The 43rd ARTIN meeting will take place at the University of Leeds on the 6th and 7th March 2015. It will be funded by the London Mathematical Society and Glasgow Mathematical Journal Trust. This meeting is a "young" researchers meeting, aimed at postdocs and postgrads of all ages. The first talk will start at 2pm on the Friday and the last talk should finish at 1.15pm on the Saturday.
All talks take place in the MALL (Physics Research Deck 9.301).
- 14:00-15:00 Melanie de Boeck (Kent): The structure of Foulkes modules for the symmetric group The action of the symmetric group S_mn on set partitions of sets of size mn into n sets of size m gives rise to a permutation module called the Foulkes module. Structurally, very little is known about Foulkes modules, even over C. In this talk, we will introduce Foulkes modules and their twisted analogues before presenting some results which shed light on the irreducible constituents of the ordinary characters of twisted Foulkes modules. Time permitting, we will also discuss the modular structure of a certain twisted Foulkes module.
- 15:30-16:30 Oliver Goodbourn (York): Reductive pairs arising from representations Reductive pairs are embeddings of algebraic groups whose properties can often be exploited to salvage some of the nice behaviour observed in characteristic zero in the positive characteristic setting. I will define reductive pairs and discuss some results that motivate what will be the main point of the talk: an overview of some work on classifying when reductive pairs arise from representations of algebraic groups, beginning with the group SL_2.
- 16:45-17:45 Short talks session
- 09:30-10:30 Christopher Fish (Sheffield): Connected quantized Weyl algebras Connected quantized Weyl algebras are generalisations of the quantized Weyl algebras where generators can have quantized Weyl-like relations with more than one other generator. We give two descriptions of these, firstly a classification in terms of generators and relations as above, secondly in terms of the quantum cluster algebras arising from certain mutation periodic quivers, and then describe a few interesting properties of these rings. This talk will not assume any knowledge of (quantum) cluster algebras.
- 11:00-12:00 Nicholas Cooney (Lancaster): Quantum Multiplicative Hypertoric Varieties I will discuss a way of quantizing spaces called Multiplicative Hypertoric Varieties, where the quantizing parameter is a root of unity. This leads to a geometric description of module categories for some interesting algebras. The talk will focus on the algebraic aspects of these results. This is work done independently by Iordan Ganev.
- 12:15-13:15 Ilke Canakci (Leicester): Ptolemy relations in terms of modules over gentle algebras The well-known Ptolemy relations relate the four sides and two diagonals of a quadrilateral. In joint work with Schroll, we show that these relations give rise to short exact sequences between indecomposable modules over gentle algebras and use this result to address a longstanding problem for a class of gentle algebras, namely constructing a basis for the extension space between indecomposable modules. Our approach is new and uses cluster algebras and cluster categories associated to marked surfaces as well as so-called snake graph combinatorics. This talk does not require any background on cluster algebras.
The last hour on the Friday afternoon will be set aside for 5 minute talks from participants on their own area of research. These are a great way to find other people with similar research interests to yourself and excellent practice in presenting your research in a concise, accessible manner. If you would like to give one of these talks, please let us know when you register.
There will be a conference dinner at Hansa's (http://hansasrestaurant.com/) on the Friday night.
We have some funding available for travel/accommodation costs, which will be distributed on a first-come-first-served basis. Funding can be requested when you register (see link below).
The meeting will take place in the Physics Research Deck on the University of Leeds campus, which is about a 20 minute walk from Leeds train station. Please note that the usual maths building is closed for refurbishment this year, so even if you've been here before please check a campus map to make sure you know where you're going. Campus maps can be found here: http://www.leeds.ac.uk/site/custom_scripts/campus_map.php, and a maths-specific map is here: http://www.mathsstudents.leeds.ac.uk/fileadmin/user_upload/Current_Maths_UG_Students/Locations_leaflet.pdf
Please register here if you plan to attend: http://goo.gl/forms/Zs3W64HBrI