Casalaina-Martin, Sebastian

Research

research overview

Casalaina-Martin performs research in mathematics. He is an algebraic geometer with a broad range of interests. His research focuses on curves, abelian varieties, vector bundles, Hodge theory, and moduli spaces.

keywords

Algebraic geometry, curves, abelian varieties, vector bundles, Hodge theory, and moduli spaces

Publications

selected publications

chapter
- A tour of stable reduction with applications. 65-117. 2013
- The geometry of the ball quotient model of the moduli space of genus four curves. Contemporary Mathematics. 107-+. 2012
- Singularities of theta divisors in algebraic geometry. Contemporary Mathematics. 25-43. 2008
conference proceeding
- On the Image of the Second l-adic Bloch Map. Progress in Mathematics. 15-96. 2019
journal article
- NON-ISOMORPHIC SMOOTH COMPACTIFICATIONS OF THE MODULI SPACE OF CUBIC SURFACES. Nagoya Mathematical Journal. 315-365. 2024
- The Moduli Space of Cubic Threefolds with a Non-Eckardt Type Involution via Intermediate Jacobians. International Mathematics Research Notices. 16104-16139. 2023
- Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models. Memoirs of the American Mathematical Society. I-+. 2023
- A functorial approach to regular homomorphisms. Algebraic Geometry. 87-129. 2023
- The Walker Abel-Jacobi map descends. Mathematische Zeitschrift. 1799-1817. 2021

Teaching

courses taught

MATH 2001 - Introduction to Discrete Mathematics
Primary Instructor - Spring 2020 / Spring 2022 / Fall 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 - Summer 2018 / Summer 2019 / Spring 2021 / Fall 2022
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 - Spring 2018 / Fall 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 2300 - Calculus 2
Primary Instructor - Fall 2018
Continuation of MATH 1300. Topics include transcendental functions, methods of integration, polar coordinates, differential equations, improper integrals, infinite sequences and series, Taylor polynomials and Taylor series. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C-). Degree credit not granted for this course and APPM 1360.
MATH 3140 - Abstract Algebra 1
Primary Instructor - Summer 2020 / Summer 2021 / Fall 2021 / Fall 2022
Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.

MATH 3850 - Seminar in Guided Mathematics Instruction
Primary Instructor - Fall 2018
Provides learning assistants with an opportunity to analyze assessment data for formative purposes and develop instructional plans as a result of these analyses. These formative assessment analyses will build on the literature in the learning sciences. Students gain direct experiences interacting with the tools of the trade, especially with actual assessment data and models of instruction. May be repeated up to 3 total credit hours. Restricted to learning assistants in Math.

MATH 4140 - Abstract Algebra 2
Primary Instructor - Spring 2020
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Same as MATH 5140.

MATH 6170 - Algebraic Geometry
Primary Instructor - Spring 2021
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 6290 - Homological Algebra
Primary Instructor - Spring 2018
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.

MATH 6360 - Functions of a Complex Variable 2
Primary Instructor - Fall 2019 / Fall 2023
Focuses on conformal mapping, analytic continuation, singularities and elementary special functions. Department enforced prerequisite: MATH 6350. Instructor consent required for undergraduates.

MATH 8174 - Topics in Algebra I
Primary Instructor - Spring 2022
Department enforced prerequisites: MATH 6130 and MATH 6140. Instructor consent required for undergraduates.

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