CURRICULUM VITAE

Luís R. A. Finotti

Address

Dept. of Mathematics  Phone: (865) 974-1321
University of Tennessee  Fax: (865) 974-6576
1403 Circle Drive  e-mail: lfinotti@utk.edu

Knoxville, TN 37996  home page: http://www.math.utk.edu/~finotti/

Research Interests

Algebraic Number Theory and Arithmetic Algebraic Geometry: • canonical and minimal degree liftings of curves and their applications;

• arithmetic of elliptic curves and Abelian varieties;

• p-adic and local fields;

• applications to coding theory and cryptography;

• computational aspects.

Appointments

• Associate Professor. University of Tennessee. Since 08/12.

• Assistant Professor. University of Tennessee. Since 08/06.

• Visiting Assistant Professor. Ohio State University. From 09/04 to 06/06.

• Visiting Assistant Professor. University of California, Santa Barbara. From 09/01 to 07/04.

• Assistant Instructor. University of Texas at Austin. From 09/00 to 08/01.

Education

• B.S. (Mathematics)

University of São Paulo (Brazil). From 03/91 to 11/94.

• M.S. (Mathematics)

University of São Paulo (Brazil). From 03/95 to 02/97.

• Ph.D. (Mathematics)

University of Texas at Austin. From 09/97 to 08/01. (Advised by J. F. Voloch.)

Financial Supports and Fellowships

• Scientific Initiation Fellowship: From 05/93 to 11/94. Funds from FAPESP (Foundation of Support to Research of the State of São Paulo).

• Master Fellowship: From 03/95 to 02/97. Funds from FAPESP.

• Ph.D. Fellowship: From 09/97 to 08/01. Funds from CAPES (Brazilian government institution).

• Bruton Fellowship for the academic year of 2000/2001. Funds from the University of Texas at Austin.

• Barrett Lectures 2019: Recent Advancements in Number Theory. Conference funding grants from NSF and IMA.

Projects and Dissertations

• Scientific Initiation Project: detailed analysis of Gauss’s “Disquisitiones Generales circa Superficies Curvas”.

• Master Dissertation: “The Absolute Hilbert Class Field of Quadratic Imaginary Extension”.

• Ph.D. Thesis: “Canonical and Minimal Degree Liftings of Curves.”

Publications

• “Degrees of the Elliptic Teichmüller Lift”. J. Number Theory, 95:123–141, 2002.

• “Minimal Degree Liftings of Hyperelliptic Curves”. J. Math. Sci. Univ. Tokyo, 11:1–47, 2004.

• “Minimal Degree Liftings in Characteristic 2”. J. Pure Appl. Algebra, 207:631–673, 2006.

• “A Formula For the Supersingular Polynomial”. Acta Arith., 139(3):265-273, 2009.

• “Lifting the j-Invariant: Questions of Mazur and Tate”. J. Number Theory, 130(3):620-638, 2010.

• “Computations with Witt Vectors of Length 3”. J. Théor. Nombres Bordeaux, 23(2):417-454, 2011.

• “Nonexistence of Pseudo-Canonical Liftings”. Int. J. Number Theory , 8(1):31-55, 2012.

• “Coordinates of j-Invariant of the Canonical Liftings”. Funct. Approx. Comment. Math., 49(1):57-72, 2013.

• “Computations with Witt Vectors and the Greenberg Transform”. Int. J. Number Theory, 10(6):1431–1458, 2014.

• “Weierstrass Coefficients of the Canonical Lifting”. Int. J. Number Theory, 16(2):397–422, 2020.

• “An Elementary Proof for the Number of Supersingular Elliptic Curves”, São Paulo J. Math. Sci., DOI 10.1007/s40863-020-00170-8, 2020.

• “Denominators of the Weierstrass Coefficients of the Canonical Lifting”, joint with Delong Li. Submitted.

• “The Discriminant in Universal Formulas for the Canonical Lifting”, Bull. Sci. Math. 169 (2021), Paper No. 102981, 20 pp.

• “Alternative Symmetries and Systems” (in Music and Mathematics). Submitted.

Conferences Organized

• Palmetto Number Theory Series XXVIII: September 16-17 2017, at the University of Tennessee Knoxville. (Co-organized with M. Jameson.)

