Adam Lizzi came to Kenyon in the fall of 2018 after completing his Ph.D. at the University of Maryland, College Park. Adam's research involves the study of mathematical objects called Jacobians of curves, which in recent years have become central players in many cryptographic systems. Specifically Adam is interested in relationships between Jacobians -- when does one of them "evenly cover" another?

Adam has a soft spot for various other computational problems that fall under the heading of number theory, the study of properties of integers (whole numbers). For instance, how does one go about efficiently breaking a large number down into its prime factors? Adam enjoys studying algorithms that solve this problem, as well as implementing them on computers.

When he's not teaching or thinking about math, he is probably playing games (most likely Magic: the Gathering), doing word puzzles (either a crossword or a game of his own invention), consuming media in Japanese, or watching unusual sports (his absolute favorite is curling).

Areas of Expertise

Number theory, algebraic and arithmetic geometry.

Education

2018 — PhD candidate from Univ Maryland College Park

2008 — Bachelor of Arts from Swarthmore College

Courses Recently Taught

The first in a three-semester calculus sequence, this course covers the basic ideas of differential calculus. Differential calculus is concerned primarily with the fundamental problem of determining instantaneous rates of change. In this course we will study instantaneous rates of change from both a qualitative geometric and a quantitative analytic perspective. We will cover in detail the underlying theory, techniques and applications of the derivative. The problem of anti-differentiation, identifying quantities given their rates of change, also will be introduced. The course will conclude by relating the process of anti-differentiation to the problem of finding the area beneath curves, thus providing an intuitive link between differential calculus and integral calculus. Those who have had a year of high school calculus but do not have advanced placement credit for MATH 111 should take the calculus placement exam to determine whether they are ready for MATH 112. Students who have 0.5 units of credit for calculus may not receive credit for MATH 111. This counts toward the core course requirement for the major. Prerequisite: solid grounding in algebra, trigonometry and elementary functions. Offered every semester.

The second in a three-semester calculus sequence, this course has two primary foci. The first is integration, including techniques of integration, numerical methods and applications of integration. This study leads into the analysis of differential equations by separation of variables, Euler's method and slope fields. The second focus is the notion of convergence, as manifested in improper integrals, sequences and series, particularly Taylor series. This counts toward the core course requirement for the major. Prerequisite: MATH 111 or AP score of 4 or 5 on Calculus AB exam or an AB sub score of 4 or 5 on the Calculus BC exam or permission of instructor. Offered every semester.

The third in a three-semester calculus sequence, this course examines differentiation and integration in three dimensions. Topics of study include functions of more than one variable, vectors and vector algebra, partial derivatives, optimization and multiple integrals. Some of the following topics from vector calculus also will be covered as time permits: vector fields, line integrals, flux integrals, curl and divergence. This counts toward the core course requirement for the major. Prerequisite: MATH 112 or a score of 4 or 5 on the BC Calculus AP exam or permission of instructor. Offered every semester.

This course will focus on the study of vector spaces and linear functions between vector spaces. Ideas from linear algebra are useful in many areas of higher-level mathematics. Moreover, linear algebra has many applications to both the natural and social sciences, with examples arising in fields such as computer science, physics, chemistry, biology and economics. In this course, we will use a computer software system, such as Maple or Matlab, to investigate important concepts and applications. Topics to be covered include methods for solving linear systems of equations, subspaces, matrices, eigenvalues and eigenvectors, linear transformations, orthogonality and diagonalization. Applications will be included throughout the course. This counts toward the core course requirement for the major. Prerequisite: MATH 213. Generally offered three out of four semesters.

Looking at a problem in a creative way and seeking out different methods toward solving it are essential skills in mathematics and elsewhere. In this course, students will build their problem-solving intuition and skills by working on challenging and fun mathematical problems. Common problem-solving techniques in mathematics will be covered in each class meeting, followed by collaboration and group discussions, which will be the central part of the course. The course will culminate with the Putnam exam on the first Saturday in December. Interested students who have a conflict with that date should contact the instructor. This does not count toward any requirement for the major. Prerequisite: MATH 112 or a score of 4 or 5 on the BC Calculus exam or permission of instructor.

The course starts with an introduction to the complex numbers and the complex plane. Next students are asked to consider what it might mean to say that a complex function is differentiable (or analytic, as it is called in this context). For a complex function that takes a complex number z to f(z), it is easy to write down (and make sense of) the statement that f is analytic at z if \n\n\n\nexists. Subsequently, we will study the amazing results that come from making such a seemingly innocent assumption. Differentiability for functions of one complex variable turns out to be a very different thing from differentiability in functions of one real variable. Topics covered will include analyticity and the Cauchy-Riemann equations, complex integration, Cauchy's Theorem and its consequences, connections to power series, and the Residue Theorem and its applications. This counts toward the Continuous/Analytic (Column B) elective requirement for the major. Prerequisite: MATH 224. Offered every other year.