilbert spaces, thereby acquiring a characterization of uniform exponential stability for scalar type spectral and eventually norm-continuous

_{0}*C*-semigroups.

_{0}**Date and Time:** Friday, October 22, 2021, at 10 AM

**Location:** Zoom on the FAMP Zoom link

**Speaker: ** Yuri Latushkin (University of Missouri)

**Title:** *Asymptotic Perturbation Theory for Extensions of Symmetric Operators*

**Abstract: **In this talk (joint work with Selim Sukhtaiev (Auburn University)), we discuss asymptotic
perturbation theory for varying self-adjoint extensions of symmetric operators. Employing
symplectic formulation of self-adjointness we obtain a new version of Krein formula
for resolvent difference, which facilitates asymptotic analysis of resolvent operators
via first order expansion for the family of Lagrangian planes associated with perturbed
operators. Specifically, we derive a Riccati-type differential equation and the first
order asymptotic expansion for resolvents of self-adjoint extensions determined by
smooth one-parameter families of Lagrangian planes. This asymptotic perturbation theory
yields a symplectic version of the abstract Kato selection theorem and Hadamard-Rellich-type
variational formula for slopes of multiple eigenvalue curves bifurcating from an eigenvalue
of the unperturbed operator. The latter, in turn, gives a general infinitesimal version
of the celebrated formula equating the spectral flow of a path of self-adjoint extensions
and the Maslov index of the corresponding path of Lagrangian planes. Applications
are given to quantum graphs, periodic Kronig-Penney model, elliptic second order partial
differential operators with Robin boundary conditions, and physically relevant heat
equations with thermal conductivity.

**If you need a disability-related accommodation or wheelchair access information, please
contact the mathematics department at 559.278.2992 or e-mail mathsa@csufresno.edu. Requests should be made at least one week in advance of the event.**

## Archived Colloquia