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Quadratic Reciprocity immediate from basic algebraic number theory | Tom Lovering's Blog
https://tlovering.wordpress.com/2013/03/20/quadratic-reciprocity-immediate-from-basic-algebraic-number-theory
Tom Lovering's Blog. Quadratic Reciprocity immediate from basic algebraic number theory. March 20, 2013 in Mathematics. This is a quick note to record some thoughts following from Toby Gee’s first lecture of his course at the Arizona Winter School, where he observes that quadratic reciprocity is a completely immediate consequence of basic algebraic number theory. I feel rather silly for never having noticed this before, and hope I don’t insult the reader by providing a post on it. And thus equal to.
Seminar on p-adic Langlands spring 2014 | Tom Lovering's Blog
https://tlovering.wordpress.com/2014/04/07/seminar-on-p-adic-langlands-spring-2014
Tom Lovering's Blog. Seminar on p-adic Langlands spring 2014. April 7, 2014 in Mathematics. This blog post is a place to collect information about the Harvard number theory learning seminar spring 2014. We meet Mondays 4:15-6pm (actual times: if you run on Harvard time, we meet at 4:08) in SC 507. 2 introductory talks by Erick on the general p-adic Langlands program). 24/03 – Introduction, Completed cohomology and promodular representations (Rong). 07/04 – p-adic Langlands done correctly (Yihang). Mumfor...
Good reduction of Shimura varieties I: Introduction and motivation | Tom Lovering's Blog
https://tlovering.wordpress.com/2013/01/04/good-reduction-of-shimura-varieties-i-introduction-and-motivation
Tom Lovering's Blog. Good reduction of Shimura varieties I: Introduction and motivation. January 4, 2013 in Mathematics. In what I hope will become a series of posts, I want to think about the following question (to which, at the time of writing of this post, I have no idea of the complete answer). Given a Shimura datum. Giving rise to a Shimura variety. Defined over the number field. Have good reduction at. In this post we sketch the significance of this question in the theory of (nice) automorphic forms.
Galois Representations attached to Automorphic Representations | Tom Lovering's Blog
https://tlovering.wordpress.com/2013/02/11/galois-representations-attached-to-automorphic-forms
Tom Lovering's Blog. Galois Representations attached to Automorphic Representations. February 11, 2013 in Mathematics. This blog post is where I will put a talk list and notes from the graduate student seminar I am organising this semester at Harvard on attaching Galois representations to automorphic representations. I will try to keep it updated reasonably often, and any comments (either by email or left on the blog, whichever is more convenient) would be strongly appreciated. 8211; Jack Thorne (tbc).
Galois descent for transcendental extensions | Tom Lovering's Blog
https://tlovering.wordpress.com/2014/09/03/galois-descent-for-transcendental-extensions
Tom Lovering's Blog. Galois descent for transcendental extensions. September 3, 2014 in Mathematics. In this note, I want to discuss the work of Weil as presented in Milne’s papers (in particuar this one. Given a finite Galois extension. Of fields, many readers will be familiar with the usual “Galois descent” procedure giving an equivalence between (for example) affine varieties over. And affine varieties over. Which one can unravel and check implies that to give a. Action is to give a descent datum.
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The Sum of Primitive Roots of Unity | Yimin Ge's Maths Blog
https://yiminge.wordpress.com/2009/06/09/the-sum-of-primitive-roots-of-unity
Yimin Ge’s Maths Blog. Laquo; The Probability of Coprimality. Automorphism Groups of Simple Graphs. The Sum of Primitive Roots of Unity. Be the canonical primitive. Th root of unity. The identity. Is well known and easy to prove. One can now ask what happens if the sum is taken only over the primitive. Th roots of unity. Be the sum of all primitive. Th roots of unity. Since every. Th root of unity is a primitive. Th root of unity for some divisor. We have, for all positive integers. Function), hence,.
blameitontheanalyst.wordpress.com
Primes Less Than a Given Number (2) | Blame It On The Analyst
https://blameitontheanalyst.wordpress.com/2011/10/07/primes-less-than-a-given-number-2
Blame It On The Analyst. Primes Less Than a Given Number (2). 07/10/2011 in For Students. Sum of reciprocals of primes. In the previous post. We discussed the number of primes less than a given number and derived some very poor estimates for this quantity. In this post, using no extra technical machinery whatsoever, we derive a slightly better estimate. In Euclid’s proof, one constructs a number which is not divisible by any of the first. Has a prime factor. Not among the first. 8221; Call this number.
eventuallyalmosteverywhere.wordpress.com
Mentoring | Eventually Almost Everywhere
https://eventuallyalmosteverywhere.wordpress.com/mentoring
A blog about probability and olympiads by Dominic Yeo. Skip to primary content. I am a mentor for the UKMT’s Senior Mentoring Scheme. A brief description of the scheme and its aims can be found at the UKMT’s website here. Where there is also a link to the problem sheets, though it is generally a month or so behind. Modular Arithmetic – Beyond the Definitions. Fermat’s Little Theorem. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Create a free...
