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What are the simply connected surfaces? July 21, 2016. July 21, 2016. There is a full classification of open surfaces (noncompact surfaces without boundary); see here. The purpose of this post is to provide two proofs of that, one unnecessarily difficult and the other elementary. It’s straightforward to see than an orientation and Riemannian metric determine such an automorphism: let. Be the unique tangent vector orthogonal to. If and only if its Nijenhuis tensor. Then pick a sequence of regular values.

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What are the simply connected surfaces? July 21, 2016. July 21, 2016. There is a full classification of open surfaces (noncompact surfaces without boundary); see here. The purpose of this post is to provide two proofs of that, one unnecessarily difficult and the other elementary. It’s straightforward to see than an orientation and Riemannian metric determine such an automorphism: let. Be the unique tangent vector orthogonal to. If and only if its Nijenhuis tensor. Then pick a sequence of regular values.

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Assorted Details Following | assorteddetails.wordpress.com Reviews

https://assorteddetails.wordpress.com

What are the simply connected surfaces? July 21, 2016. July 21, 2016. There is a full classification of open surfaces (noncompact surfaces without boundary); see here. The purpose of this post is to provide two proofs of that, one unnecessarily difficult and the other elementary. It’s straightforward to see than an orientation and Riemannian metric determine such an automorphism: let. Be the unique tangent vector orthogonal to. If and only if its Nijenhuis tensor. Then pick a sequence of regular values.

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A different classification of surfaces | Assorted Details Following

https://assorteddetails.wordpress.com/2016/04/06/a-different-classification-of-surfaces

A different classification of surfaces. April 6, 2016. April 6, 2016. This is one of the surfaces on the following list: …”. While I like the combinatorics of the proof, it somehow doesn’t quite satisfy me, since the fact that every surface is a connected sum of tori and real projective planes is a result, rather than input – somehow what I find to be the key property of surfaces is just a bonus instead of something we see. I don’t really feel “why” the theorem is true. Its complement. Because. Is zero&#...

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The dimension barrier | Assorted Details Following

https://assorteddetails.wordpress.com/2015/05/06/the-dimension-barrier/comment-page-1

May 6, 2015. May 7, 2015. There is a curious phenomenon in geometric topology: some problems seem to get easier as you increase the dimension you’re looking at. The catchphrase is that “high dimensional topology is easy because you have more room to move around” – let’s see what this means. Dimensional topological (resp. smooth) Poincaré conjecture says that if a closed. Manifold is homotopy equivalent to. Then it is homeomorphic (resp. diffeomorphic) to. The question of determining the number of diffeom...

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A different classification of surfaces | Assorted Details Following

https://assorteddetails.wordpress.com/2016/04/06/a-different-classification-of-surfaces/comment-page-1

A different classification of surfaces. April 6, 2016. April 6, 2016. This is one of the surfaces on the following list: …”. While I like the combinatorics of the proof, it somehow doesn’t quite satisfy me, since the fact that every surface is a connected sum of tori and real projective planes is a result, rather than input – somehow what I find to be the key property of surfaces is just a bonus instead of something we see. I don’t really feel “why” the theorem is true. Its complement. Because. Is zero&#...

4

What are the simply connected surfaces? | Assorted Details Following

https://assorteddetails.wordpress.com/2016/07/21/what-are-the-simply-connected-surfaces

What are the simply connected surfaces? July 21, 2016. July 21, 2016. There is a full classification of open surfaces (noncompact surfaces without boundary); see here. The purpose of this post is to provide two proofs of that, one unnecessarily difficult and the other elementary. It’s straightforward to see than an orientation and Riemannian metric determine such an automorphism: let. Be the unique tangent vector orthogonal to. If and only if its Nijenhuis tensor. Then pick a sequence of regular values.

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Mike Miller | Assorted Details Following

https://assorteddetails.wordpress.com/author/assorteddetails

What are the simply connected surfaces? July 21, 2016. July 21, 2016. There is a full classification of open surfaces (noncompact surfaces without boundary); see here. The purpose of this post is to provide two proofs of that, one unnecessarily difficult and the other elementary. It’s straightforward to see than an orientation and Riemannian metric determine such an automorphism: let. Be the unique tangent vector orthogonal to. If and only if its Nijenhuis tensor. Then pick a sequence of regular values.

