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Exploring the works of Gilbert Baumslag | The Berstein Seminar, Spring 2015, Cornell Mathematics Department

The Berstein Seminar, Spring 2015, Cornell Mathematics Department

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Exploring the works of Gilbert Baumslag | The Berstein Seminar, Spring 2015, Cornell Mathematics Department | berstein2015.wordpress.com Reviews

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The Berstein Seminar, Spring 2015, Cornell Mathematics Department

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Algorithmic properties of nilpotent and residually torsion-free nilpotent groups | Exploring the works of Gilbert Baumslag

https://berstein2015.wordpress.com/2015/08/09/algorithmic-properties-of-nilpotent-and-residually-torsion-free-nilpotent-groups

Exploring the works of Gilbert Baumslag. The Berstein Seminar, Spring 2015, Cornell Mathematics Department. Direct decompositions of finitely generated torsion-free nilpotent groups →. Algorithmic properties of nilpotent and residually torsion-free nilpotent groups. August 9, 2015. The theme of this post is the word, conjugacy and isomorphism problems in nilpotent and residually torsion-free nilpotent (RTFN) groups. Definition 0 (lower central series). For group G, define. The lower central series is.

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March | 2015 | Exploring the works of Gilbert Baumslag

https://berstein2015.wordpress.com/2015/03

Exploring the works of Gilbert Baumslag. The Berstein Seminar, Spring 2015, Cornell Mathematics Department. Monthly Archives: March 2015. Nilpotent groups and a theorem of Mal’cev. March 23, 2015. Similar to this previous post, the theme of this post is another property, Property R. It is inspired by the this result on nilpotent groups: Theorem 1 (Mal’cev) Let be a finitely generated nilpotent group and a subgroup. Then is … Continue reading →. Free groups and Marshall Hall’s theorem. March 19, 2015.

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January | 2015 | Exploring the works of Gilbert Baumslag

https://berstein2015.wordpress.com/2015/01

Exploring the works of Gilbert Baumslag. The Berstein Seminar, Spring 2015, Cornell Mathematics Department. Monthly Archives: January 2015. Free products with amalgamation. January 30, 2015. In this post we describe a construction for building new groups from old. It will be a key tool for arguments in our next two posts. The ingredients are a pair of groups and with subgroups and , respectively, such … Continue reading →. What are combinatorial and geometric group theory? January 29, 2015.

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Direct decompositions of finitely generated torsion-free nilpotent groups | Exploring the works of Gilbert Baumslag

https://berstein2015.wordpress.com/2015/08/13/direct-decompositions-of-finitely-generated-torsion-free-nilpotent-groups

Exploring the works of Gilbert Baumslag. The Berstein Seminar, Spring 2015, Cornell Mathematics Department. Algorithmic properties of nilpotent and residually torsion-free nilpotent groups. Group Cryptography I: a public key cryptography system using the modular group →. Direct decompositions of finitely generated torsion-free nilpotent groups. August 13, 2015. This post is about two talks given by Gretchen Ostheimer. Given at Cornell on 04/21/2015 in the. Topology and Geometric Group Theory Seminar.

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August | 2015 | Exploring the works of Gilbert Baumslag

https://berstein2015.wordpress.com/2015/08

Exploring the works of Gilbert Baumslag. The Berstein Seminar, Spring 2015, Cornell Mathematics Department. Monthly Archives: August 2015. Group Cryptography II: Key Transport Protocols. August 26, 2015. Group Cryptography I: a public key cryptography system using the modular group. August 24, 2015. Direct decompositions of finitely generated torsion-free nilpotent groups. August 13, 2015. This post is about two talks given by Gretchen Ostheimer given at Cornell on 04/21/2015 in the Berstein Seminar and ...

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Almost all continuous functions are nowhere differentiable | Mathematical Notes

https://chiasme.wordpress.com/2013/05/18/almost-all-continuous-functions-are-nowhere-differentiable

On some mathematical topics I found interesting. Almost all continuous functions are nowhere differentiable. Is a Baire space if a countable intersection of open dense sets is still dense in. Then Baire category theorem consists in:. Baire) A complete metric space is a Baire space. It is a surprising consequence of Baire category theorem that almost all continuous functions are nowhere differentiable in the following sense: Let. Be the set of continuous functions. Endowed with the sup norm. Then, for all.

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Free groups acting on the circle | Mathematical Notes

https://chiasme.wordpress.com/2014/02/27/free-groups-acting-on-the-circle

On some mathematical topics I found interesting. Free groups acting on the circle. We present here an unusual application of Baire category theorem between topology, group theory and dynamical systems. Roughly speaking, we prove that almost all pairs of homeomorphisms of the circle are unrelated; in particular, it leads to natural occurrences of free groups. More precisely, if. Denotes the set of orientation-preserving homeomorphisms of the circle, endowed with the distance. The set of pairs. And show th...

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Amin Saied

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Here are notes taken during some graduate courses at Cornell. They were live-TeX-ed, so expect typos. Bernstein Seminar, Tim Riley. Exploring the works of Gilbert Baumslang. We are making a blog in parallel with this seminar [ blog. Seminar in Algebra, Tim Riley. The Geometry of Solvable Groups [ pdf. Bernstein Seminar, Karen Vogtmann. Moduli spaces and their compactifications [ pdf. Pdf] – From homological stability, to representation stability and FI-modules. And some pretty pictures to boot!

