I am a Postdoctoral Fellow at the Max Planck Institute for Mathematics. Until June 2018, I was a Ph.D. student at the University of Chicago. My advisor was Matthew Emerton. From 2018 to 2021 I was a Hedrick Assistant Professor (i.e. postdoc) at UCLA. 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. Here is my CV. |

Email: |
`manning` [at] `mpim-bonn` [dot] `mpg` [dot] `de` |
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Mail: |
Jeffrey Manning Office 307 Vivatsgasse 7 53111 Bonn Germany |

*EZADS inputs which produce half-factorial block monoids.*

Semigroup Forum 90.3 (2015), pp. 775-799.*Patching and Multiplicity 2*, Algebra and Number Theory Vol. 15 (2021), No. 2, 387-434^{k}for Shimura Curves

ArXiV version*Ihara's lemma for Shimura curves over totally real number fields via patching.*(with Jack Shotton), Math. Ann. 379 (2021), 187-234

ArXiV version*Wiles defect for Hecke algebras that are not complete intersections*, (with Gebhard Böckle and Chandrashekhar Khare), Compositio Mathematica 157 (2021), no. 9, 2046-2088

ArXiV version*Wiles defect of Hecke algebras via local-global arguments*, (with Gebhard Böckle and Chandrashekhar Khare),*submitted*

ArXiV version*Congruence modules and the Wiles-Lenstra-Diamond numerical criterion in higher codimensions*, (with Srikanth Iyengar and Chandrashekhar Khare),*submitted*

ArXiV version*Freeness of Hecke modules at non-minimal levels*, (with Srikanth Iyengar and Chandrashekhar Khare),*submitted*

ArXiV version*Mod l multiplicities in certain U(4) Shimura varieties*

*in preparation*

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 *(current version: December 2019)* 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, derived deformation rings and Hecke algebra, etc.).

Math 11N: Gateway to Mathematics, Number theory (Winter 2019)

Math 115A: Linear algebra (Winter 2019)

Math 61: Introduction to Discrete Structures (Spring 2019)

Math 61: Introduction to Discrete Structures (Fall 2019)

Math 11N: Gateway to Mathematics, Number theory (Winter 2020)

Math 32A: Calculus of Several Variables (Winter 2020)

Math 115B: Linear algebra (Spring 2020)

Math 215A: Commutative algebra (Fall 2020)

Math 110A: Abstract algebra (ring theory) (Winter 2021)

Math 110B: Abstract algebra (group theory) (Spring 2021)

Math 11N: Gateway to Mathematics, Number theory (Spring 2021)

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)