GAGTA 2019 Bar Ilan University, ISRAEL May 2019 | ||

Sunday, May 26, Nanotechnology building (bldg #206) | ||

09:30-10:00 | Registration | |

10:00-10:45 | Alexei Miasnikov (Stevens Institute of Technology, NJ) | Diophantine problem in finitely generated nilpotent and metabelian groups |

10:50-11:35 | Tatiana Smirnova Nagnibeda (U Geneva, Switzerland) | Spectral theory of groups and group actions (abstract) |

11:35-11:55 | Coffee break | |

11:55-12:40 | Nir Avni (Northwestern) | First order rigidity, biinterpretation, and higher rank lattices. (abstract) |

12:40-14:10 | Lunch break | |

14:10-14:55 | Zlil Sela (Hebrew U) | Basic conjectures and preliminary results in non-commutative algebraic geometry (abstract) |

14:55-15:15 | Coffee break | |

15:15-15:45 | Boaz Tsaban (Bar Ilan) | Nonabelian Cryptology and Algebraic Span Cryptanalysis (abstract) |

15:50-16:15 | Oleg Bogopolski (Heinrich Heine U, Dusseldorf) | Algebraically and verbally closed subgroups of groups: Equations in acylindrically hyperbolic groups (abstract) |

16:20-16:45 | Radhika Gupta (Utah) | Cannon-Thurston maps for CAT(0) groups with isolated flats (abstract) |

Monday, May 27, Nanotechnology building (bldg #206) | ||

10:00-10:45 | Susan Hermiller (U Nebraska) | Word problem solutions by finite state automata (abstract) |

10:45-11:05 | Coffee break | |

11:05-11:50 | Alex Lubotzky (Hebrew U) | Groups approximation, stability and high dimensional expanders (abstract) |

12:00-12:25 | Arie Levit (Yale) | Surface groups are flexibly stable (abstract) |

12:25-13:55 | Lunch break | |

Monday, May 27, Parallel Session 1 - Bldg 505, Room 61 | ||

13:55-14:20 | William Menasco (Buffalo) | Distance and intersection number in the curve complex (abstract) |

14:30-14:55 | Elizabeth Field (Illinois) | Trees, dendrites, and the Cannon-Thurston map (abstract) |

14:55-15:20 | Coffee break | |

15:20-15:45 | Javier de la Nuez González (U Basque) | Elementary equivalence of graph products of groups (abstract) |

15:55-16:20 | Boris Kunyavskii (Bar-Ilan University) | Wide simple groups and Lie algebras (abstract) |

Monday, May 27, Parallel Session 2 - Bldg 505, Room 62 | ||

13:55-14:25 | Simon Blackburn (Royal Holloway, U London) | The Walnut Digital Signature Algorithm (abstract) |

14:35-15:05 | Vladimir Shpilrain (CUNY) | Unconditionally secure public key transport (with possible errors) (abstract) |

15:05-15:25 | Coffee break | |

15:25-15:50 | Noam Kolodner (Hebrew U) | Algebraic extensions in free groups and Stallings graphs (abstract) |

16:00-16:10 | Adi Ben-Zvi (Bar Ilan) | The simultaneous conjugacy problem in right-angled-artin groups (abstract) |

16:15-16:25 | Ivan Levcovitz (Technion) | Comparing the Roller and B(X) boundaries of CAT(0) cube complexes (abstract) |

Monday, May 27, Parallel Session 3 - Bldg 505, Room 63 | ||

13:55-14:20 | Doron Puder (Tel Aviv) | Group theory at the service of Number theory: the case of Markoff triples (abstract) |

14:30-14:55 | Oren Becker (Hebrew U) | Group theoretic stability (abstract) |

14:55-15:20 | Coffee break | |

15:20-15:45 | Curtis Kent (Brigham Young, UT) | Metrics on fundamental groups (abstract) |

15:50-16:00 | Itay Glazer (Weizmann) | On uniform behavior of families of random walks induced by word maps (abstract) |

16:05-16:15 | Artem Shevlyakov (Russian Acad Sci) | Group equations with automorphisms. (abstract) |

16:20-16:30 | Becca Winarski (Michigan) | Twisted rabbits and invariant trees (abstract) |

