Mathematician and Teacher

# DALE FRYMARK

## ABOUT ME

I'm currently a Postdoctoral Researcher at the Nuclear Physics Institute of the Czech Academy of Sciences and live in Prague. I'm a member of the Mathematical Physics group within the Department of Theoretical Physics and the Doppler Institute. Before that, I was a Postdoctoral Fellow in Analysis at Stockholm University for 2 years, working with Annemarie Luger. I received my Ph.D. in Mathematics from Baylor University in August 2018, where I was a student of Constanze Liaw. At Baylor, I was the AMS Graduate Student Chapter President, 2-time Graduate Student Association Representative for the Math department, and founding Treasurer of the AWM Baylor Chapter. I also have a B.A. in Mathematics from Washington College in Maryland, where I was on the Varsity Rowing team and in Phi Delta Theta Fraternity.

My research is primarily focused on the intersection of Perturbation Theory and the Spectral Theory of Differential Operators. More specifically, I am interested broadly in Dirac operators, reproducing kernel Hilbert spaces, Sturm-Liouville operators, orthogonal polynomials, self-adjoint extension theory, semi-bounded forms, boundary triples and Nevanlinna-Herglotz functions, to name just a few. I am always looking for new collaborators so if you are interested in similar topics or my papers, feel free to send me an email or use the contact form at the bottom of the site. The CV is correct as of November 2020.

In my free time, I'm learning Czech and trying not to forget the Swedish that I know. I also enjoy running, listening to music, reading and hiking.

## RESEARCH

Find full articles on arXiv here.

### BOUNDARY CONDITIONS ASSOCIATED WITH THE GENERAL LEFT-DEFINITE THEORY FOR DIFFERENTIAL OPERATORS

Joint work with Constanze Liaw and Matthew Fleeman. J. Approx. Theory 239 (2019), 1-28.

### SPECTRAL ANALYSIS, MODEL THEORY AND APPLICATIONS OF FINITE-RANK PERTURBATIONS

Joint work with Constanze Liaw. Invited contribution accepted to the Proceedings of IWOTA 2018, Ronald G. Douglas Memorial Edition. To appear in Operator Theory: Advances and Applications series, Birkhäuser Verlag.

### SPECTRAL ANALYSIS OF ITERATED RANK-ONE PERTURBATIONS

Joint work with Constanze Liaw. Submitted.

### PROPERTIES AND DECOMPOSITIONS OF DOMAINS FOR POWERS OF THE JACOBI DIFFERENTIAL OPERATOR

Joint work with Constanze Liaw. J. Math. Anal. Appl. 489 (2020), 124-155.

### BOUNDARY TRIPLES AND WEYL M-FUNCTIONS FOR POWERS OF THE JACOBI DIFFERENTIAL OPERATOR

J. Differential Equations 269 (2020), 7931-7974.

### SINGULAR BOUNDARY CONDITIONS OF STURM--LIOUVILLE OPERATORS VIA PERTURBATION THEORY

Joint work with Michael Bush and Constanze Liaw. Submitted.

### PERSPECTIVES ON GENERAL LEFT-DEFINITE THEORY

Joint work with Constanze Liaw. Invited contribution submitted to Baylor Analysis Fest - From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory (Lance L. Littlejohn 70th Birthday Volume). To appear in Operator Theory: Advances and Applications series, Birkhäuser Verlag.

## TEACHING

Courses and Credentials

### TEACHER OF RECORD

Taught Precalculus (x2), Business Calculus (x3), Calculus II (x2) and Calculus III at Baylor University. Responsibilities included preparing all lecture materials, syllabi, quizzes, homework, exams, and assigning all grades.

### TEACHING CAPSTONE IN HIGHER EDUCATION

Completed a year-long Teaching Capstone in Higher Education (TeaCHE) which included attending 12 Seminars for Excellence in Teaching, preparing teaching documents, and several classroom observations.

### INQUIRY-BASED LEARNING

Trained in inquiry-based learning techniques by the Academy for IBL, as an alternative to lecturing. The weeklong workshop was help at DePaul University in June 2017. Implemented many of the techniques while teaching at Baylor.

### TEACHING ASSISTANT

Served as a Teaching Assistant for Advanced Real Analysis (x2) at Stockholm University, a masters-level course. Duties consisted of holding two-hour seminars once a week to discuss problems with material from the lectures and introduce some supplementary material.