Jin Hyung To

Email: jinto@iu.edu

Position: Visiting Lecturer of Mathematics

My CV My Teaching Statement My Research Statement

● Teaching Experience:
I am currently teaching at Indiana University at Bloomington. I have over 20 years college-level math teaching experience at the several institutes. I have a unique teaching experience as a mathematician. I have an outstanding college teaching experience, both traditional and non-traditional, and web-based teaching.

● Research:
i) free abelian group generated by closed subvarieties
ii) arithmetic of varieties
iii) curves in P^3 and intersection
iv) moduli space of holomorphic chains

● Some math writings
Given n objects how many ways to choose r with repetition?
Deformation Theory: families of vector bundles over the dual numbers
Flatness in algebraic geometry: a family of conics in the affine space

● Lecture Note Presentations and Syllabi creation by Jin Hyung To:
• Differential Geometry (Math 423): Abstract and Topics to be covered,
  Lecture 1 , Lecture 2 , Lecture 3 , Derivative and Jacobian Matrix (Lecture 3), Lecture 4 , ..., Lecture 42.
• Applied Complex Variables (Math 446)Edited: Lecture 1, Lecture 2, Lecture 3, Lecture 4, ..., Lecture 40.
• Abstract Linear Algebra (Math 416): Abstract and Topics to be covered,
  Lecture 1, Lecture 2, Lecture 3, Lecture 4, ..., Lecture 40.
• Complex Variables (Math 448): Abstract and Topics to be covered,
  Lecture 1, Lecture 2, Lecture 3, Lecture 4, ..., Lecture 40.
• Abstract Algebra (Math 417): Abstract and Topics to be covered,
  Lecture 1, Lecture 2, Lecture 3, Lecture 4, ..., Lecture 16, ..., Lecture 27.
• Elementary Real Analysis (Math 444): Abstract and Topics to be covered,
  Lecture 1, Lecture 2, Lecture 3, Lecture 4, ..., Lecture 39.

● Algebraic Number Theory Reading Seminar
Learning Seminar: P-adic modular forms, Spring 2020
Learning Seminar: Prismatic cohomology, Fall 2019
Learning Seminar: Langlands correspondence, Fall 2018

● Algebraic Geometry Seminar
2020 Spring
2019 Spring

● Graduate Student Algebraic Geometry Seminar
2020 Spring
2019 Spring
2018 Fall
2018 Spring

● Enumerative Geometry Beyond Numbers
2018 Spring Program at MSRI
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● Automorphic Forms and the Langlands Program
2017 Summer school at MSRI

● National Math and Science Competition (NMSC)
NMSC national math competition

● Highschool math competition problems
Alcumus, Art of Problem Solving
AMC Problem Solving
AMC Problem Solving 2
AMC12
AMC10
AMC8
AIME

● Publications:
• Holomorphic chains of type (n, 1; d, 0) on the projective line, in preparation
• Holomorphic chains of type (2, 1; L, 0) of a fixed determinant L, in preparation
• Holomorphic chains of type (2, 1; d, 0) on the projective line: from a Grassmannian to projective space, in preparation
• Holomorphic chains composed of semistable vector bundles, in preparation
• Holomorphic chains composed of line bundles, preprint
• Holomorphic chains on the projective line, Ph.D. Thesis

● Research Interests:
• I challenge Riemann hypothesis and Tate conjecture
• My research area is moduli spaces in algebraic geometry. Moduli spaces is a way of finding algebraic varieties not by polynomial equations but by Geometric Invariant Theory(GIT)
• Moduli spaces of holomorphic chains on the projective line and non-reductive GIT
• Moduli spaces of holomorphic chains on the projective line and the derived categories of quiver sheaves on the projective line
• Non-reductive GIT and symplectic reduction
• Geometric Invariant Theory and symplectic reduction
• Maps between moduli spaces of vector bundles
• Stability of vector bundles under operations(ex. tensor product, wedge product, symmetric product and etc)
• Local description of the moduli space of holomorphic chains
• Algebraic groups
• Abelian varieties
• Riemannian geometry: curvature form and metric
• The existence α-stable of holomorphic chains
• Complex geometry
• Principle bundles in relation with vector bundles
• Moduli spaces and Geometric Invariant Theory
• Moduli spaces: categorical sense
• Quiver bundles as a generalization of holomorphic chains
• Algebraic geometry
• Higher rank Brill-Noether Theory
• Survey of the moduli spaces of vector bundles
• Co-Higgs bundles and holomorphic chains(on the projective line)
• Moduli spaces of holomorphic chains on (semi)stable vector bundles
• Connections on a complex vector bundle
• Gröbner basis
• Commutative algebra
• Derived category towards the moduli space of holomorphic chains on the projective line
• Derived category
• Morse theory
• From Moduli problem to linear algebra problem
• Topological invariants of moduli spaces
• Finding well-known varieties isomorphic to moduli spaces
• Symplectic geometry
• Symplectic geometry and Geometric Invariant Theory
• Non-reductive algebraic group actions and Geometric Invariant Theory

● Professional membership:
• Association of Christians in the Mathematical Sciences
• American Mathematical Society

AIM Problem Lists Project

The Stacks Project

● Links:
• Upcoming Conferences: Conferences in algebraic geometry on Ravi Vakil's homepage,
Conferences in arithmetic geometry on Kiran Kedlaya's homepage,
• Algebraic Geometry in Math arxiv: Algebraic Geometry arXiv
• Korean-American Scientists and Engineers Association: KSEA
• Mathematical Association of America: MAA
• Association of Christians in the Mathematical Sciences ACMS
• American Mathematical Society AMS


Department of Mathematics
273 Altgeld Hall, MC-382
1409 W. Green Street, Urbana, IL 61801 USA
Telephone: (217) 333-3350    Fax: (217) 333-9576     Email: math@illinois.edu


College of Liberal Arts and Sciences

University of Illinois at Urbana-Champaign