The algebraic geometry seminar in Term 3 2024/2025 will usually meet on Wednesdays at 3 pm, though we may sometimes change to allow speakers from other time zones.

Each talk will be either in B3.02 or MB0.07 -- see specific information below.

A link to talks from the previous term is here.

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Thursday 1 May 2025, 3pm. B3.03 Speaker: Ruadhaí Dervan (Glasgow/Warwick) (Note unusual time and location!)

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Wednesday 7 May 2025, 3pm. Speaker:

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Wednesday 14 May 2025, 3pm. Speaker: Stefano Mereta (KTH)

Title: The space of valuated preorders and the congruence spectrum of $S[x_1, \dots , x_n]$ as the spectrum of a ring

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In the late '60s, Hochster introduced the notion of spectral space and proved that every spectral space is the spectrum of a commutative ring. Unfortunately the proof of this fact is not constructive. More recently, Jun, Ray and Tolliver have proven constructively that every spectral space is the $k$-spectrum of an idempotent semiring, and that the congruence spectrum of an idempotent semiring is a spectral space.

In this talk we will introduce the notion of a valuated preorder on the monomials of $K[x_1, \dots , x_n]$ for a valued field $K$ and realise it, relying partially on work by Jóo and Mincheva, as the $k$-spectrum of a semiring, as the congruence spectrum of a polynomial semiring and, most importantly, as the spectrum of a commutative ring.

This commutative ring is constructed as the "unit ball" of respect a generalised Bézout valuation.

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Wednesday 21 May 2025, 3pm. Speaker:

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Wednesday 28 May 2025, 3pm. Speaker:

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Wednesday 4 June 2025, 3pm. Speaker:

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Wednesday 11 June 2025, 3pm. Speaker: Lisa Marquand (NYU)

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Wednesday 18 June 2025, 3pm. Speaker:

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Wednesday 25 June 2025, 3pm. Speaker:

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