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Special Topics (Fall 2020): Mod Space Shears & Vafuen Theory


Advanced courses on special topics; given as need arises.


The Geometry of Moduli Spaces of Sheaves, Huybrechts, Cambridge University Press, 2nd Edition.

Credit Hours: 

The course of "Toric on Hilbert schemes" intends to cover the basic materials of Hilbert schemes. The Hilbert schemes are a very important and interesting schemes in algebraic geometry. We begin the functor point of view on Hilbert schemes, talk about the basic notions and properties of Hilbert schemes, and finally pay more attention on the Hilbert scheme of points on surfaces and threefolds. The recent development on enumerative geometry (especially on Donaldson-Thomas theory) gives new phenomenon to look at the Hilbert schemes. If time permits, we will introduce the basic notion of Donaldson-Thomas theory and the interesting role of Hilbert schemes in the theory. This course is a second start up for Algebraic Geometry, and also a warm-up for the research area on Gromov-Witten theory and Donaldson-Thomas theory in modern enumerative algebraic geometry.

(Jiang 2020 )

Events Calendar

Using Math

CTE course transformation grant helps Emily Witt, assistant professor of math, develop active learning with student groups in calculus.  Positive results using modules developed with Justin Lyle and Amanda Wilkens, math graduate students, were attained.  Read more

Math and COVID-19: Sources on how math is being used to track the virus and its spread.  AMS link.

A mathematician-musician's breakthrough melds East, West. Read more.

Researcher's innovative approach to flood mapping support emergency management and water officials. Read more.

Nicole Johnson found a way to express her baton twirling using math. See video.