BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jun Su (University of Cambridge) DTSTART:20201013T133000Z DTEND:20201013T143000Z DTSTAMP:20260421T121543Z UID:CamNT/1 DESCRIPTION:Title: Au tomorphy of Hecke modules from geometry\nby Jun Su (University of Camb ridge) as part of Cambridge Number Theory Seminar\n\n\nAbstract\nCohomolog y of locally symmetric spaces/varieties and their compactifications make f undamental bridges between Galois and automorphic representations. While t hese cohomology groups have natural Hecke actions and connection to functi on spaces\, 1. if these Hecke modules are built up by automorphic represen tations (automorphy) and 2. which automorphic representations appear are b oth non-trivial questions in general. In this talk we’ll plug various in teresting cohomology groups into these questions\, while our main examples will be a. cohomology of automorphic local systems over locally symmetric spaces and b. automorphic vector bundles on locally symmetric varieties\, whose automorphy are proved in 1995 and 2018 respectively.\n LOCATION:https://researchseminars.org/talk/CamNT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Ashwin Iyengar (King's College London) DTSTART:20201027T143000Z DTEND:20201027T153000Z DTSTAMP:20260421T121543Z UID:CamNT/5 DESCRIPTION:Title: Fa milies of p-adic L-functions\nby Ashwin Iyengar (King's College London ) as part of Cambridge Number Theory Seminar\n\n\nAbstract\nI will discuss a formulation of a two-variable Iwasawa main conjecture over the normaliz ation of the N-new components of the extended eigencurve of tame level N\, building on previous work of David Hansen\, and will discuss some ideas a bout how to prove such a statement.\n LOCATION:https://researchseminars.org/talk/CamNT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Hanneke Wiersema (King's College London) DTSTART:20201110T143000Z DTEND:20201110T153000Z DTSTAMP:20260421T121543Z UID:CamNT/6 DESCRIPTION:Title: Mi nimal weights of mod p Galois representations\nby Hanneke Wiersema (Ki ng's College London) as part of Cambridge Number Theory Seminar\n\n\nAbstr act\nThe strong form of Serre's conjecture states that every two-dimension al continuous\, odd\, irreducible mod p representation of the absolute Gal ois group of $\\mathbb{Q}$ arises from a modular form of a specific minima l weight\, level and character. In this talk we use modular representation theory to prove the minimal weight is equal to a notion of minimal weight inspired by work of Buzzard\, Diamond and Jarvis. Moreover\, using the Br euil-Mézard conjecture we give a third interpretation of this minimal wei ght as the smallest k>1 such that the representation has a crystalline lif t of Hodge-Tate type $(0\, k-1)$. Finally\, we will report on work in prog ress where we study similar questions in the more general setting of mod $ p$ Galois representations over a totally real field.\n LOCATION:https://researchseminars.org/talk/CamNT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Graham (Imperial College London) DTSTART:20201124T143000Z DTEND:20201124T153000Z DTSTAMP:20260421T121543Z UID:CamNT/7 DESCRIPTION:Title: An ticyclotomic Euler systems for conjugate self-dual representations of $GL( 2n)$\nby Andrew Graham (Imperial College London) as part of Cambridge Number Theory Seminar\n\n\nAbstract\nAn Euler system is a collection of Ga lois cohomology classes which satisfy certain compatibility relations unde r corestriction\, and by constructing an Euler system and relating the cla sses to L-values\, one can establish instances of the Bloch--Kato conjectu re. In this talk\, I will describe a construction of an anticyclotomic Eul er system for a certain class of conjugate self-dual automorphic represent ations\, which can be seen as a generalisation of the Heegner point constr uction. The classes arise from special cycles on unitary Shimura varieties and are closely related to the branching law associated with the spherica l pair $(GL(n)\\times GL(n)\, GL(2n))$. This is joint work with S.W.A. Sha h.\n LOCATION:https://researchseminars.org/talk/CamNT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:George Boxer (ENS de Lyon) DTSTART:20210126T143000Z DTEND:20210126T153000Z DTSTAMP:20260421T121543Z UID:CamNT/8 DESCRIPTION:Title: Hi gher Coleman Theory\nby George Boxer (ENS de Lyon) as part of Cambridg e Number Theory Seminar\n\n\nAbstract\nThe goal of Higher Coleman Theory i s to introduce higher coherent cohomological analogs of overconvergent mod ular forms on Shimura varieties and to explain how they relate to classica l automorphic forms. We also discuss how they vary in p-adic families. Thi s is joint work with Vincent Pilloni.