UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

January 24, 2017

939 Evans Hall

3:45PM: Monodromy and Log Geometry

Arthur Ogus

A proper semistable family over a disc gives rise to a smooth proper and saturated morphism $X/S$ of log analytic spaces over the log disc. We will explain how the underlying map of topological spaces $X_{top}/S_{top}$ can be recovered from the restriction $X_0/S_0$ of $X/S$ to the log point. We will also give simple formulas for the action of the monodromy and the differentials on the $E_2$ terms of the ``nearby cycles'' spectral sequence in terms of the log structure on $X_0/S_0$. This is joint work with Piotr Achinger.

5:00PM: The Degree of SO(n)

Madeline Brandt

In this talk, I will give a closed formula for the degree of the projective closure of SO(n) over an algebraically closed field of characteristic zero, and outline the proof of this result. I will also describe some symbolic and numerical techniques used for computing this degree for small values of n.

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