My main research interests lie in the distribution of algebraic, rational, and integral points on algebraic varieties from the various points of view of number theory  finiteness, nondensity, effectiveness, quantitativeness, etc. All these are closely connected to one another. For instance, finiteness leads to a question of effectiveness (i.e., whether it is possible to determine all those finitely many objects under consideration explicitly) and quantitativeness (i.e., how the finite numbers vary under some involved parameters). Another research interest subject of mine is algebraic geometry  more geometryoriented. An example is what we can say about lowerdimensional subvarieties of a fixed higherdimensional variety and how we can apply the results to the study of the higherdimensional variety, or the other way around. This looks fascinating in itself, but also has something close to do with the numbertheoretical questions stated above.
keywords
number theory, arithmetic geometry, distribution of algebraic, rational, and integral points on algebraic varieties, algebraic geometry, arithmetic and geometric aspects of higherdimensional algebraic varieties
MATH 3140  Abstract Algebra 1
Primary Instructor

Spring 2019
Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.
MATH 4440  Mathematics of Coding and Cryptography
Primary Instructor

Fall 2018
Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed. Same as MATH 5440.
MATH 5440  Mathematics of Coding and Cryptography
Primary Instructor

Fall 2018
Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed; prepares students for the more advanced ECEN 5682. Same as MATH 4440.
MATH 6110  Introduction to Number Theory
Primary Instructor

Fall 2018
Examines divisibility properties of integers, congruences, diophantine equations, arithmetic functions, quadratic residues, distribution of primes and algebraic number fields. Department enforced prerequisite: MATH 3140. Instructor consent required for undergraduates.
MATH 6190  Analytic Number Theory
Primary Instructor

Spring 2018
Acquaints students with the Riemann Zetafunction and its meromorphic continuation, characters and Dirichlet series, Dirichlet's theorem on primes in arithmetic progressions, zerofree regions of the zeta function and the prime number theorem. Department enforced prerequisites: MATH 6110 and MATH 6350. Instructor consent required for undergraduates.