Dr. Jin Hyung To

Email: jinto@illinois.edu
Office: NetMath House,
912 South Fifth Street Champaign, IL 61820
Phone: (217)300-4954

● Netmath Position:
I am currently developing 400 level courses towards master degree program. I am in charge of teaching 10 undergraduate courses and a main instructional developer.
Netmath is a uinque web-based distance-learning interface that has provided mathematics education to a wide range of student populations including Rural High School students, Post-AP High School students, home-schooled students, University students, Adult professionals, and Military personnel. Students who register for Netmath courses explore mathematical concepts with the aid of the computer algebra system Mathematica.
NetMath is the distance learning program of the Department of Mathematics at the University of Illinois at Urbana-Champaign. Our goal is to bring academic resources from one of the nation's top public universities to students around the world. I am developing the resources required to provide students with the unique method of learning that NetMath offers. For 25 years, the NetMath program has been breaking down distance barriers in education and making University based math courses more widely available for students throughout the United States and the world as well.

● Teaching:
I have 18 years college teaching experience. In detail, University of Illinois at Urbana-Champaign(over 13 years since 2003) and Governors State University at the south Chicago area (1 semester) and Kyungpook National University, S. Korea(over 4 years). I have a unique teaching experience as a mathematician. I have an outstanding college teaching experience, both traditional and non-traditional, and computer based teaching experience.


● Some math writings
Given n objects how many ways to choose r with repetition?

● 2018 Graduate Algebraic Geometry Seminar
Click here for semester's topic and time/room

● Enumerative Geometry Beyond Numbers
2018 Spring Program at MSRI
Click here for facebook

● Automorphic Forms and the Langlands Program
2017 Summer school at MSRI

● 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:
• 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:
• Korean-American Scientists and Engineers Association
• Mathematical Association of America
• Association of Christians in the Mathematical Sciences
• American Mathematical Society

AIM Problem Lists Project

The Stacks Project

● Links:
• Korean-American Scientists and Engineers Association: KSEA
• Mathematical Association of America: MAA
• Netmath official Webpage: Netmath
• Upcoming Conferences: Upcoming conferences in algebraic geometry on Ravi Vakil's homepage
• Algebraic Geometry Math Arxiv: Algebraic Geometry arXive
• 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