Algebraic Geometry Seminar
Fall 2008
Regular Day: Tuesday
Regular Time: 3:30PM - 4:30PM
Regular Location: LCB 222
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September 2 |
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September 9 |
Diane Maclagan
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I will describe joint work with Angela Gibney describing bounds on
the nef cones of varieties. These are obtained from suitable embeddings
of the varieties into toric varieties and use tropical techniques. Our
motivating example is the moduli space of stable rational genus zero
curves with n marked points.
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September 16 |
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September 23 |
Jaume Amorós
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A connected complex Lie group acting locally freely on a closed Kaehler
manifold must be abelian. After a review of holomorphic tangent vector
fields on such manifolds, I will present joint work with M. Manjarin
and M. Nicolau on the topology and classification of such manifolds.
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September 30 |
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October 7 |
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October 21 |
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October 28 |
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November 8 9 |
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November 10 3:00pm, LCB 225 |
Hsian-Hua Tseng
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Let G be a finite group. A G-gerbe over a space X may be
intuitively thought of as a fiber bundle over X with fibers being the
classifying space (stack) BG. In particular BG itself is the G-gerbe over a
point. A more interesting class of examples consist of G-gerbes over BQ,
which are equivalent to extensions of the finite group Q by G.
Considerations from physics have led to conjectures asserting that the
geometry of a G-gerbe Y over X is equivalent to certain "twisted" geometry
of a "dual" space Y'. A lot of progresses have be made recently towards
proving these conjectures in general. In this talk we'll try to explain
theses conjectures in the elementary concrete examples of G-gerbes over a
point or BQ.
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November 18 |
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November 21 See also: Comm. Algebra Seminar |
Maurice Rojas
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Hilbert's Tenth Problem (HTP) asks for an algorithm to decide the existence of integer solutions to arbitrary polynomial equations. HTP was solved in the negative by Davis, Putnam, Robinson, and Matiyasevich around 1970 and, about two decades later, Z. W. Sun proved that undecidability starts already with polynomials in 11 variables. However, while it is a simple matter to find all integer solutions for polynomials in 1 variable, the minimal number of variables where undecidability starts remains a mystery. Furthermore, effective bounds for the size of integer points on curves (when there are only finitely many) also remain unknown in complete generality.
We prove a result relating integer points on curves and 3-folds that provides evidence for undecidability starting at 3 variables. We then conclude with a refined result for a p-adic analogue of HTP in 1 variable. The latter result depends subtly on the distribution of primes in arithmetic progressions.
We assume no background in number theory.
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November 25 |
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December 9 |
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