Libra Lecture Series – Prof. Eknath Ghate
September 18 @ 3:00 pm – 4:00 pm
Libra Lecture Series, University of Maine Mathematics
Prof. Eknath Ghate, Visiting Libra Professor, University of Maine and TIFR Mumbai India
Title : Reductions of semi-stable representations using the Iwahori mod p LLC.
Lecture 1: Friday, September 18 at 3pm in 208 Neville Hall
Abstract: Semi-stable p-adic representations arise in nature when one takes the local Galois representations at p attached to newforms for which p exactly divides the level of the form and there is no character at p.
In this series of talks, we shall speak about an interesting alternating pattern that emerges when one computes the mod p reductions of semi-stable representations of weights k at most p+1. The method uses Langlands correspondences and works (in principle) for all weights k. The pattern leads to a proof of the zig-zag conjecture.
The plan is to:
1) State the main theorem about the alternating pattern
2) Introduce the Iwahori mod p Local Langlands Correspondence
3) Introduce some classical facts about p-adic functions on Q_p
4) Use these facts to define certain GL_2(Q_p)-Banach spaces
5) Show how to reduce these Banach spaces to prove the theorem.
This will be a teaching style series of talks mostly at the master’s level.
References:
1. A. Chitrao and E. Ghate: Reductions of semi-stable representations using the Iwahori mod p LLC, arXiv, v2 (2024).
2. E. Ghate: The semi-stable Langlands correspondence, IJPAM (2026).
