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, Gromov-Witten theory, moduli of curves, Picard groups
Teaching
courses taught
MATH 2001 - Introduction to Discrete Mathematics
Primary Instructor
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Spring 2021
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 2022 / 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 2135 - Introduction to Linear Algebra for Mathematics Majors
Primary Instructor
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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 3001 - Analysis 1
Primary Instructor
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Fall 2024
Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral.
MATH 3450 - Introduction to Complex Variables
Primary Instructor
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Spring 2021
Theory of functions of one complex variable, including integrals, power series, residues, conformal mapping, and special functions. Formerly MATH 4450.
MATH 6150 - Commutative Algebra
Primary Instructor
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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
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Spring 2019 / Spring 2023
Introduces algebraic geometry, including affine and projective varieties, rational maps and morphisms and differentials and divisors. Additional topics might include Bezout's Theorem, the Riemann-Roch Theorem, elliptic curves, and sheaves and schemes. Department enforced prerequisite: MATH 6140. Instructor consent required for undergraduates.
MATH 6175 - Algebraic Geometry 2
Primary Instructor
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Spring 2024
Continuation of MATH 6170. Develops algebraic geometry using schemes. Topics include coherent and quasicoherent sheaves, sheaf cohomology, Serre duality, lifting criteria, smoothness, base change theorems, algebraic curves and surfaces, and additional topics at the discretion of the instructor. Instructor consent required for undergraduates. Department enforced prerequisite: MATH 6170. Recommended prerequisites: MATH 6150 or MATH 6290.
MATH 6290 - Homological Algebra
Primary Instructor
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Spring 2020 / Fall 2023
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.
