London Number Theory Seminar
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London Number Theory Seminar |
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The London Number Theory Seminar is held weekly during term times. The site rotates between KCL, Imperial College and UCL.
This term, the seminar will be hosted by University College and will be held on Wednesdays from 4 pm to 5 pm in room 707 of the Department of Mathematics. This term's organiser is Andrei Yafaev.
The seminar is preceded by the Study Group on "Motivic L-functions" from 14:00 to 15:30 in room 707.
| 13 January | Michael Schein "On families of irreducible supersingular mod p representations of GL_2(F)" |
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| 20 January | Mathieu Florence (Paris) "Equivariant birational geometry of Grassmannians" Abstract: Let k be a field, and A a finite-dimensional k-algebra. Let d be an integer. Denote by Gr(d,A) the Grassmannian of d-subspaces of A (viewed as a k-vector space), and by GL_1(A) the algebraic k-group whose points are invertible elements of A. The group GL_1(A) acts naturally on Gr(d,A) (by the formula g.E=gE). My aim is to study some birational properties of this action. More precisely, let r be the gcd of d and dim(A). Under some hypothesis on A (satisfied if A/k is etale), I will show that the variety Gr(d,A) is birationally and GL_1(A)-equivariantly isomorphic to the product of Gr(r,A) by an affine space (on which GL_1(A) acts trivially). By twisting, this result has a few corollaries in the theory of central simple algebras. For instance, let B and C be two central simple algebras over k, of coprime degrees. Then the Severi-Brauer variety SB(B \otimes C) is birational to the product of SB(B) \times SB(C) by an affine space of the correct dimension. These corollaries are in the spirit of Krashen's generalized version of Amitsur's conjecture. |
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| 27 January | Fernando Villegas (Texas) "Hypergeometric motives" |
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| 3 February | Toby Gee (Harvard) "The Sato-Tate conjecture for Hilbert modular forms" Abstract: I will discuss the Sato-Tate conjecture for Hilbert modular forms, which I recently proved in collaboration with Thomas Barnet-Lamb and David Geraghty. |
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| 10 February | Jonathan Pila (Bristol) "A model-theoretic approach to problems of Manin-Mumford-Andre-Oort-type" Abstract: I will describe a result, joint with Alex Wilkie, about the distribution of rational points on certain non-algebraic sets in real space. The natural setting is an 'o-minimal structure over the real numbers', a notion from model-theory. A surprising strategy, proposed by Umberto Zannier, uses this result to approach diophantine problems in the Manin-Mumford-Andre-Oort circle of conjectures. I will describe some implementations of this strategy, including an unconditional proof of the Andre-Oort conjecture for products of modular curves. |
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| 17 February | Frank Neumann (Leicester) "Moduli stacks of vector bundles on curves and Frobenius morphisms" Abstract: After giving a brief introduction into moduli problems and moduli stacks I will indicate how to calculate the l-adic cohomology ring of the moduli stack of vector bundles on an algebraic curve in positive characteristic and explicitly describe the actions of the various geometric and arithmetic Frobenius morphisms on the cohomology ring. It turns out that using the language of algebraic stacks instead of geometric invariant theory this becomes surprisingly easy. If time permits I will indicate how to prove some analogues of the classical Weil conjectures for the moduli stack. This is work in progress with Ulrich Stuhler (Goettingen). |
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| 24 February | Wansu Kim (Imperial) "tba" |
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| 3 March | Lawrence Breen (Paris) "tba" |
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| 10 March | Sarah Zerbes (Exeter) "Wach modules and Iwasawa theory for modular forms" |
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| 17 March | Cecile Armana (Paris/Barcelona) "tba" |
A list of previous seminar talks is here.
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