Tuesday, May 28, Brain Science Building (bldg #901) | ||

10:00-10:45 | Gilbert Levitt (Caen) | On the first order theory of Baumslag-Solitar groups (abstract) |

10:45-11:05 | Coffee break | |

11:05-11:50 | Alexei Kanel-Belov (Bar Ilan) | Weil algebra and polynomial symplectoeutomorphisms (abstract) |

12:00-12:25 | Alejandra Garrido (Newcastle, Australia) | Locally compact topological full groups of Cantor set homeomorphisms (abstract) |

12:25-12:25 | FREE AFTERNOON | |

Wednesday, May 29, Brain Science Building (bldg #901) | ||

10:00-10:45 | Karen Vogtmann (Warwick) | The rational Euler characteristic of Out(F_{n}) (abstract) |

10:45-11:05 | Coffee break | |

11:05-11:50 | Aner Shalev (Hebrew U) | Words, probability and representations (abstract) |

12:00-12:25 | Olga Kharlampovich (Hunter College CUNY) | First order properties of Group Algebras of Free and Limit Groups (abstract) |

12:35-13:25 | Emmy Noether Lecture by Gregory Lawler, 2019 Wolf Prize laureate | Random Fractals and Critical Phenomena (abstract) |

13:25-14:35 | Light lunch break | |

Wednesday, May 29, Parallel Session 1 - Bldg 505, Room 61 | ||

14:35-15:00 | Jean Pierre Mutanguha (Arkansas) | Hyperbolic Immersions of Free Groups (abstract) |

15:10-15:35 | Motiejus Valiunas (Southampton) | Acylindrical hyperbolicity of graph products (abstract) |

15:35-15:55 | Coffee break | |

15:55-16:20 | Soumya Dey (IISER Bhopal, India) | Generalized braid groups and their commutator subgroups (abstract) |

16:25-16:35 | Fabienne Chouraqui (Haifa) | Some approaches to the Herzog-Schonheim conjecture (abstract) |

16:40-16:50 | Alan Logan (Heriott-Watt U) | The Post Correspondence Problem for free groups (abstract) |

16:55-17:05 | Vladimir Remeslennikov (Newcastle) | Classification of torsion-free R-groups (abstract) |

Wednesday, May 29, Parallel Session 2 - Bldg 505, Room 62 | ||

14:35-15:00 | Bogdan Stankov (Ecole Normale Superieure) | Limit behaviour of random walks on Schreier graphs (abstract) |

15:10-15:35 | Daniel Woodhouse (Technion) | One-ended hyperbolic groups that are not abstractly co-hopfian (abstract) |

15:35-15:55 | Coffee break | |

15:55-16:20 | Chenxi Wu (Rutgers) | Kazhdan's theorem on metric graphs (abstract) |

16:25-16:35 | Stephan Tornier (U Newcastle, Australia) | One question to ask yourself about everything you do (abstract) |

16:40-16:50 | Tengiz Bokelavadze (Akaki Tsereteli State U, Kutaisi, Georgia) | Subgroup lattices and the Geometry of Halls W-power group (abstract) |

16:55-17:05 | Ji-Young Ham (Chung-Ang U, Seoul) | Golden ratio on nonorientable surfaces of odd genus (abstract) |

Wednesday, May 29, Parallel Session 3 - Bldg 505, Room 63 | ||

14:35-15:05 | Christophe Petit (U Birmingham and Oxford) | Rubik's for cryptographers: Babai's conjecture, hash functions and quantum gates (abstract) |

15:10-15:40 | Vitali Roman'kov (Omsk State U) | Cryptanalysis via linear algebra and protection against it (abstract) |

15:40-16:00 | Coffee break | |

16:00-16:25 | Ben Fine (Fairfield U) | The Axiomatics of Free group Rings (abstract) |

16:30-16:40 | Thibault Godin (Montpellier & Lorraine) | Mealy automata, groups and growth (abstract) |

16:45-16:55 | Gil Goffer (Weizmann Inst) | The conjugacy problem for almost automorphisms of a tree (abstract) |

Thursday, May 30, Brain Science Building (bldg #901) | ||

10:00-10:45 | Volodymyr Nekrashevych (Texas A&M) | Amenable torsion groups (abstract) |

