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Ih, Su-Ion Associate Professor

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Research Areas research areas

Research

research overview

  • 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

Publications

selected publications

Teaching

courses taught

  • MATH 2001 - Introduction to Discrete Mathematics
    Primary Instructor - Fall 2019
    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. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C-).
  • 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 / Fall 2019
    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 / Fall 2019
    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 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.

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