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| Feb 25 |
Tue |
Alex Torzewski (Kings) |
Number Theory seminar |
| 14:00 |
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How common is Galois complex multiplication?
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Hicks Seminar Room J11 / Google Meet |
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Abstract:
An elliptic curve over a characteristic zero field is said to have complex multiplication when its endomorphism ring is larger than Z ("E has extra endomorphisms"). Generic elliptic curves don't have complex multiplication. Similarly, when the Tate module of E has extra endomorphisms we say E has "Galois" complex multiplication. Over a number field, E has Galois complex multiplication if and only if it has complex multiplication. Over a local field this need not be the case. We investigate how often this happens via basic computations in p-adic Hodge theory.
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| Mar 4 |
Tue |
Jens Funke (Durham) |
Number Theory seminar |
| 14:00 |
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Indefinite theta series via incomplete theta integrals |
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Hicks Seminar Room J11 / Google Meet |
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Abstract:
Positive definite theta series have been a classical tool in the arithmetic of quadratic forms and also in the theory of modular forms. In comparison, the indefinite case has been less studied. In this talk we will explain how indefinite theta series naturally arise in the context of symmetric spaces of orthogonal type and discuss recent developments inspired by mathematical physics. This is joint work with Steve Kudla.
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| Mar 18 |
Tue |
Elena Collacciani (Padova) |
Number Theory seminar |
| 14:00 |
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Extending Local Langlands framework over finite fields: a conjecture by Vogan
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Hicks Seminar Room J11 / Google Meet |
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Abstract:
The Local Langlands correspondence establishes (conjecturally, in general) a surjective map from the set of smooth admissible representations of a p-adic group to the set of Langlands parameters. The fibers of this map, known as L-packets, are finite and are parametrized by the irreducible representations of a finite group associated with the corresponding Langlands parameter.
In 2020, Vogan proposed a conjecture extending this framework to representations of finite groups of Lie type, aiming for a parameterization compatible with the p-adic case. In this talk, we will provide a overview of Vogan's conjecture. We will focus on two leading examples: the case of Gln , where the conjecture has been established through the work of MacDonald, Silberger, and Zink, and the one of SLn, where further progress has been made in my own research.
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| Mar 25 |
Tue |
Rose Berry (UEA) |
Number Theory seminar |
| 14:00 |
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The Derived Unipotent Block of GLn(F) |
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Hicks Seminar Room J11 / Google Meet |
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Abstract:
Complex representations of p-adic groups are in many ways well-understood. The category has the Bernstein decomposition into blocks, and for many groups each block is known to be equivalent to modules over a Hecke Algebra. Over \bar{Fl} the situation is more complicated: the Bernstein Block decomposition can fail, and there is no longer in general an equivalence with the Hecke algebra. However, some groups, such as GLn and its inner forms, still have a Bernstein decomposition. Furthermore, Vigernas showed that the principal block of GLn(F) contains a subcategory that is equivalent to modules over a mild extension of the Hecke Algebra, the Schur Algebra, and this subcategory generates the principal block under extensions. Building on this work, we show that the derived category of the principal block is, in some cases, triangulated-equivalent to the perfect complexes over a dg-enriched Schur algebra. We prove this by combining general finiteness results about Schur algebras with the explicit structure of the unipotent blocks of the reductive quotient.
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| Apr 29 |
Tue |
Jenny Roberts (Bristol) |
Number Theory seminar |
| 14:00 |
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Hicks Seminar Room J11 / Google Meet |
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| May 6 |
Tue |
Miriam Norris (University of Manchester) |
Number Theory seminar |
| 14:00 |
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Hicks Seminar Room J11 / Google Meet |
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| May 13 |
Tue |
Roger Plymen (Manchester) |
Number Theory seminar |
| 14:00 |
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K-Theory and Langlands Duality |
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Hicks Seminar Room J11 |
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