# CARMA Discrete Mathematics Seminar

## 3:00 pm

## Thursday, 31^{st} Jul 2014

**V129, Mathematics Building**

# Prof Brian Alspach

(CARMA, The University of Newcastle)*A graph theory research project*

I shall be describing a largely unexplored concept in graph theory which is, I believe, an ideal thesis topic. I shall be presenting this at the CIMPA workshop in Laos in December.

# PhD Confirmation Seminar

## 10:00 am

## Thursday, 7^{th} Aug 2014

**V206, Mathematics Building**

# Cyriac Grigorious

(The University of Newcastle)*Conditional Resolvability of Graphs*

We give some background to the metric basis problem (or resolving set) of a graph. We discuss various resolving sets with different conditions forced on them. We mainly stress the ideas of strong metric basis and partition dimension of graphs. We give the necessary literature background on these concepts and some preliminary results. We present our new results obtained so far as part of the research during my candidature. We also list the research problems I propose to study during the remainder of my PhD candidature and we present a tentative timeline of my research activities.

# CARMA Seminar

## 4:00 pm

## Thursday, 7^{th} Aug 2014

**TBA,**

# Laura Ciobanu

(University of Neuchatel)*Equations in groups*

The Diophantine Problem in group theory can be stated as: is it algorithmically decidable whether an equation whose coefficients are elements of a given group has at least one solution in that group?

The talk will be a survey on this topic, with emphasis on what is known about solving equations in free groups. I will also present some of the algebraic geometry over groups developed in the last 20 years, and the connections to logic and geometry. I will conclude with results concerning the asymptotic behavior of satisfiable homogeneous equations in surface groups.

# CARMA Colloquium

## 4:00 pm

## Thursday, 7^{th} Aug 2014

**V205, Mathematics Building**

# Dr Mike Meylan

(CARMA, The University of Newcastle)*TBA*

# CARMA Colloquium

## 4:00 pm

## Thursday, 14^{th} Aug 2014

**V206, Mathematics Building**

# Volker Diekert

(University of Stuttgart)*Conjugacy in Baumslag's group, generic case complexity, and division in power circuits*

In my talk I will report on a recent joint work with Alexei Myasnikov and Armin Weiss which was presented at the conference LATIN 2014 in Montevideo. The motivation stems from algorithmic group theory. It concerns the conjugacy problem for two prominent groups: the Baumslag-Solitar group BS(1,2) and the Baumslag's group BG(1,2). The groups are quite different although the second one, B(1,2) is still a one-relator group and obtained by a single HNN extension of the Baumslag-Solitar group BS(1,2) The word problem and the conjugacy problem in the Baumslag-Solitar group is easy, but this does not transfer to BG(1,2).

Our main result shows that conjugacy in BG(1,2) can be solved in polynomial time in a strongly generic setting. The result is surprising because our algorithm has non-elementary average case complexity; and we conjecture that this is the best we can expect. This is interesting in a broader sense since it relates a natural conjugacy problem in algorithmic group theory to integer division in power circuits. A power circuit is a data structure which allows to represent huge numbers involving tower functions by small graphs. Actually, the complexity of the division problem in power circuits is an open and interesting problem in arithmetic.

# AMSI Event

*EViMS 2: Effective use of Visualisation in the Mathematical Sciences*

## 9:00 am

## Friday, 21^{st} Nov 2014

[Australian National University]The Mathematical Sciences Institute will host a three day workshop on more effective use of visualization in mathematics, physics, and statistics, from the perspectives of education, research and outreach. This is the second EViMS meeting, following the highly successful one held in Newcastle in November 2012. Our aim for the workshop is to help mathematical scientists understand the opportunities, risks and benefits of visualization, in research and education, in a world where visual content and new methods are becoming ubiquitous.

Visit the conference website for more information.

# External Event

*2014 ANZAMP annual meeting*

## 9:00 am

## Monday, 8^{th} Dec 2014

[The University of Melbourne]The annual meeting of the Australian and New Zealand Association of Mathematical Physics will be incorporated into the 8th Australia New Zealand Mathematics Convention at the University of Melbourne. For details, please visit the convention website.

# AMSI Event

*AMSI Summer School in the Mathematical Sciences*

## 9:00 am

## Saturday, 3^{rd} Jan 2015

Details will be available later.

# External Event

*Spring School on Variational Analysis VI*

## 9:00 am

## Sunday, 19^{th} Apr 2015

[Paseky nad Jizerou]Ffollowing a longstanding tradition, the Faculty of Mathematics and Physics of Charles University in Prague and the Academy of Sciences of the Czech Republic will organize the Spring School on Variational Analysis VI. The School will be held in Paseky nad Jizerou, in a chalet in the Krkonose Mountains, April 19 - 25, 2015. The program will consist of series of lectures on Variational Analysis and its Applications.

The lectures will be given by

- Jonathan M. Borwein (The University of Newcastle, Australia)

Theory and Applications of Convex and Non-convex Feasibility Problems - Marian Fabian (Academy of Sciences of the Czech Republic)

Separable Reductions and Rich Families in Theory of Frechet Subdifferentials - Alexander Ioffe (Technion, Haifa, Israel)

Variational Analysis and Optimization Theory - David Russel Luke (Georg-August-Universitaet Goettingen, Germany)

Variational Methods in Numerical Analysis

Further informations can be found on the website http://www.karlin.mff.cuni.cz/katedry/kma/ss/apr15.