Dr. Wise studies moduli spaces using tools from logarithmic geometry, tropical geometry, and deformation theory. He is particularly interested in the moduli spaces of curves and related moduli spaces, such as the universal Picard group, and their compactifications.
keywords
algebraic geometry, logarithmic geometry, tropical geometry, sheaf theory, deformation theory, GromovWitten theory, moduli of curves, Picard groups
MATH 2135  Introduction to Linear Algebra for Mathematics Majors
Primary Instructor

Fall 2018 / Spring 2020
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 plan to major in Mathematics. Degree credit not granted for this course and MATH 2130 or APPM 3310. Formerly MATH 3135.
MATH 6150  Commutative Algebra
Primary Instructor

Fall 2018
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 6170  Algebraic Geometry
Primary Instructor

Spring 2019
Introduces algebraic geometry, including affine and projective varieties, rational maps and morphisms and differentials and divisors. Additional topics might include Bezout's Theorem, the RiemannRoch Theorem, elliptic curves, and sheaves and schemes. Department enforced prerequisite: MATH 6140. Instructor consent required for undergraduates.
MATH 6290  Homological Algebra
Primary Instructor

Spring 2020
Studies categories and functors, abelian categories, chain complexes, derived functors, Tor and Ext, homological dimension, group homology and cohomology. If time permits, the instructor may choose to cover additional topics such as spectral sequences or Lie algebra homology and cohomology. Department enforced prerequisites: MATH 6130 and MATH 6140.