BENJAMIN MERLIN BUMPUS

I do research at the nexus of mathematics and computer science in the Formal Analysis, Theory and Algorithms group under the supervision of Kitty Meeks . I study graph decompositions and graph connectivity in the context of parameterized algorithms. I am particularly interested in building a theory of decompositions for more general classes of objects than just finite simple graphs. My research involves a blend of graph theory and category theory.


Non-technical research summary: I am interested in finding ways of "splitting up" (decomposing) large objects into small parts in an algorithmically useful way. The idea is that, given some hard computational problem, we solve the problem on the parts and then deduce an answer on the whole.

I am finishing my PhD in 2021 and I am looking for Postdoctoral opportunities across Europe in the following areas:

-- graph theory (including digraphs, temporal graphs and infinite graphs)

-- parameterized complexity

-- graph decompositions

-- graph containment relations

-- graph homomorphisms



List of keywords: tree-width, branch-width, rank-width, clique-width, modular decompositions (directed variants of all of these as well), graph minors, graph immersions, vertex minors.

 
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RESEARCH

Here are my Orchid ID and my ResearchGate profile.

 

PUBBLICATIONS AND PRE-PRINTS


  • Spined categories: generalizing tree-width beyond graphs. [Bumpus, Kocsis] (2021+) Here we develop a general theory of categories that admit a functorial invariant called the triangulation functor which generalizes the tree-width of graphs. Our triangulation functor provides a uniform construction for various tree-width-like invariants including hypergraph tree-width, and the tree-width of the modular quotient in the category of modular partition functions.

  • Directed branch-width: A directed analogue of tree-width [Bumpus, Meeks, Pettersson] (submitted) We introduce a new digraph width measure called directed branch-width. To do this, we generalize a characterization of graph classes of bounded tree-width in terms of their line graphs to digraphs. We show that problems such as directed Hamilton path and Max-Cut (which are hard when parameterized by other known directed width measures) are in FPT when parameterized by directed branch-width. More generally, we obtain an algorithmic meta-theorem for the model-checking problem for a restricted variant of MSO2-logic on classes of bounded directed branch-width.

Past Research Experience: During my undergraduate degree at the University of Stirling, I undertook multiple posts as a research intern. These projects all had industrial and policy applications within the field of mathematical modeling for biology using techniques from evolutionary computing and metaheuristics under the supervision of: Anthony O'Hare, Jessica Enright and Adam Kleczkowski.

CONFERENCES

Organised

2020

2016

  • Stirling Graph Theory Spring School. Invited speakers: Jessica Enright, Kitty Meeks, John Faben.

Took part in (presentations):


2020

  • Karl-sruhe IT discrete math seminar


2019

2018

SUMMER SCHOOLS AND READING GROUPS

Organised

Attended

Reading Groups

AWARDS

  • 3.5 years EPSRC Doctoral Research Scholarship, University of Glasgow (value: £ 111,000)

  • Best in Europe (i.e. top 4% worldwide) in the MCM mathematical modelling competition

  • Prize for An outstanding Performance in the Final Year of a Mathematics Degree

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OUTREACH

 

PWSAFRICA

I was part of organizing and tutoring team of Programming Workshop for Scientists in Africa.  The team memebers I worked with are: Sofiat Olaosebikan (the project founder) Tom Wallis, Fionnuala Johnson, Fatma Elsafoury, Ifeoma Okoh, Paul John and Alexandrina Pancheva.

  • In 2019 I was the course coordinator for our course in Kigali, Rwanda. I developed the curriculum for the two-week long Python programming workshop. The workshop was delivered in a “Project-Based Learning” style inspired by textbooks such as Lovász’s “Combinatorial Problems and Exercises”. The workshop was a huge success with students who had never programmed before being able to understand and write a small language interpreter within only two weeks. (The credit should go to the students, though!). You can find the course materials HERE.

  • In 2018 we went to Ibadan, Nigeria. If you are interested in reading more about this experience, then you should read the article I wrote for the March 2019 edition of the London Mathematical Society Newsletter!

TUTOR FOR PROJECT GRASP

Project Grasp is an initiative targeting students from local Glasgow high schools, organised at the University of Glasgow by Adam Kurkiewicz, Jordan Baillie and Samko Gurský in partnership with Skyscanner.

UNIVERSITY OF GLASGOW

Supervision:

  • Rory Barnett. Undergraduate Dissertation on "Finding k-blocks in practice". A k-block describes a highly connected vertex-set in a graph. Rory implemented an algorithm described in a paper by Carmesin, Diestel, Hamman and Hudtermark which finds all k-blocks in a graph (either for all k or for fixed k).

Tutor:

  • ALGORITHMS & DATA STRUCTURES 2

  • ALGORITHMS AND DATA STRUCTURES (Masters level)

EDUCATION

 

September 2017 - May 2021

PHD CANDIDATE

I am a PhD candidate in the School of Computing Science at the University of Glasgow. Here I am part of the "Formal Analysis, Theory and Algorithms" research group. It's a vibrant and active group which you (yes you!) should visit!

September 2013 - June 2017

B.SC. (HONOURS) MATHEMATICS AND ITS APPLICATIONS, FIRST-CLASS

I was awarded the Prize for An outstanding Performance in the Final Year of a Mathematics Degree. In Stirling I worked as a summer research intern with Anthony O'Hare, Jessica Enright and Adam Kleczkowski. They are all lovely people who do lots of intersting work, so I encourage you to seek them out if you are interested in their research!

September 2008 - June 2013

Upon graduating I became a certified "Perito Agrario" ("Agronomist" in English).

BIO

I am half Italian and half US-American. I was born and raised in Italy (except for half a decade or so during which I lived in Florida) and I moved to Scotland to pursue higher education.

Given my current area of work, many would be surprized to know that I am a certified "Perito Agrario" ("Agronomist" in English). This of course means that I have a passion for agriculture and related topics.
If I'm not in my office, you can probably find me in the Botanic Gardens! Although you should probably try peering through the many plants around my desk to make sure I'm really not there before you seek me out elsewhere. If you're looking for more conversation topics, try one of these: 

  • I love rock-climbing and bouldering,

  • I play the guitar and the mandolin.

 

GET IN TOUCH

Mailing Address:

Sir Alwyn Williams Building
University of Glasgow
Glasgow G12 8RZ
SCOTLAND
United Kingdom

Visiting address:

Room G161
Sir Alwyn Williams Building
Glasgow G12 8RZ
Scotland

 

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