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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: Joey 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 Schr√∂dinger Operators in Generalized  Distributional Quantum Theory

Abstract: FAMP abstract for 10-15-2021


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 lp (1 \le p < \infty) of p-summable sequence and c0 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 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: FAMPDS abstract for December 10, 2021 talk


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 C0-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 C0-semigroups of normal operators on complex Hilbert spaces, to the more general case    of C0-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 C0-semigroups on complex Hilbert spaces, thereby acquiring a characterization of uniform exponential stability for scalar type spectral and eventually norm-continuous C0-semigroups.


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