Workshop Open for Business
We will hold an Newton Gateway Open For Business Workshop “Pure Maths in the Age of AI” on 14th July. Please, check the workshop’s website.
Seminars
Seminars take place in EBS 2.65 from 11am. Tea and cakes will be served in the same room from 10.30am.
Monday 13th July
Speaker: Peiran Wu (KU Leuven)
Title: Managing bibliographic records with Autobib
Abstract: Autobib is an open-source command-line tool in beta release that helps you manage bibliographic records. It turns identifiers of articles and books into BibTeX entries by fetching the data from online, with support for arXiv, zbMATH, MathSciNet etc, as well as DOI and ISBN. Fetched records are cached locally and can be edited, given aliases, and merged. Autobib can also scan a TeX source file for citation keys and generate the BibTeX file one needs.
I will demonstrate how to use Autobib and how you can import your existing BibTeX entries into it. Bring your laptop to follow along.
Tuesday 14th July (NO SEMINAR)
Wednesday 15th July
Speaker: Hongyi Huang (HUN-REN Alfréd Rényi Institute of Mathematics)
Title: Simple groups, Sylow subgroups and intersections
Abstract: Given a finite group G and a prime p, when can we find two Sylow p-subgroups that intersect trivially? If G is simple, then a theorem of Mazurov and Zenkov from 1996 shows that this question has a positive answer for every prime p, and their proof uses earlier work on defect groups of p-blocks for simple groups of Lie type.
In this talk, we will apply a probabilistic approach to study the intersections of randomly chosen Sylow subgroups. For non-alternating simple groups, we will use this tool to verify a very recent conjecture of Lisi and Sabatini on “synchronised intersections” of Sylow subgroups. In addition, our approach allows us to give an independent proof of Mazurov-Zenkov theorem for these groups, and we are able to complete the proof of a strong form of a conjecture of Vdovin from 2002 on intersections of nilpotent subgroups of simple groups. Along the way, we establish new asymptotic results on the probability that two random Sylow p-subgroups in a simple group of Lie type have trivial intersection, complementing recent work of Diaconis et al. and Eberhard on symmetric and alternating groups.
Joint work with Tim Burness (Bristol).
Thursday 16th July
Speaker: Dibyendu Das (Indian Statistical Institute, Bangalore)
Title: Solvability of Automorphism Groups of Commutative Algebras and Isolated Hypersurface Singularities
Abstract: Let A be a finite-dimensional commutative associative algebra with unity over an algebraically closed field K, and let Aut_K(A) denote the group of all K-algebra automorphisms of A. In this talk, I will discuss the solvability of Aut_K(A) and its connections with isolated hypersurface singularities.
Friday 17th July
Speaker: Benjamin Martin (University of Aberdeen)
Title: Some applications of model theory to groups
Abstract: A theorem of Honda states that if G is a finite group, g is a commutator in G and a power g^r generates the same subgroup as g does, then g^r is also a commutator. Using the first-order Lefschetz Principle from model theory, one can show that the same result holds if G is a linear algebraic group over an algebraically closed field. I will sketch the proof of this result and discuss some model-theoretic questions related to solvable linear groups
Social activities
Tea and cakes will be served from 3pm every day in 4SW.6.18.
On Wednesday afternoon, we will go to the minigolf in Colchester Castle Park We will be in touch with participants
about it.
Participants
- Michael Bate
- Dominic Bunnett
- Elena Denisova
- Shuo Feng
- Sema Gunturkun
- Joshua Jackson
- Kanwal Khalid
- Mikko Korhonen
- Lufeng Li
- Alastair Litterick
- Runqi Liu
- Joseph Malbon
- Benjamin Martin
- Jesus Martinez-Garcia
- Bernhard Muehlherr
- Rachel Pengelly
- David Penman
- Cheryl Praeger
- Aluna Rizzoli
- Gerhard Roehrle
- Colva Roney-Dougal
- Charlotte Satchwell
- Harvey Sykes
- Adam Thomas
- Gerald Williams
- Billy Woods