My vote is no. We also present a non-arithmetic pair with identical invariants for which we cannot determine commensurability. Then the poster decides that the non-answer is embarassingly wrong and deletes it.

We prove a number of properties of positive graphs, including the fact that they have a homomorphic image which has at least half the original number of nodes but in which every edge has an even number of pre-images. So the wrong answer can stay safely deleted with no loss of information. The mod 2 homology of free spectral Lie algebras.

Our scripts also allow one to determine arithmeticity of such groups and the isomorphism class of the invariant quaternion algebra by analyzing its ramification. Are they more pathetic than I meant for them to be. SemenoffDaniel Sheinbaum. For pairs of groups with identical invariants, not all is lost: CommentTimeNov 5th Anton and Willie: Also, may I Anton geraschenko thesis that said policy not extend to deleted answers.

The theory of compact nilspaces is a generalization of the theory of compact abelian groups. Should the commenter then post a separate answer saying something strange like, "One could make the following error, in which case If an answer has multiple contributors, I think any one of them should have the power to undelete it.

Should the commenter have a say in whether the answer show be resurrected. CommentTimeNov 5th Anton and Ryan: In this situation, if I were the bonehead, I would opt to preserve the interaction as it happened. Then we show that finite dimensional compact connected nilspaces are nilmanifolds. Because of his rather insightful comment.

The results, combined with a computer program, imply that the conjecture is true for all graphs up to 9 nodes. We give a detailed structural analysis of abstract and compact topological nilspaces.

Research Classifying spaces for commutativity of low-dimensional Lie groups with Simon Gritschacher and Bernardo Villarreal. CommentTimeNov 5th WillieWong: Someone points out a trivial mistake in a comment, and then proceeds to give a rather technical description of the subtlety of the question and answer disclaimer: Recent developments in ergodic theory, additive combinatorics, higher order Fourier analysis and number theory give a central role to a class of algebraic structures called nilmanifolds.

We derive a rigorous classification of topologically stable Fermi surfaces of non-interacting, discrete translation-invariant systems from electronic band theory, adiabatic evolution and their topological interpretations.

We conjecture that all positive graphs can be obtained by taking two copies of an arbitrary simple graph and gluing them together along an independent set of nodes.

Adapting a definition of Behrens, we introduce mod 2 homology operations for algebras over this operad and prove these operations account for all the mod 2 homology of free algebras on suspension spectra of simply-connected spaces. We introduce nilspaces as structures satisfying a variant of the Host-Kra axiom system for parallelepiped structures.

Computational Mathematics Computing arithmetic invariants for hyperbolic reflection groups with Gregory R. Chromatic fracture cubes with Tobias Barthel. We present many computed examples of these invariants. You can email me at omar matem. We prove the conjecture for various classes of graphs including all trees.

For systems on a half-space and with a gapped bulk, our derivation naturally yields a K-theory classification. In the present paper we continue a program started by Host and Kra.

The commenter should be able to re-post whatever he wrote as a new answer. A simple universal property of Thom ring spectra with Tobias Barthel. The OP loses the ability to delete when there is an answer with at least two upvotes. Among various results it will be proved that compact nilspaces are inverse limits of finite dimensional ones.

Stacky Resolutions of Singular Schemes by Anton Geraschenko, David Rydh, and Shenghao Sun. I am grateful for many inspiring conversations with Arthur Ogus. Most of all, I am indebted to my advisor, Martin Olsson, whose inﬂuence is present Although the following is not the main point of the thesis, it should nonetheless be mentioned.

Anton Geraschenko: Empirical observation says the kids were right and I was wrong. The sun is currently well below the horizon, and the moon is about 35 degrees above the horizon (plenty high) as a fairly narrow crescent.

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Thesis by Michel van Garrel In Partial Ful llment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Anton Geraschenko, Daniel Halpern-Leistner, Hadi Hedayatzadeh, Cl ement Hongler, Brian Hwang, Khoa Nguyen, Rom Rains, Mark Shoemaker, Zhiyu Tian, Nahid Walji, Tony Wong and Gjergji Zaimi.

v. Anton Geraschenko The purpose of this paper and its sequel is to introduce and develop a theory of toric stacks which encompasses and extends several notions of toric stacks defined in the.

Stacky Resolutions of Singular Schemes by Matthew Bryan Satriano Doctor of Philosophy in Mathematics University of California, Berkeley Professor Martin C. Olsson, Chair Given a singular scheme Xover a ﬁeld k, we consider the problem of resolving the singularities of Xby an algebraic stack.

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