Peter Phelan Email & Phone Number

Galway, County Galway, Ireland

DGA Structures on Minimal Free Resolutions of Binomial Edge Ideals of Complete Graphs.PhD Thesis authored by Peter Phelan. Supervised by Prof. Emil Sköldberg - (Currently awaiting Viva).• Employed a method algebraic Morse theory to prove the existence of a DGA structure on the minimal free resolution of the initial ideal of the binomial edge ideal of a complete graph.• Wrote Python code implemented in SageMath to compute products and differentials of elements in the DGAs… Show more DGA Structures on Minimal Free Resolutions of Binomial Edge Ideals of Complete Graphs.PhD Thesis authored by Peter Phelan. Supervised by Prof. Emil Sköldberg - (Currently awaiting Viva).• Employed a method algebraic Morse theory to prove the existence of a DGA structure on the minimal free resolution of the initial ideal of the binomial edge ideal of a complete graph.• Wrote Python code implemented in SageMath to compute products and differentials of elements in the DGAs explicitly.• Proved the non-existence of a DGA structure on the minimal free resolution of the binomial edge ideals of complete graphs with five or more vertices when the ground field has characteristic 2 or 3. Proof was aided by computations carried out using Python.Parity Binomial Edge Ideals with Pure Resolutions.Research Article authored by Peter Phelan. Supervised by Prof. Emil Sköldberg.• Employed a method of induced subgraphs, and a method of long exact Tor sequences to determine graded Betti numbers of parity binomial edge ideals.• Proved that if the parity binomial edge ideal of a simple connected graph has a pure resolution, then the graph must be bipartite or an odd cycle.• Proved that the minimal free resolution of a parity binomial edge ideal is pure if and only if the corresponding graph is a complete bipartite graph, or a disjoint union of paths and odd cycles. Show less

Galway, County Galway, Ireland

Research Assistant for study on staff gender balance in Irish mathematical sciences departments,supported by HEA Gender Equality Enhancement Fund.• Analysed complex datasets in Excel and visualized insights through bar charts and other graphicalrepresentations using R programming.

Limerick, County Limerick, Ireland

• Design course and prepare lecture materials, such as notes, tutorial sheets, class tests and examinations for Abstract Algebra course.• Deliver lectures and tutorials, respond to mathematical questions posed by final year undergraduate students.• Share updates and lecture materials with students through Moodle.• Assess student learning by grading class tests and assignments, and providing students with feedback and assistance.

Galway, County Galway, Ireland

SUMS is a mathematical support service provided by NUI Galway. This service is aimed at 1st/2nd year students and students in Foundation/Access courses. Its purpose is to aid students in developing problem-solving skills and to progress independent learning, rather than providing solutions to problems.• Provide assistance to students through one-on-one tuition and open discussions with small groups in several areas of pure mathematics. These include: Calculus, Real and Complex Analysis… Show more SUMS is a mathematical support service provided by NUI Galway. This service is aimed at 1st/2nd year students and students in Foundation/Access courses. Its purpose is to aid students in developing problem-solving skills and to progress independent learning, rather than providing solutions to problems.• Provide assistance to students through one-on-one tuition and open discussions with small groups in several areas of pure mathematics. These include: Calculus, Real and Complex Analysis, Geometry, Linear Algebra and Topology. Show less

Galway, County Galway, Ireland

• Prepare and deliver tutorials, manage general queries and respond to mathematical questions posed by undergraduate mathematics students.• Assist with student evaluation by invigilating exams and grading continuous assessment.• Teaching Assistant for "Complex Analysis", "Fields and Applications", "Euclidean and Non-Euclidean Geometry", "Rings" and "Mathematics of Finance" in previous semesters.

Dublin City, County Dublin, Ireland

Research article authored by Daniel Mulcahy and Peter Phelan. Supervised by Prof. Vladimir Dotsenko. Supported by the Hamilton Trust Summer Internship Fund.• Studied the Young diagram method used to prove smoothness of Hilbert schemes of points in 2 dimensions. Expanded this method to the case of Hilbert schemes of points in 3 dimensions and nested Hilbert Schemes of points in 2 dimensions.• Proved that whenever the region between two diagrams at a point of a nested scheme is… Show more Research article authored by Daniel Mulcahy and Peter Phelan. Supervised by Prof. Vladimir Dotsenko. Supported by the Hamilton Trust Summer Internship Fund.• Studied the Young diagram method used to prove smoothness of Hilbert schemes of points in 2 dimensions. Expanded this method to the case of Hilbert schemes of points in 3 dimensions and nested Hilbert Schemes of points in 2 dimensions.• Proved that whenever the region between two diagrams at a point of a nested scheme is rectangular, the corresponding point is smooth. Formulated a counter example to exhibit that this condition is sufficient but not necessary.• Proved that whenever the horizontal layers of a Young diagram at a point of a three dimensional scheme are rectangular, the corresponding point is smooth.• Compiled research article using LaTeX and submitted preprint to ArXiv research repository. Delivered seminar and poster presentation on the results. Show less

Dublin City, County Dublin, Ireland

Research project authored by Daniel Mulcahy, Peter Phelan and Oisín Flynn-Connolly. Supervised by Prof. Sergey Mozgovoy. Supported by the Hamilton Trust Summer Internship Fund.• Investigated the construction of an abelian envelope of the category of quasi-parabolic vector bundles, and the extension of quasi-parabolic vector bundles to the category of quasi-parabolic coherent sheaves.• Proved that these two approaches yield equivalent categories. This result was already known but not… Show more Research project authored by Daniel Mulcahy, Peter Phelan and Oisín Flynn-Connolly. Supervised by Prof. Sergey Mozgovoy. Supported by the Hamilton Trust Summer Internship Fund.• Investigated the construction of an abelian envelope of the category of quasi-parabolic vector bundles, and the extension of quasi-parabolic vector bundles to the category of quasi-parabolic coherent sheaves.• Proved that these two approaches yield equivalent categories. This result was already known but not stated in the literature.• Compiled a report on the research using LaTeX. Delivered seminar and poster presentation on the results. Show less

Waterford, County Waterford, Ireland

• Provided tuition in Calculus and Linear Algebra to undergraduate students in preparation for repeat examinations.• Devised comprehensive study notes and designed helpful problem sets through LaTeX to aid in student learning.• Students were successful in their exams and progressed to the following academic year.

Waterford, County Waterford, Ireland

• Updated and balanced sales and purchases on Sage• Filed and organised sales and purchases ledgers• Sales queries and working with customers

Waterford, County Waterford, Ireland

• Handled technical support queries via landline• Customer Relations• Worked with Microsoft Word and Excel

Doctor Of Philosophy - Phd (Outcome Pending), Mathematics

Activities and Societies: • Committee member of SIAM, University of Galway Chapter (April 2022 - April 2024) • Postgraduate Representative.

B.A. Mathematics, Mathematics, Second Class Honours: 2.1

Activities and Societies: Mathsoc (Mathematics society), VTP (Voluntary Tuition Programme) Sophister Modules Include: Commutative Algebra.

Leaving Certificate, 545 Points

Activities and Societies: