Property (FA) is one of the `rigidity properties’ defined for groups, concerning the way a group can act on trees. We’ll take a look at why you might be interested in an action on a tree, what the property is, and then investigate which automorphism groups of free products have it.
The last decade or so has seen substantial progress in the theory of (outer) automorphism groups of right-angled Artin groups (RAAGs), spearheaded by work of Charney and Vogtmann. Many of the techniques used for RAAGs also apply to a wider class of groups, graph products of finitely generated abelian groups, which includes right-angled Coxeter groups (RACGs). In this talk, I will give an introduction to automorphism groups of such graph products, and describe recent developments surrounding the outer automorphism groups of RACGs, explaining the links to what we know in the RAAG case.
Snap-through buckling is a type of instability in which an elastic object rapidly jumps from one state to another. Such instabilities are familiar from everyday life: you have probably been soaked by an umbrella flipping upwards in high winds, while snap-through is harnessed to generate fast motions in applications ranging from soft robotics to artificial heart valves.
It is unnecessary to emphasize important place of algorithms in computer science. Many efficient and convenient algorithms are designed by borrowing or revising ancient mathematical algorithms and methods. For example, recursive method, exhaustive search method, greedy method, “divide and conquer” method, dynamic programming method, reiteration algorithm, circulation algorithm, among others.
From the perspective of the history of computer science, it is necessary to study the history of algorithms used in the computer computations. The history of algorithms for computer science is naturally regarded as a sub-object of history of mathematics. But historians of mathematics, at least those who study history of mathematics in China, have not realized it is important in the history of mathematics. Historians of Chinese mathematics paid little attention to these studies, mainly having not considered from this research angle. Relevant research is therefore insufficient in the field of history of mathematics.
The mechanization thought and algorithmization characteristic of Chinese traditional (and therefore, East Asian) mathematics, however, are coincident with that of computer science. Traditional Chinese algorithms, therefore, show their importance historical significance in computer science. It is necessary and important to survey traditional algorithms again from the point of views of computer science. It is also another angle for understanding traditional Chinese mathematics.
There are many things in the field that need to be researched. For example, when and how were these algorithms designed? What was their mathematical background? How were they applied in ancient mathematical context? How are their complexity and efficiency of ancient algorithms?
In the present paper, we will study the circulation structure in traditional Chinese mathematical algorithms. Circulation structures have great importance in the computer science. Most algorithms are designed by means of one or more circulation structures. Ancient Chinese mathematicians were familiar them with the circulation structures and good at their applications. They designed a lot of circulation structures to obtain their desirable results in mathematical computations. Their circulation structures of dozen ancient algorithms will be analyzed. They are selected from mathematical and astronomical treatises, and also one from the Yijing (Book of Changes), the oldest of the Chinese classics.
In this talk, I will present our recent progress collaborated with Prof. Gui-Qiang G. Chen and Prof. Paolo Secchi on two kinds of characteristic discontinuities: relativistic vortex sheets in three-dimensional Minkowski spacetime and multi-dimensional thermoelastic contact discontinuities.
A virtue of the special geometry underlying the string theory moduli space of Calabi--Yau manifolds is the existence of a canonical choice of moduli space coordinates. In heterotic theories, as much as we would desire it, there is no obvious choice of coordinates and so we should be covariant. I will discuss some issues in doing this.
1:15-2:15 Isoperimetric inequalities of Groups and Isoperimetric Profiles of surfaces - Panos Papazoglou
It is an interesting question whether Gromov's `gap theorem' between a sub-quadratic and a linear isoperimetric inequality can be generalized in higher dimensions. There is some evidence (and a conjecture) that this might be the case for CAT(0) groups. In this talk I will explain how the gap theorem relates to past work of Hersch and Young-Yau on Cheeger constants of surfaces and of Lipton-Tarjan on planar graphs. I will present some related problems in curvature-free geometry and will use these ideas to give an example of a surface with discontinuous isoperimetric profile answering a question of Nardulli-Pansu. (joint work with E. Swenson).
2:30-3:30 Title tba - Laura Ciobanu
Abstract tba
3:30-4:15 Tea/coffee
4:15-5:15 CAT(0) groups need not be biautomatic - Ian Leary
Ashot Minasyan and I construct (or should that be find?) examples of groups that establish the result in the title. These groups also fail to have Wise's property: they contain a pair of elements no powers of which generate either a free subgroup or a free abelian subgroup. I will discuss these groups.
The notion of a higher Segal object was introduces by Dyckerhoff and Kapranov as a general framework for studying (higher) associativity inherent
in a wide range of mathematical objects. Most of the examples are related to Hall algebra type constructions, which include quantum groups. We describe a construction that assigns to a simplicial object S a datum H(S) which is naturally interpreted as a "d-lax A-infinity algebra” precisely when S is a (d+1)-Segal object. This extends the extensively studied d=2 case.