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ayoucis.wordpress.com

Archive by type | Hard Arithmetic

https://ayoucis.wordpress.com/archive-by-type

Below are the posts on this blogged sorted into their natural types. A computation a day. These posts are largely focused around just computing things, with little focus on background or intuition (outside of any very relevant to the problem). A Computation a Day: Compactly Supported Cohomology. A Computation a Day: the Brauer Group of a Number Ring. A Computation a Day: a Pullback Pushforward. A Computation a Day: a (Harder) Pullback Pushforward. Weird Example: Pullback of Noetherian is Not Noetherian.

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A computation a day: a (harder) pullback pushforward | Hard Arithmetic

https://ayoucis.wordpress.com/2016/09/27/a-computation-a-day-a-harder-pullback-pushforward

A computation a day: a (harder) pullback pushforward. We discuss the computation of. Are the obvious maps. A curious case of reverse engineering. Inspired mostly by the computation performed here. I wanted to see what. Looked like when embedding punctured. Why this is interesting to me is that the computations that Method 1 and Method 2 result in are (again, only for me) undoable. Then we can understand. As a direct limit of cohomology groups:. Travels over neighborhoods of. Are open balls around. Is the...

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alexyoucis | Hard Arithmetic

https://ayoucis.wordpress.com/author/alexyoucis

The Fontaine-Winterberger theorem: going full tilt. This is the first in a series of posts whose goal is quite ambitious. Namely, we will attempt to give an intuitive explanation of why the recent push of several prominent mathematicians (Fargues, Scholze, etc.) to ‘geometrize’ the ‘arithmetic’ local Langlands program is intuitively feasible (at least, why it seems intuitive to me! And, more to the point, to understand some of the major objects/ideas necessary to discuss it. Posted in Algebraic Geometry.

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Some notes on local/global Galois groups | Hard Arithmetic

https://ayoucis.wordpress.com/2016/09/19/some-notes-on-localglobal-galois-groups

Some notes on local/global Galois groups. While I’m posting things. Here are some notes that I wrote for a Galois representations learning seminar. I was tasked with giving the first talk about local fields, global fields, their Galois groups, and their connection. Trying to establish, via multiple analogies, a ‘geometric understanding’ of what. Is measuring with regards to. 8211;how it is studying the ‘local arithmetico-geometric data of a (punctured). Is the wild ramification group. I proof read these ...

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Some motivation for p-adic Hodge theory | Hard Arithmetic

https://ayoucis.wordpress.com/2016/11/02/some-motivation-for-p-adic-hodge-theory

Some motivation for p-adic Hodge theory. These are some notes that I wrote for a learning course at Berkeley–the goal being to understand the statement of the global Langlands conjecture. The goal of the talk (that these notes were written for) was, specifically, to motivate. Adic Hodge theory with an eye, in particular, towards where it might be useful in understanding the statement of Langlands. Posted in Algebraic Geometry. And tagged Compatible system. P-adic Hodge theory motivation. November 2, 2016.

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Some notes on automorphic representations | Hard Arithmetic

https://ayoucis.wordpress.com/2016/10/11/some-notes-on-automorphic-representations

Some notes on automorphic representations. I was asked to give a series of talks in an `automorphic representations’ learning seminar at Berkeley. Specifically, I was asked to talk about the local representation theory of. And aspects of the global representation theory of. These are ongoing but I thought I’d post my notes for the first two talks. The first is on the representation theory of. And the second is on the representation theory of. With a focus on the relationship to modular forms.

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Assorted Details Following

What are the simply connected surfaces? July 21, 2016. July 21, 2016. There is a full classification of open surfaces (noncompact surfaces without boundary); see here. The purpose of this post is to provide two proofs of that, one unnecessarily difficult and the other elementary. It’s straightforward to see than an orientation and Riemannian metric determine such an automorphism: let. Be the unique tangent vector orthogonal to. If and only if its Nijenhuis tensor. Then pick a sequence of regular values.

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