Dr. Jin Hyung To
Email: jinto@illinois.edu
Office: NetMath House,
912 South Fifth Street Champaign, IL 61820
Phone: (217)3004954
● 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 webbased distancelearning interface that has provided mathematics
education to a wide range of student populations including Rural High School students, PostAP High
School students, homeschooled 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 UrbanaChampaign.
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 UrbanaChampaign(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 nontraditional, and computer based teaching experience.
● My CV
● 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
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2018 Spring Program at MSRI
•
Click here for facebook
● Automorphic Forms and the Langlands Program
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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 nonreductive GIT
• Moduli spaces of holomorphic chains on the projective line and
the derived categories of quiver sheaves on the projective line
• Nonreductive 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 αstable 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 BrillNoether Theory
• Survey of the moduli spaces of vector bundles
• CoHiggs 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 wellknown varieties isomorphic to moduli spaces
• Symplectic geometry
• Symplectic geometry and Geometric Invariant Theory
• Nonreductive algebraic group actions and Geometric Invariant Theory
● Professional membership:
• KoreanAmerican 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:
• KoreanAmerican 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