10:45-10:50 | Alan Logan | GAGTA 2020 |

10:50-11:10 | Coffee break | |

11:10-11:55 | Eliyahu Rips / Agata Atkarskaya (Hebrew U / Bar Ilan) | A Group-like Small Cancellation Theory for Rings (abstract) |

12:05-12:50 | Ruth Charney (Brandeis) | Outer Space for RAAGs (abstract) |

12:50-14:20 | Lunch break | |

14:20-14:45 | Arman Darbinyan (ENS Paris) | On a problem of Collins about the word and conjugacy problems in groups (abstract, slides) |

14:55-15:40 | Arie Juhasz (Technion) | A solution of the word problem in even Artin groups (abstract) |

By order of appearance

Using techniques and concepts from geometric group theory and from low dimensional topology, we formulate concrete conjectures on the structure of these varieties, and prove preliminary results in the direction of these conjectures.

This talk is partially based on a joint work with Adi Ben-Zvi and Arkadius Kalka

As a corollary, we solve a problem of Myasnikov and Roman'kov from [2]. Note that verbal, algebraic, existential, and elementary types of closedness of subgroups in groups are being intensively studied in GGT and model theory. Let F(X) be the free group with infinite countable basis x

MAIN THEOREM. Let G be a finitely presented group and H a finitely generated subgroup of G. Suppose that H is acylindrically hyperbolic and does not have nontrivial finite normal subgroups. Then H is verbally closed in G if and only if H is a retract of G.

The condition that G is finitely presented and H is finitely generated can be replaced by the condition that G is finitely generated over H and H is equationally noetherian.

COROLLARY 1. (Solution of Problem 5.2 from [2]). Verbally closed subgroups of torsion-free hyperbolic groups are retracts.

Recall: A subgroup H of a group G is called algebraically closed in G if for any finite system of equations with coefficients in H, this system has a solution in G if and only if it has a solution in H.

Surprisingly, under some mild assumption, the notions of verbal closedness, algebraic closedness, and retractness become the same after taking free products. More precisely:

COROLLARY 2. Suppose that H is a finitely generated subgroup of a finitely presented group G. Then for any nontrivial finitely presented group A with |A|>2 the following conditions are equivalent.

(1) H*A is algebraically closed in G*A.

(2) H*A is verbally closed in G*A.

(3) H*A is a retract of G*A.

Note that for A=1, these conditions are not equivalent in general.

References: [1] O. Bogopolski, Equations in acylindrically hyperbolic groups and verbal closedness, 2018. [2] A.G. Myasnikov and V. Roman'kov (Verbally closed subgroups of free groups, J. of Group Theory, 17, no. 1 (2014), 29-40).

Based on joint projects with N. Corwin, G. Golan, A. Johnson, and Z. Sunic, with M. Brittenham and T. Susse, and with D. Holt, S. Rees, and T. Susse.

We answer some of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L

The strategy is via the notion of "stability" : some 2nd cohomology vanishing is proven to imply stability and some high dimensional expanders are used to give existance of non residually finite groups ( central extensions of some lattices in p-adic Lie groups) which are stable and hence cannot be approximated. All notions will be explained.

Based on joint works with M. De Chiffre, L. Glebsky and A. Thom and with I. Oppenheim.

This is a joint work with Nir Lazarovich and Yair Minsky.

This is joint work with Dan Margalit and additionally features joint work with Joan Birman and Dan Margalit.

In a similar vein, we say that a Lie algebra is wide if its derived algebra [L,L] contains an element which is not representable as a single Lie bracket. A natural question to ask is whether there exist wide simple Lie algebras. We present first examples of such Lie algebras.

This talk is based on a work in progress, joint with Andriy Regeta.

This is joint work with Mariya Bessonov and Dima Grigoriev.

This is joint work with Chen Meiri.

I will present a characterization of stability among amenable groups in terms of invariant random subgroups and discuss stability of Kazhdan groups and a quantitative aspect of stability.

Based on joint works with Alex Lubotzky, Andreas Thom and Jonathan Mosheiff.

After remaining open for 25 years, this problem was solved by Bartholdi-Nekyrashevych using iterated monodromy groups. In joint work with Belk, Lanier, and Margalit, we present an alternate solution using topology and geometric group theory that allows us to solve a more general problem.

