## Contact Information

Address: |
Ayres Hall 251 1403 Circle Drive Department of Mathematics University of Tennessee Knoxville, TN 37996-1320 |

Phone: |
(865) 974-1321 |

Fax: |
(865) 974-6576 (Attn: Luís Finotti) |

E-Mail: |
lfinotti@utk.edu |

Office Hours: |
By appointment only (possibly with Zoom). |

## Introduction

I'm an Associate Professor here at the Department of Mathematics of the University of Tennessee Knoxville. My area is Algebraic Number Theory and Arithmetic Geometry.

Here is a picture of me. But be warned, after you see it, you can't unsee it!

## To my current students (Spring 2023)

Go to: Math 559 - "Linear Algebra", Data 201 - " Data Knowledge and Discovery", Math 397 - Junior Honors Seminar.

## Research

*"Canonical Liftings of Edwards Curves"*(with Liam Bitting): pdf. Submitted.*"Improved Bounds for Denominators in the Formulas of the Canonical Lifting"*(with Delong Li): pdf. Submitted.*"The Discriminant in Universal Formulas for the Canonical Lifting"*(with Delong Li): pdf. "Bulletin des Sciences MathÃ©matiques", 169, 2021.*"Denominators of the Weierstrass Coefficients of the Canonical Lifting"*(with Delong Li): pdf. Submitted.-
*"Weierstrass Coefficients of the Canonical Lifting"*: pdf.*"International Journal of Number Theory"*, 16(2):397-422, 2020. *"An Elementary Proof for the Number of Supersingular Elliptic Curves"*: pdf.*"SÃ£o Paulo Journal of Mathematical Sciences"*, DOI 10.1007/s40863-020-00170-8, 2020.-
*"Coordinates of the j-Invariant of the Canonical Lifting"*: dvi, ps, pdf.*"Functiones et Approximatio Commentarii Mathematici"*, 49(1): 52-75, 2013. -
*"Nonexistence of Pseudo-Canonical Liftings"*: dvi, ps, pdf.*"International Journal of Number Theory"*, 8(1):31-51, 2012. -
*"Computations with Witt Vectors and the Greenberg Transform"*: dvi, ps, pdf.*"International Journal of Number Theory"*, 10(6):1431-1458, 2014. (Some files used to check computations in the paper can be found here.) -
*"Computations with Witt Vectors of Length 3"*: dvi, ps, pdf.*"Journal de Théorie des Nombres de Bordeaux"*, 23(2):417-454, 2011. (Some files used to check computations in the paper can be found here.) -
*"Lifting the j-Invariant: Questions of Mazur and Tate"*: dvi, ps, pdf.*"Journal of Number Theory"*, 130(3):620-638, 2010. -
*"A Formula for the Supersingular Polynomial"*: dvi, ps, pdf .*"Acta Arithmetica"*, 139(3):265-273, 2009. -
*"Minimal Degree Liftings in Characteristic 2"*: dvi, ps, pdf.*"Journal of Pure and Applied Algebra"*, 207:631-673, 2006. -
*"Minimal Degree Liftings of Hyperelliptic Curves"*: dvi, ps, pdf.*"Journal of Mathematical Sciences, University of Tokyo"*, 11:1-47, 2004 -
*"Degrees of the Elliptic Teichmuller Lift"*: dvi, ps, pdf.*"Journal of Number Theory"*, 95:123-141, 2002. - My canonical lifts page. Formulas, programs, etc.
- Vita: dvi, ps, pdf.
- Research Statement (for specialists): dvi, ps, pdf.
- Ph.D. Thesis: dvi, ps, pdf.

