Jeffrey Manning


I am a Hedrick Assistant Professor (i.e. postdoc) in the UCLA math department.

Until June 2018, I was a Ph.D. student at the University of Chicago. My advisor was Matthew Emerton.

Broadly, I am interested in algebraic number theory and Langlands program. I primarily study modular and automorphic forms, Shimura varieties and Galois representations, with an emphasis on the Taylor-Wiles-Kisin patching method and automorphy lifting theorems.

I am (jointly with Niccolo' Ronchetti) organizing the UCLA number theory seminar. You can find a (partial) schedule of future talks here.


Contact Info:

Email: jmanning [at] math [dot] ucla [dot] edu
Mail: Jeffrey Manning
Math Sciences Building 6913
UCLA Mathematics Department
Los Angeles, CA 90095
Office: MS 6913
Office Hours: Math 61: Tuesday 3-4:30, Thursday 4:30-6

Papers:

  1. EZADS inputs which produce half-factorial block monoids.
    Semigroup Forum 90.3 (2015), pp. 775-799.
  2. Patching and Multiplicity 2k for Shimura Curves
    ArXiV version 2019
  3. New cases of Ihara's lemma for Shimura curves over totally real number fields. with Jack Shotton
    In preparation.

Expository writing:

This is an overview of the construction (due to Eichler and Shimura) of a two dimensional Galois representation associated to a weight two modular form (or more precisely, to a cuspform which is an eigenform for all of the Hecke operators). It is (a somewhat expanded version of) my topic proposal, which I wrote during the second year of my Ph.D. at UChicago.

This is an expanded version of the appendix to my thesis. It's roughly my attempt to present the commutative algebra behind the Taylor-Wiles-Kisin patching argument (one of the main tools used in the proof of Fermat's Last Theorem) as cleanly and systematically as possible, using the "ultrapatching" approach introduced by Scholze. It is very much a work in progress, and I hope to eventually expand it to include some of the more sophisticated uses of patching (e.g. patching functors, Ihara avoidance, the Calegari-Geraghty method etc.).


Teaching:

At UCLA: (websites on CCLE)

Math 110A: Abstract algebra (ring theory) (Fall 2018)
Math 11N: Gateway to Mathematics, Number theory (Winter 2019)
Math 115A: Linear algebra (Winter 2019)
Math 61: Introduction to Discrete Structures (Spring 2019)

At UChicago:

Math 15100: Calculus I (Fall 2014)
Math 15200: Calculus II (Winter 2015)
Math 15300: Calculus III (Spring 2015)
Math 19520: Math Methods for Soc. Sci (Fall 2015)
Math 19620: Linear Algebra (Winter 2016)
Math 19520: Math Methods for Soc. Sci (Spring 2016)
Math 19520: Math Methods for Soc. Sci (Fall 2016)
Math 19620: Linear Algebra (Winter 2017)
Math 19520: Math Methods for Soc. Sci (Fall 2017)
Math 19620: Linear Algebra (Winter 2018)
Math 19520: Math Methods for Soc. Sci (Spring 2018)