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, non-density, 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 geometry-oriented. An example is what we can say about lower-dimensional sub-varieties of a fixed higher-dimensional variety and how we can apply the results to the study of the higher-dimensional variety, or the other way around. This looks fascinating in itself, but also has something close to do with the number-theoretical 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 higher-dimensional algebraic varieties
MATH 2001 - Introduction to Discrete Mathematics
Primary Instructor
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Fall 2019 / Fall 2020 / Spring 2021 / Fall 2022 / Spring 2024
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
MATH 2130 - Introduction to Linear Algebra for Non-Mathematics Majors
Primary Instructor
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Fall 2020 / Fall 2023
Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who do not plan to major in Mathematics. Degree credit not granted for this course and MATH 2135 or APPM 3310. Formerly MATH 3130.
MATH 3140 - Abstract Algebra 1
Primary Instructor
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Spring 2019
Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.
MATH 3450 - Introduction to Complex Variables
Primary Instructor
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Spring 2022
Theory of functions of one complex variable, including integrals, power series, residues, conformal mapping, and special functions. Formerly MATH 4450.
MATH 4440 - Mathematics of Coding and Cryptography
Primary Instructor
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Fall 2018 / Fall 2019 / Fall 2021
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 6110 - Introduction to Number Theory
Primary Instructor
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Fall 2018 / Fall 2021 / Fall 2023
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 6150 - Commutative Algebra
Primary Instructor
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Fall 2022 / Fall 2024
Introduces topics used in number theory and algebraic geometry, including radicals of ideals, exact sequences of modules, tensor products, Ext, Tor, localization, primary decomposition of ideals and Noetherian rings. Department enforced prerequisite: MATH 6140. Instructor consent required for undergraduates.
MATH 6190 - Analytic Number Theory
Primary Instructor
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Spring 2018
Acquaints students with the Riemann Zeta-function and its meromorphic continuation, characters and Dirichlet series, Dirichlet's theorem on primes in arithmetic progressions, zero-free regions of the zeta function and the prime number theorem. Department enforced prerequisites: MATH 6110 and MATH 6350. Instructor consent required for undergraduates.
