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REU 2018
REU 2018
The inaugural year of the Northeastern REU had 9 undergraduate participants working in several different areas. The postdoc coordinator was Ivan Martino.
Student: Alon Duvall
Mentor: Brian Hepler
Title: Abstract Regular Polytope
Abstract: Introduction to Abstract Regular Polytopes through a combinatorial geometry approach. C-Groups, Coxeter Groups and 2^k-constructions are also studied.
Student: Kevin Su
Mentor: Jonier Antunes
Title: Graph Limits and Extremal Combinatorics
Abstract: "One of the problems in extremal combinatorics is asking how many edges a graph on n nodes may have while avoiding some specific subgraphs. For example, Mantel’s theorem says that the most edges a graph on n nodes can have while avoiding K_3 is n^2/4. These statements can also be represented in terms of inequalities of numbers of homomorphisms or in terms of homomorphism densities. Many of these inequalities may be proved using Cauchy-Schwarz (as an inequality on sums of squares) or pictorially due to a gluing algebra on the space of graphs. We summarize some of the graph algebra background involved here and look at how graph limit theory gives a way of proving results in extremal combinatorics."
Student: Timothy Jackman
Mentor: Whitney Drazen
Title: Graph Theory
Abstract: This is an introduction to spectral graph theory until the concepts of (quantum) state transfer.
Student: Felipe Castellano-Macias
Mentor: Alex Sorokin
Title: Leavitt Path Algebras
Abstract. We describe different properties of Leavitt path algebras of a graph over a field, providing the appropriate background. In addition, we investigate similar results about Leavitt path algebras of a graph over a commutative unital ring. We will mainly explore the connection between the diagonalizability of matrices over a given Leavitt path algebra and the structure of its underlying graph, as well as the classification of such algebras up to isomorphism.
Name: Benjamin Bonenfant
Mentor: Reuven Hodges
Student: Walker Miller-Breetz
Mentor: Rahul Singh
Title: Young Tableaux
Abstract: After a short introduction on group theory and group actions, the work focuses on the symmetric group and its action on flagged spaces.
Student: Christina Nguyen
Mentor: Whitney Drazen
Title: Non-backtracking Walks on Graphs
Abstract: The main goal of the REU was to obtain a new proof of the non-backtracking version of Ploya’s Theorem for random walks. We began with a discussion of spectral graph theory before studying the backtracking version of Ploya’s Theorem.
Student: Noah Lichtblau
Mentor: Mikhail Mironov
Title: On the Morphism of Schemes
Student: Zheying Yu
Mentor: Celine Bonandrini
Title: Topology
Faculty Organizer: Emanuele Macri
Image credit: Tom Ruen, Jaap Scherphuis’s Tiling Viewer, Robert Webb's Stella
Calendar
Calendar
Mon May 9, 9:30 AM: Kick Off Meeting
Wed May 18, 3-4 PM: Colloquium
Wed May 25, 3-4 PM: Colloquium
Fri June 3, 10 AM: Preliminary Presentations (20 min/group)
Wed June 8, 3-4 PM: Colloquium
Wed June 15, 3-4 PM: Colloquium
Fri Jun 24, 9 AM: Final Presentations (45 min/group)
Wed July 6: Final Paper Due
Final Paper: The jointly written paper should be at least 10 pages. Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof. No maximum page limit, but writing should be clear and concise.
Final Presentation: (45 min for each group) Should introduce audience to area of research, convince them it is interesting through examples, definitions and results. Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on. Narrative and slides and/or boardwork should be clear.
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