• 49th John H. Barrett Memorial Lectures: May 28-30, 2019, at the University of Tennessee Knoxville. (Co-organized with M. Jameson.)

Conferences Attended

• 1999 Arizona Winter School: “Local-to-Global Principles in Arithmetical Algebraic Geometry” Presented part of the students project “Application of the method of Coleman and Chabauty.”

• 2000 Arizona Winter School: “Topics in the Arithmetic of Function Fields”

• Aspects of Algebraic Geometry and Commutative Algebra. May 18-20, 2000 at Texas A&M University.

• 2001 Arizona Winter School: “Modular Forms”

• 2002 Arizona Winter School: “Periods”

• 2003 Arizona Winter School: “Logic and Number Theory”

• Third CICMA-CRM Far Hills Workshop: “L-functions and p-adic cohomology: computational

perspectives”

January 02-04, 2004 in Val-Morin, Quèbec (Canada)

• Joint Mathematics Meeting. January 07-10 2004 in Phoenix, AZ.

• 2006 Arizona Winter School: “Computational and Algorithmic Aspects of Algebra and Arithmetic”

• Palmetto Number Theory Series I: December 9-10 2006, at the University of South Carolina • 2007 Arizona Winter School: “p-adic Geometry”

• 2008 Arizona Winter School: “Special Functions and Transcendence”

• Number Theory as an Applied and Experimental Science. Thematic semester at the Centre de Recherches Mathématiques (Montreal, Canada). From January to May 2010.

• Palmetto Number Theory Series XVI: September 10-11 2011, at the Emory University.

• Palmetto Number Theory Series XIX: December 1-2 2012, at the University of South Carolina.

• Palmetto Number Theory Series XXI: December 7-8 2013, at the Clemson University.

• Palmetto Number Theory Series XXIII: December 6-7 2014, at the University of South Carolina.

• Modular Forms and Curves of Low Genus: Computational Aspects: September 28 to October 02 2015, at the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, RI.

• 2017 Arizona Winter School: “Perfectoid Spaces”, March 11-15 2017, at the University of Arizona.

• Palmetto Number Theory Series XXVIII: September 16-17 2017, at the University of Tennessee Knoxville. (Co-organizer.)

• Palmetto Number Theory Series XXIX: December 2-3 2017, at Clemson University.

• Latin American Week on Coding and Information: July 25-27 2018, at Unicamp (Campinas, Brazil).

Talks

• 1997 to 2001:

∘ University of Texas at Austin: “Number Theory Seminar” and “Graduate Number Theory

Seminar”. ∘ University of California Santa Barbara: “Arithmetic and Geometry Seminar”.

• 2002:

∘ University of California Santa Barbara: “Arithmetic and Geometry Seminar”. ∘ University of Texas at Austin: “Number Theory Seminar” (as invited speaker) ∘ University of São Paulo (Brazil) ∘ University of São Paulo and University of São Paulo at São Carlos (Brazil)

• 2003:

∘ University of California Santa Barbara: “Arithmetic and Geometry Seminar”.

∘ AMS Sectional Meeting in Boulder, CO. Special session: “Applications of Number Theory and

Algebraic Geometry to Coding”.

• 2004:

∘ University of Nebraska Lincoln

∘ University of Wyoming

∘ Ohio State University: “Number Theory Seminar”.

• 2005:

∘ AMS Sectional Meeting in Santa Barbara, CA. Special session “Arithmetic Geometry”.

• 2006:

∘ Colloquium talk at the University of Tennessee.

• 2007:

∘ Junior Colloquium Talk for undergraduates at the Univ. of Tennessee: Applications of Number

Theory in Cryptography.

• 2008:

∘ Palmetto Number Theory Series V, at Furman University, SC. ∘ Colloquium talk at the University of Tennessee. ∘ Palmetto Number Theory Series VIII, at University of South Carolina.

• 2010:

∘ Counting Points: Theory, Algorithms and Practice, at the Centre de Recherches Mathématiques. ∘ Palmetto Number Theory Series XV, at Clemson University.