## Teaching

**Courses taught at the University of Tennessee:**

- Spring 2024: Math 559 - "Linear Algebra", Data 201 - " Data Knowledge and Discovery", Math 397 - Junior Honors Seminar.
- Spring 2023: Math 351 - "Algebra I", Data 201 - " Data Knowledge and Discovery", Math 397 - Junior Honors Seminar.
- Fall 2022: FYS 129 - "Mathematics and Finances", Data 201 - " Data Knowledge and Discovery".
- Spring 2022: Math 351 - "Algebra I", Math 499 - "Applied and Computational Number Theory".
- Fall 2021: Math 497 - "Undergraduate Honors Seminar", Math 651 - "Arithmetic of Elliptic Curves".
- Spring 2021: FYS 129 - "Mathematics and Finances", Math 397 - "Junior Honors Seminar", Math 499 - "Applied and Computational Number Theory".
- Fall 2020: M300 - "Introdution to Advanced Mathematics", FYS129 - "Mathematics and Finances".
- Spring 2020: M351 - "Algebra I", M499 - "Applied and Computational Number Theory".
- Fall 2019: M651 - "Algebraic Number Theory", FYS129 - "Mathematics and Finances".
- Summer 2019: M506 - "Algebra for Teachers".
- Spring 2019: Math 552 - "Modern Algebra II".
- Fall 2018: M499 - "Applied and Computational Number Theory", M551 - "Modern Algebra I".
- Summer 2018: M504 - "Discrete Math for Teachers".
- Spring 2018: Math 241 - "Calculus III", Math 351 - "Algebra I".
- Fall 2017: FYS 129 - "Mathematics and Finances", Math 351 - "Algebra I".
- Summer 2017: M506 - "Algebra for Teachers".
- Spring 2017: Math 556 - "Number Theory II".
- Fall 2016: FYS 129 - "Mathematics and Finances", Math 307 - "Introduction to Advanced Math (Honors)", Math 555 - "Number Theory I".
- Summer 2016: M504 - "Discrete Math for Teachers".
- Spring 2016: Math 351 - "Algebra I", Math 652 - "Advanced Modern Algebra II".
- Summer 2015: M506 - "Algebra for Teachers".
- Spring 2015: FYS 129 - "Mathematics and Finances", Math 351 - "Algebra I", Math 552 - "Modern Algebra II".
- Fall 2014: FYS 129 - "Mathematics and Finances", Math 141 - "Calculus I", Math 551 - "Modern Algebra I".
- Summer 2014: M504 - "Discrete Mathematics for Teachers".
- Spring 2014: FYS 129 - "Mathematics and Finances", Math 421 - "Combinatorics", Math 458 - "Honors Abastract Algebra II".
- Fall 2013: FYS 129 - "Mathematics and Finances", Math 141 - "Calculus I", Math 457 - "Honors Abastract Algebra I".
- Spring 2013: Math 307 - "Introduction to Abstract Mathematics (Honors)", Math 659 - "Algebra Seminar".
- Fall 2012: FYS 129 - "Mathematics and Finances", Math 251 - "Matrix Algebra I", Math 455 - "Abstract Algebra I".
- Summer 2012: M460 - "Geometry".
- Spring 2012: Math 141 - "Calculus I", Math 552 - "Modern Algebra II".
- Fall 2011: FYS 129 - "Mathematics and Finances", Math 551 - "Modern Algebra I".
- Summer 2011: M251 - "Matrix Algebra I".
- Spring 2010: Math 141 - "Calculus I", Math 556 - "Number Theory II".
- Fall 2010: FYS 129 - "Logs, Exponentials, and Finance", M251 - "Matrix Algebra I", M555 - "Number Theory I".
- Summer 2010: M251 - "Matrix Algebra I".
- Fall 2009: Math 300 - "Introduction to Abstact Mathematics", Math 351 - "Algebra I".
- Summer 2009: M251 - "Matrix Algebra I".
- Spring 2009: M251 - "Matrix Algebra I", M556 - "Number Theory II".
- Fall 2008: M300 - "Introduction to Abstract Mathematics", M555 - "Number Theory I".
- Spring 2008: M552 - "Modern Algebra II".
- Fall 2007: M251 - "Matrix Algebra I", M551 - "Modern Algebra I".
- Spring 2007: M456 - "Abstract Algebra II".
- Fall 2006: M455 - "Abstract Algebra I".

Notes for the **Project GRAD Summer Institute 2009**: "A Gentle Introduction to
Number Theory and
Cryptography".

Here is a spreadsheet (Open Document format, MS Excel format) that can be used to computed interest, final value with interest and payments, calculate value of payments, and how long to pay off or save a specific value. You will need to read the instructions to use it.

For information on courses taught at the University of California Santa Barbara, or at at the Ohio State University, please e-mail me.

## Some Math Links

- Dept. of Mathematics of the University of Tennessee Knoxville.
- Dept. of Mathematics of the Ohio State University, where I worked for two years.
- Number Theory Group at the Dept. of Mathematics of the University of California Santa Barbara, where I worked for three years. My sponsor was Bisi Agboola.
- Number Theory Group at the Dept. of Mathematics of the University of Texas at Austin, where I got my Ph.D., studying with Felipe Voloch.
- Number Theory Web - great place for number theorists.
- Institute of Mathematics and Statistics of the University of São Paulo - where I got my bachelor and master degrees.
- IMPA - a great center for mathematics in Brazil.
- Sage - a free and open source math package based on Python. You can try it online with Cocalc.
- Magma - very nice, but non-free, Mathematics package.
- PARI - another nice and free Number Theory package.
- MathSciNet - References. (Need to be on a site subscribed to this service, like UT and many other universities.)

Every time you go outside, go slowly

Looking for a piece of mind, don't lose your ground

Every time you lose your ground, fall softly

You become what you do, become what you feel

Become what you need, then softly fall

Stand up, don't you crawl, you have to be only reason you go that slowly

*"5/4"*by the iamthemorning.