Short notes
Lecture series
- Modular curves and cyclotomic fieldsPDF
Lecture notes for the Arizona Winter School · 2018
Talks & slides
- Eisenstein cocycles and their specializationsPDF
ICMS workshop · 25 November 2024
- Eisenstein cocycles in motivic cohomologyPDF
CRM workshop · 19 October 2020
- Iwasawa modules of higher codimensionPDF
AMS · 22 March 2019
- Reciprocity maps with restricted ramificationPDF
AMS · 6 January 2017
- Eisenstein congruences in arithmetic and geometryPDF
UCLA colloquium · 22 October 2015
- The arithmetic of modular symbolsPDF
CMS Winter Meeting · 8 December 2014
- Iwasawa algebras and dualityPDF
BIRS · 6 March 2013
- Cup products and Selmer groups of reducible representationsPDF
CNTA X · 8 July 2008
- Reciprocity maps and p-adic L-functionsPDF
CNTA IX · July 2006
- Iwasawa theory for Kummer extensionsPDF
AMS · 7 January 2005
- Computations on Milnor K2 of integer ringsPDF
Schloss Dagstuhl · 17 May 2004
- The various faces of a pairing on p-unitsPDF
IU Bremen colloquium · May 2004
- Iwasawa theory and the Eisenstein idealPDF
Miami Winter School · 18 December 2003
- Massey products and ideal class groupsPDF
MPIM seminar · 27 August 2003
- Galois groups and restricted ramificationPDF
UCSB colloquium · February 2003
- Cup products and local embeddings of p-unitsPDF
Stark’s Conjectures conference · 9 August 2002
Computations of a pairing
- Magma routines for computing the pairingMagma
- Table of the pairing for p < 10000Data
- Table of the pairing for 10000 < p < 15000Data
- Table of the pairing for 15000 < p < 20000Data
- Table of the pairing for 20000 < p < 25000Data
- Magma routines used in determining nontriviality 1Magma
- Magma routines used in determining nontriviality 2Magma
- Output of nontriviality routines for p = 37Data
AI
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Prime gaps at most 182: application and analytic companions
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GPT-6 Astra (OpenAI), prompted by Romyar Sharifi · 4 September 2026