CMC Algebra Seminar

Upcoming Seminars

2026. 7. 8 (Wed) 16:00-17:30  Room Online
Lambert A'Campo (IHES)

Local-global compatibility at l=p for automorphic Galois representations over CM fields

ABSTRACT. In joint work with Hevesi, Thorne and Whitmore we prove that the Galois representations associated with cohomological cuspidal automorphic representations over CM fields are potentially semi-stable and compatible with the local Langlands correspondence, up to semisimplification. The novelty of our work is that we make no assumptions on residual Galois representation. Our method relies on a bound on the torsion in the cohomology of certain Shimura varieties, which can be seen as a generalisation of the Caraiani-Scholze vanishing theorem. (Zoom link: https://researchseminars.org/seminar/HCMCAlg)

2026. 7. 15 (Wed) 16:00-17:30  Room Online
Claudius Heyer (University of Paderborn)

On Second Adjointness for mod p Representations

ABSTRACT. The parabolic induction functor for smooth representations admits the Jacquet functor as a left adjoint. For complex representations it is a deep result of Bernstein, called Second Adjointness, that the Jacquet functor for the opposite parabolic is (up to a twist) also right adjoint to parabolic induction. A similar result is also known for mod ℓ≠p representations, yet for mod p representations the story is a bit more intricate. Due to recent work of Hoff–Meier–Spieß the (derived) right adjoint of parabolic induction is now fairly well understood. In this talk I will explain Second Adjointness for smooth mod p representations, which is joint work with Manuel Hoff, Sarah Meier and Michael Spieß. (Zoom link: https://researchseminars.org/seminar/HCMCAlg)

2026. 7. 22 (Wed) 16:00-17:30  Room Online
Douglas Molin (Chalmers University of Technology)

TBA

ABSTRACT. TBA

2026. 7. 29 (Wed) 16:00-17:30  Room Online
Reinier Sorgdrager (University of Paris-Saclay)

Gelfand-Kirillov bound for GL_2

ABSTRACT. Let G be a p-adic Lie group. In this talk I will introduce the Gelfand-Kirillov dimension of p-adic representations of G, which is a non-commutative generalization of the Krull dimension in this setting. For this, one uses Schneider-Teitelbaum's duality theory which allows one to think of p-adic Banach representations of G as (duals of) modules over a completed group ring of G.The ``Miracle Flatness'' observation Gee-Newton shows how knowledge of this dimension can have strong structural consequences, with potential applications to completed cohomology and patching. I will discuss the example of such an application found in the work of Breuil-Herzig-Hu-Morra-Schraen: as a consequence of their GK-dim computation they deduce the non-vanishing of the candidates via patching for the p-adic Langlands correspondence for GL_2 of an unramified p-adic field.I will then discuss the following result (arXiv:2602.08856): let p>2 and K be a p-adic field; an admissible p-adic Banach representation of GL_2K whose locally analytic vectors admit an infinitesimal character has GK-dimension at most [K:Q_p]. This bound is optimal and improves the previous bound <2[K:Q_p] of Dospinescu-Paškūnas-Schraen. In my thesis I have generalized this result to families of p-adic Banach representation with an infinitesimal character in families (in the sense of Dospinescu-Paškūnas-Schraen) and I will explain how this leads to a generalization of the GK-dim computation and non-vanishing of candidates result of Breuil-Herzig-Hu-Morra-Schraen to GL_2K where K now can have arbitrary ramification. (Zoom link: https://researchseminars.org/seminar/HCMCAlg)

Past Seminars

2026 Seminars
2025 Seminars
2024 Seminars
2023 Seminars

ORGANIZERS	Young-Hoon Kiem   -   Korea Institute for Advanced Study
	Chul-hee Lee   -   Korea Institute for Advanced Study
	Heejong Lee   -   Korea Institute for Advanced Study