● **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

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Learning Seminar: P-adic modular forms, Spring 2020

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Learning Seminar: Prismatic cohomology, Fall 2019

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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

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2018 Spring Program at MSRI

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● Automorphic Forms and the Langlands Program

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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

● 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 |