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Not all finitely-presented groups are fundamental groups of closed 3-manifolds | Mathematical Notes

https://chiasme.wordpress.com/2015/04/12/not-all-finitely-presented-groups-are-fundamental-groups-of-closed-3-manifolds

On some mathematical topics I found interesting. Not all finitely-presented groups are fundamental groups of closed 3-manifolds. In our previous note Amalgamated products and HNN extensions (IV): Markov properties. We saw that for every. And for every finitely-presented group. Dimensional closed manifold whose fundamental group is. However, such a result does not hold for. See for example the note On subgroups of surface groups. The present note is devoted to the 3-dimensional case. We say that the triple.

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Amalgamated products and HNN extensions (IV): Markov properties | Mathematical Notes

https://chiasme.wordpress.com/2014/05/28/amalgamated-products-and-hnn-extensions-iv-markov-properties

On some mathematical topics I found interesting. Amalgamated products and HNN extensions (IV): Markov properties. This is the fourth and last note of our series. Dedicated to constructions using amalgamated products and HNN extensions. Our main goal is to exhibit several insoluble decision problems in group theory, assuming that there exists a finitely-presented group with an insoluble word problem. Be a property of finitely presented groups. We say that. Be a finitely presented group satisfying. A HNN e...

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Another application of Baire category theorem | Mathematical Notes

https://chiasme.wordpress.com/2015/08/30/another-application-of-baire-category-theorem

On some mathematical topics I found interesting. Another application of Baire category theorem. There exist a large number of, sometimes surprising, applications of Baire category theorem. For instance, in this blog, we saw that. Two generic orientation-preserving homeomorphisms of the circle. Generate a non abelian free subgroup,. A generic continuous function. See the previous notes Free groups acting on the circle. And Almost all continuous functions are nowhere differentiable. Now, we want to prove:.

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On subgroups of surface groups | Mathematical Notes

https://chiasme.wordpress.com/2014/08/27/on-subgroups-of-surface-groups

On some mathematical topics I found interesting. On subgroups of surface groups. It is known that a closed (ie. connected, compact without boundary) surface is homeomorphic to a sphere or to a connected sum of finitely-many tori or projective spaces. Let. Denote the connected sum of. Tori (resp. projective spaces). Because. We easily deduce the Euler characteristics. Is a group isomorphic to the fundamental group of one of these surfaces. If. Is a surface group, two cases happens: either. Are homeomorphi...

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A prime as a sum of two squares | Mathematical Notes

https://chiasme.wordpress.com/2015/09/26/a-prime-as-a-sum-of-two-squares

On some mathematical topics I found interesting. A prime as a sum of two squares. In this note, we are interested in the following well-known result:. Can be written as the sum of two squares if and only if. There exist many different proofs of this theorem, but a surprising one is exposed by D. Zagier in his article. A one-sentence proof that every prime. Is a sum of two squares. Our note is dedicated to this proof. First of all, it is easy to prove that the sum of two squares is either congruent to.

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– | Mathematical Notes

https://chiasme.wordpress.com/groupe-de-travail

On some mathematical topics I found interesting. This content is password protected. To view it please enter your password below:. Enter your password to view comments. Exploring the works of Gilbert Baumslag. Gödel Lost Lettre and P=NP. Geometry and the Imagination. Here there be dragons. Create a free website or blog at WordPress.com.

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Some SQ-universal groups | Mathematical Notes

https://chiasme.wordpress.com/2015/02/26/some-sq-universal-groups

On some mathematical topics I found interesting. Whenever every countable group can be embedded into a quotient of. In some sense, SQ-universality is a “largeness property”. Motivating by this idea, we prove the two following properties:. A SQ-universal group contain a non-abelian free group (of countable rank). Be a SQ-universal group. In particular, there exists a quotient. Containing a free group of infinite rank. Be a lift of. If there existed a non-trivial relation between the. And the other, comple...

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Here there be dragons | Exploring the subgroups of non-positively curved groups

Here there be dragons. Exploring the subgroups of non-positively curved groups. Farewell (and what did we miss? July 7, 2011. 8220;I believe in everything until it’s disproved. So I believe in fairies, the myths, dragons.” — John Lennon. Our tour of subgroups of non–positively curved groups has reached its end. What did we miss? Probably lots — apologies to any aggrieved authors out there. Here are a couple of corners of the landscape that we are conscious of having failed to explore. July 3, 2011. Is a ...

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Exploring the works of Gilbert Baumslag | The Berstein Seminar, Spring 2015, Cornell Mathematics Department

Exploring the works of Gilbert Baumslag. The Berstein Seminar, Spring 2015, Cornell Mathematics Department. Group Cryptography II: Key Transport Protocols. August 26, 2015. Described one of Gilbert Baumslag’s contributions to group-theoretic cryptography; this, our final post, describes a second. It is based on a talk given at Cornell by Delaram Kahrobaei. On 5/5/2015. Gilbert was Delaram’s PhD advisor. Here they are in 2004 on the day she defended. In our previous post. Is alternative method. A prime.

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