My talk concerns recent progress made in the positive resolution of Kontsevich's conjecture, which states that, the procedure utilizes the following essential features. First, the Weyl algebra over an algebraically closed field of characteristic zero may be identified with a subalgebra in a certain reduced direct product (reduction modulo infinite prime) of Weyl algebras in positive characteristic -- a fact that allows one to use the theory of Azumaya algebras and is particularly helpful when eliminating the infinite series. Second, the lifting is performed via a direct homomorphism Aut W

(joint work with A. Elishev and J.-T. Yu)

Simple groups play an important role in the emerging theory of totally disconnected locally compact groups, especially the compactly generated ones.

I will report on some joint work with Colin Reid and Dave Robertson, where we study topological full groups (rather, piecewise full groups) that admit a non-discrete locally compact second countable topology. We show that all such groups are abstractly simple and their topology is determined by the group structure. Moreover, taking the piecewise full group of totally disconnected locally compact groups acting 'nicely' on a Cantor set yields many new examples of compactly generated, abstractly simple, totally disconnected locally compact (non-discrete) groups, akin to Neretin's group of almost automorphisms of a regular tree.

In this talk I will explicitly describe an action of a graph product on a space quasi-isometric to a tree, which gives an alternative way to prove acylindrical hyperbolicity of graph products. I will discuss some applications, including (but possibly not limited to) a proof that the property of being equationally noetherian is preserved under forming certain graph products.

In a number of monographs and papers, we have shown that in many systems of algebraic cryptography, where the platform group G is a subset in a linear space over a finite or infinite field, we can efficiently solve the computational Diffie-Hellman-like problems and hence to compromise the corresponding cryptographic systems. Other and in some points similar approach was established by Tsaban et al.

Also we discuss a {non-linear decomposition} attack that can be applied in many other cases, in particular, when the platform is a polycyclic group. We present two general schemes for which many schemes are specific realizations. One of these two schemes joins schemes based on two-side multiplications, the second scheme joins schemes based on automorphisms. The two mentioned above attacks show vulnerability of these two general schemes.

In the second part of the talk, we introduce a novel method that is resistant against linear algebra attacks. In particular, we propose an improved version of the famous Anshel-Anshel-Goldfeld algebraic cryptographic key-exchange scheme, that is in particular resistant against the Tsaban et al. linear span cryptanalysis. Unlike the original version, that based on the intractability of the simultaneous conjugacy search problem for the platform group, the proposed version is based on much more hard simultaneous membership-conjugacy search problem and needs to solve the membership problem for a subset of the platform group that can be easily and efficiently built as very complicated and without any good structure. A number of other hard problems should be previously solved by any intruder to start solving of the simultaneous membership-conjugacy search problem to obtain the exchanged key. We also show how this new approach can be used to improve many schemes based on the conjugacy search algorithmic problem.

Joint with Anthony Gaglione, Martin Kreuzer, Gerhard Rosenberger and Dennis Spellman.

We present a solution to the conjugacy problem for this group, which uses its unique dynamics when acting on the tree boundary. This is a work in progress, joint with Waltraud Lederle

Let a group $G$ be given by generators and defining relations. It is known that we cannot extract specific information about the structure of $G$ using the defining relations in general case. However, if this defining relations satisfy small cancellation conditions, then we possess a great deal of knowledge about $G$.

Let $kF$ be the group algebra of the free group $F$ over some field $k$. Assume $F$ has a fixed system of generators, then its elements are reduced words in these generators that we call monomials. Let $\mathcal{I}$ be ideal of $kF$ generated by a set of polynomials and let $kF / \mathcal{I}$ be the corresponding quotient algebra. Drawing inspiration from small cancellation conditions on a presentation of a group, we state conditions on these polynomials that enable a combinatorial description of the quotient algebra $kF / \mathcal{I}$, which is similar to a description of small cancellation quotients of the free group. So, the obtained object can be called a group-like small cancellation ring.

We suggest two possible applications of rings defined in the present work. It is known that finitely presented small cancellation groups are hyperbolic. Although the notion of hyperbolic ring does not yet exists, a structure theory developed in this work can be the first step towards a definition of a hyperbolic ring. Also it is known that construction of groups with exotic properties makes an extensive use of small cancellation theory and its generalizations. Generalizations of our approach allows to construct various examples of algebras with exotic properties.

This is a joint work with A. Kanel-Belov, E. Plotkin and E. Rips.