• 2011:

∘ Algebra Seminar at Emory University. ∘ AMS Sectional Meeting in Lincoln, NE. Special session: “Coding Theory”.

• 2012:

∘ Sage Days 36: p-adics at the University of California San Diego. ∘ Witt Vectors in Arithmetic, Geometry, and Topology at the University of New Mexico. ∘ Number Theory Seminar at the University of Texas at Austin.

• 2013:

∘ Joint Mathematics Meeting in San Diego, CA. AMS Special Session: “Witt Vectors, Lifting

and Descent”. ∘ Number Theory Seminar at the University of California Santa Barbara. ∘ Mathematical Congress of the Americas in Guanajuato, Mexico. Special Session in Number

Theory. ∘ First Alumini Meeting of the Graduate Program of the Institute of Mathematics and Statistics

of the University of São Paulo in São Paulo, Brazil.

• 2014:

∘ XXIII Brazilian Algebra Meeting in Maringá, Brazil.

• 2015:

∘ Algebra Seminar at the University of São Paulo, São Carlos, Brazil. ∘ Number Theory and Combinatorics Seminar at the University of Texas at Austin.

• 2016:

∘ Palmetto Number Theory Series XXVII, at University of South Carolina.

Teaching

• Courses taught at UCSB: ∘ M34A and M34B – Calculus for Social and Life Sciences (2 quarter sequence) ∘ M3A, M3B, M3C – Calculus for Engineering and Natural Sciences (3 quarter sequence) ∘ M5B – Multivariable Calculus ∘ M5H – Honors Calculus ∘ M103 – Introduction to Group Theory ∘ M116 – Combinatorial Analysis ∘ M137A – first quarter of Graph Theory • Courses taught at Ohio State University:

∘ Math 151 – Calculus and Analytic Geometry I ∘ Math 366, 566 – Discrete Mathematical Structures I and II ∘ Math 772 – Graduate Abstract Algebra III (Field Theory) ∘ Ross Program, as an assistant instructor. (See http://www.math.ohio-state.edu/ross/).

• Courses taught at the University of Tennessee: ∘ First Year Studies 129 – Mathematics of Finances ∘ Math 141 – Calculus I ∘ Math 251 – Matrix Algebra I ∘ Math 300 – Introduction to Abstract Mathematics ∘ Math 351 – Algebra I ∘ Math 421 – Combinatorics ∘ Math 455, 456 – Abstract Algebra I and II ∘ Math 460 – Geometry ∘ Math 499 – Applied and Computational Number Theory. (New course!) ∘ Math 551, 552 – Modern Algebra I and II (Graduate) ∘ Math 555, 556 – Number Theory I and II (Graduate) ∘ Math 651, 652 – Topics in Algebra I and II (Graduate) ∘ Project GRAD Summer Institute (a program for high school students of areas of lower income):

2008 to 2012, 2014 to 2019 – Algebra II. ∘ Research Experience for Undergraduates 2008. (Co-advisor of project on factorization of tetra-

nomials over 𝔽_{3}.) ∘ Math 504 – Discrete Mathematics for Teachers. On line course. ∘ Math 506 – Algebra for Teachers. On line course.

• Theses and Dissertations Directed ∘ “On Cyclotomic Primality Tests”, master thesis by T. Boucher, 2011. ∘ “The Galois Groups of x^{n} − x^{n−1} − ⋯ − x − 1”, master thesis by D. Walker, 2016. ∘ “p-adic Numbers”, honors thesis by A. Belt, 2016. ∘ “Gröbner Basis”, honors thesis by S. Pablo, 2017. ∘ “The Prime Number Theorem”, honors thesis by N. Sharda, 2020. ∘ “Denominators of the Weierstrass Coefficients of the Canonical Lifting”, Ph.D. thesis by D. Li,

2020. ∘ “Primality Testing”, M.S. project by N. Velez.

Computer Skills

MAGMA, Sage, Python, PARI-GP, Mathematica, L^{A}TEX, HTML/CSS, PHP, Shell Scripting, Linux.

Membership in Professional Societies

Member of the American Mathematical Society since 1998.

Personal Data

Born March 30, 1973, in Uberlândia, MG, Brazil. US Permanent Resident.