\n LOCATION:https://researchseminars.org/talk/CamNT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Lassina Dembélé (University of Luxembourg) DTSTART:20210209T143000Z DTEND:20210209T153000Z DTSTAMP:20260421T121543Z UID:CamNT/9 DESCRIPTION:Title: Se mistable abelian varieties with good reduction outside 73\nby Lassina Dembélé (University of Luxembourg) as part of Cambridge Number Theory Se minar\n\n\nAbstract\nIn this talk\, we describe all simple semistable abel ian varieties over $\\mathbf{Q}$\, with good reduction outside $73$\, up t o isogeny. Our classification depends on GRH.\n LOCATION:https://researchseminars.org/talk/CamNT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Justin Trias (University of East Anglia) DTSTART:20210223T143000Z DTEND:20210223T153000Z DTSTAMP:20260421T121543Z UID:CamNT/10 DESCRIPTION:Title: T owards an integral local theta correspondence: universal Weil module and f irst conjectures\nby Justin Trias (University of East Anglia) as part of Cambridge Number Theory Seminar\n\n\nAbstract\nThe theta correspondence is an important and somewhat mysterious tool in number theory\, with arit hmetic applications ranging from special values of L-functions\, epsilon f actors\, to the local Langlands correspondence. The local variant of the t heta correspondence is described as a bijection between prescribed sets of irreducible smooth complex representations of groups $G_1$ and $G_2$\, wh ere $(G_1\,G_2)$ is a reductive dual pair in a symplectic p-adic group. Th e basic setup in the theory (Stone-von Neumann theorem\, the metaplectic g roup and the Weil representation) can be extended beyond complex represent ations to representations with coefficients in any algebraically closed fi eld R as long as the characteristic of R does not divide p. However\, the correspondence defined in this way may no longer be a bijection depending on the characteristic of R compared to the pro-orders of the pair $(G_1\,G _2)$. In the recent years\, there has been a growing interest in studying representations with coefficients in as general a ring as possible. In thi s talk\, I will explain how the basic setup makes sense over an A-algebra B\, where A is the ring obtained from the integers by inverting p and addi ng enough p-power roots of unity. Eventually\, I will discuss some conject ures towards an integral local theta correspondence. In particular\, one e xpects that the failure of this correspondence for fields having bad chara cteristic does appear in terms of some torsion submodule in integral isoty pic families of the Weil representation with coefficients in B.\n LOCATION:https://researchseminars.org/talk/CamNT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Edna Jones (Rutgers University) DTSTART:20210309T143000Z DTEND:20210309T153000Z DTSTAMP:20260421T121543Z UID:CamNT/11 DESCRIPTION:Title: A n Asymptotic Local-Global Principle for Integral Kleinian Sphere Packings< /a>\nby Edna Jones (Rutgers University) as part of Cambridge Number Theory Seminar\n\n\nAbstract\nWe will discuss an asymptotic local-global princip le for certain integral Kleinian sphere packings. Examples of Kleinian sph ere packings include Apollonian circle packings and Soddy sphere packings. Sometimes each sphere in a Kleinian sphere packing has a bend (1/radius) that is an integer. When all the bends are integral\, which integers appea r as bends? For certain Kleinian sphere packings\, we expect that every su fficiently large integer locally represented everywhere as a bend of the p acking is a bend of the packing. We will discuss ongoing work towards prov ing this for certain Kleinian sphere packings. This work uses the circle m ethod\, quadratic forms\, and spectral theory.\n LOCATION:https://researchseminars.org/talk/CamNT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Xuhua He (Chinese University of Hong Kong) DTSTART:20210504T133000Z DTEND:20210504T143000Z DTSTAMP:20260421T121543Z UID:CamNT/12 DESCRIPTION:Title: A ffine Deligne-Lusztig varieties and Generalized affine Springer fibers \nby Xuhua He (Chinese University of Hong Kong) as part of Cambridge Numbe r Theory Seminar\n\n\nAbstract\nThe notion of affine Springer fiber was in troduced by Kazhdan and Lusztig in 1988. It plays a crucial role in the ge ometric representation theory and the Langlands program. The generalized a ffine Springer fibers were first studied by Kottwitz and Viehmann for the hyperspecial level structure in 2012 and by Lusztig for arbitrary parahori c level structure in 2015. Many geometric properties for the hyperspecial level structure were further studied by Bouthier and Chi.\n\nIn this talk\ , I will propose a new approach to study the generalized affine Springer f ibers. The key observation is that the affine Deligne-Lusztig varieties\, in some sense\, may be regarded as the ``shadow'' of generalized affine Sp ringer fibers. I will also explain some ingredients used to deduce some ge ometric properties (nonemptiness\, dimension\, irreducible components) of generalized affine Springer fibers from the properties of the affine Delig ne-Lusztig varieties. This talk is based a work in progress.\n LOCATION:https://researchseminars.org/talk/CamNT/12/ END:VEVENT END:VCALENDAR