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Olympiad | Eventually Almost Everywhere
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A blog about probability and olympiads by Dominic Yeo. Skip to primary content. When I was younger, I was fortunate to have the opportunity to represent the United Kingdom at various international mathematics competitions, including the International Mathematical Olympiad. The competitions and the training that preceded them were certainly some of the most valuable experiences of my schooldays. The premier international competition is the IMO. Maintained by Joseph Myers. And Hong Kong 2016. Address never...
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Notes | Eventually Almost Everywhere
https://eventuallyalmosteverywhere.wordpress.com/notes
A blog about probability and olympiads by Dominic Yeo. Skip to primary content. 8211; Prof. A. Scott. Graduate Lecture Course) – complete as of 4/12/12. I haven’t proof-read this enormously carefully, so do let me know if there are any obvious (or otherwise) errors. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). You are commenting using your WordPress.com account. ( Log Out. Notify me of new comments via email.
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Eventually Almost Everywhere | A blog about probability and olympiads by Dominic Yeo | Page 2
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A blog about probability and olympiads by Dominic Yeo. Skip to primary content. Skip to secondary content. Newer posts →. Linear Algebra II: Eigenvectors and Diagonalisability. February 25, 2016. This post continues the discussion of the Oxford first-year course Linear Algebra II. We’ve moved on. And are now considering eigenvalues and eigenvectors of matrices and linear maps. A good question to ask is: what’s the point of knowing about eigenvectors? We could always choose the canonical basis in. Where D...
blameitontheanalyst.wordpress.com
For Mathematicians | Blame It On The Analyst
https://blameitontheanalyst.wordpress.com/for-mathematicians
Blame It On The Analyst. Enter your email address to subscribe to this blog and receive notifications of new posts by email. Join 57 other followers. Burt Totaro's Geometry Bulletin Board. Theorem of the week. Comments feed for this article. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). You are commenting using your WordPress.com account. ( Log Out. You are commenting using your Twitter account. ( Log Out.
March | 2009 | Yimin Ge's Maths Blog
https://yiminge.wordpress.com/2009/03
Yimin Ge’s Maths Blog. Archive for March, 2009. Some More Thoughts on r-Ary Functions over Finite Fields. March 20, 2009. Note, I proved that every. Ary function on a finite field. Elements can be represented by a unique polynomial. A more direct way to see this is, given a function. To consider the polynomial. The polynomial defined above. We know that. But can we find the exact value? For this purpose, consider the following very useful lemma. Be an integral domain and. Then for every integer. Being od...
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For Everyone | Blame It On The Analyst
https://blameitontheanalyst.wordpress.com/high-school
Blame It On The Analyst. Enter your email address to subscribe to this blog and receive notifications of new posts by email. Join 57 other followers. Burt Totaro's Geometry Bulletin Board. Theorem of the week. Comments feed for this article. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). You are commenting using your WordPress.com account. ( Log Out. You are commenting using your Twitter account. ( Log Out.
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For Students | Blame It On The Analyst
https://blameitontheanalyst.wordpress.com/for-students
Blame It On The Analyst. Enter your email address to subscribe to this blog and receive notifications of new posts by email. Join 57 other followers. Burt Totaro's Geometry Bulletin Board. Theorem of the week. Comments feed for this article. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). You are commenting using your WordPress.com account. ( Log Out. You are commenting using your Twitter account. ( Log Out.
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ramblings of a dabbler
Ramblings of a dabbler. July 17, 2015. Updated July 22, 2015. I recently had the fun opportunity to participate in the 23rd edition of SHARE. Organized by two writers, my friend Margaret Malone. Here’s the description from their website:. SHARE is a bi-monthly event in. Oregon that brings a. I’ll update this post when they put up. Check out their blog post of artists’ process and outcomes from SHARE 23. Below is my account of what I experienced. 8212;———. Wrote a bestseller, Newspaper Blackout. I brought...
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Tom Lovering's Blog | For Mathematical Musings
Tom Lovering's Blog. Cyclotomic Fields and Fermat’s Last Theorem Tutorial Notes and Problems. February 8, 2015 in Mathematics. During Spring Semester 2015 I am teaching an undergraduate course on “Cyclotomic Fields and Fermat’s Last Theorem” at Harvard. Meeting times and places are currently:. Mondays 4:15-5:45 in SC530. Wednesdays 4:30-6 in SC530. The latest edition of the notes is here: Cyclotomic Fields and FLT. Please email me any corrections. The problem sheets are below. Problem Sheet 1 (due Feb 24).
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