# Anthony Vasaturo

Operator Theorist, Complex Analyst, and experienced Instructor of Mathematics

## Welcome To My Site!

Feel free to browse around. If you have any questions, do not hesitate to contact me!

## My CV

Below lies my education and employment history, as well as links to view my CV, Teaching Statement, and Research Statement.

### Where Do I Work?

#### University of Toledo

Department of Mathematics and Statistics

Position: Graduate Teaching Assistant

Department Phone: 419-530-2568

### Education

I am in the final year of my Ph.D. in Pure Mathematics at the University of Toledo.

#### University of Toledo

Degree: Ph.D. in Pure Mathematics

Subjects: Operator Theory, Complex Analysis, and Functional Analysis

Thesis: Invertibility of Toeplitz Operators via Berezin Transforms

Advisor: Professor Željko Čučković

#### University of Toledo

Degree: Master of Arts

Subject: Pure Mathematics

#### University of Toledo

Degree: Bachelor of Science

Subject: Pure Mathematics, Physics Concentration

### My Research

I study Operator Theory on Spaces of Holomorphic Functions, including the Bergman, Hardy, Segal-Bargmann Spaces, and Model spaces. Topics include invertibility, positivity, compactness, boundedness, and invariant subspaces of Toeplitz, Hankel, and composition operators.

### My Papers

##### Carleson measures and Douglas' question on the Bergman space with Željko Čučković, 2017 To appear in Rendiconti del Circolo Matematico di Palermo.

Motivated by Douglas' question about the invertibility of Toeplitz operators on the Hardy Space, we study a related question concerning the Berezin transform and averaging function of a Carleson measure for the weighted Bergman space of the disc. As a consequence, we obtain a necessary and sufficient condition for the invertibility of Toeplitz operators whose symbols are averaging functions of these Carleson measures.

##### Invertibility and Positivity of Truncated Toeplitz Operators on Certain Model Subspaces of the Hardy Space with Krishna Subedi, submitted to Archiv der Mathematik in October 2017.
We study the degree to which both the invertibility and positivity of certain Truncated Toeplitz Operators are determined by the Berezin transforms of their symbols on Model Subspaces of the Hardy Space corresponding to the inner functions $u = z^2$ and $u = z^3$.
##### Carleson measures and Douglas' question on the Bargmann-Fock space with Željko Čučković, 2017.
Near submission...

### Courses I've Taught

I've taught, designed, and graded for a wide variety of traditional, hybrid, and online mathematics courses. In addition, I have more than six years of public and private tutoring, mentoring, and advising experience.

##### At the University of Toledo
• Fall 2017: MATH 1760
(Calculus II, Life Sciences)
• Spring 2017: MATH 1330
(Trigonometry)
• Fall 2016: MATH 1330
(Trigonometry)
• Summer 2016: MATH 1850
(Calculus I)
• Spring 2016: MATH 1890
(Elementary Linear Algebra)
• Fall 2015: MATH 1850
(Calculus I)
• Spring 2015: MATH 1330
(Online Trigonometry)
• Fall 2014: MATH 1320
(Trigonometry)
• Spring 2014: MATH 1320
(College Algebra)
• Fall 2013: MATH 2460
(Calculus II for Engineering Technology, TA)
• Spring 2013: MATH 2460
(Calculus II for Engineers, TA)
• Fall 2012: MATH 1750
(Calculus I for Life Sciences, TA)
##### Tutoring
• Test Prep:
GRE, ACT, SAT, Teaching Certification
• Fundamentals:
College Algebra, Precalculus
• Calculus:
Calculus I/II/II, all disciplines, Differential Equations
Linear Algebra, Topology, Real Analysis
Statistics, Financial Mathematics, Accounting
Real Analysis, Statistics, Complex Analysis, Functional Analysis

### Gripsport and Weightlifting

I participate in high-level grip and armwrestling training, and have an unofficial weight class world record in a grip event called the Flask!

# Flask: 86 lb.

## Contact

Feel free to contact me at any time at avasatu@rockets.utoledo.edu!

## Student Evaluations

"Anthony is a great instructor, and definitely cares more about his job than any professor I've seen."

"Mr. Vasaturo is the best math instructor that I've had at the University of Toledo. He is very thorough with his lectures and always tries to make sure that students have a real understanding of the material before moving on to the next topic. He was very easy to work with as far as homework and tests. I wish he taught more advanced math classes."

"Vasaturo concisely teaches what is relevant, reviews appropriately before exams, communicates effectively via email, and on a daily basis encourages students to ask for help and reminds us that he is available for tutoring at the library. He's also down to earth, approachable, very laid back which is important. Great professor!"

"Anthony was a great instructor. He was very clear on what information we needed to know for exams. Homework wasn't heavy and he answered homework questions every class if you had them. He was awesome!"

"He always lets you feel comfortable that you can ask him about any sentence he said in class, at any time."

"The instructor is always so helpful, enthusiastic, and encouraging without fail. I feel he personally wants me to succeed."

"Anthony really does an excellent job. He has the fastest response rate of any professor I've had."

"I'm actually never happy if I have to miss the class. Professor Anthony is really good at driving the concepts of Calculus home in a way my previous instructor did not. I really do appreciate the effort he puts in."