Summer Math Research Program
This is the website for the Northeastern Summer Math Research Program (NSMRP), a paid summer program funded by the math department's Research Training Grant.
Other undergraduate math research opportunities at Northeastern.
Research Experience for Undergraduates
REU 2024
Additional funding for the Summer 2024 program was provided by the College of Science and Department of Mathematics.
Calendar
Mon May 6, 11:30 AM: Kick Off Luncheon
Thurs May 16, 2-3PM: Colloquium (Gabor Lippner)
Fri May 31, 10AM: Preliminary Presentations (20 min/group)
Mon June 17, 2-3PM: Colloquium (Hunter Dinkins)
Tue June 18, 3-4:30PM: Career/Grad school panel
Fri June 21, 8AM: Final Presentations (45 min/group)
Wed July 3: 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.
Research projects and mentors
Participants: Ang Barrett, Daniel Kiem, and Mitchell Wadas
Faculty mentor: Harm Derksen
Graduate student mentor: Shengnan Huang
Participants: Zachary Greenfield, Jonah Marcus, and Jordan Martino
Graduate student mentors: Sean Carroll and Vitor Gulisz
Participants: Aden Lu and Roland Waterson
Graduate student mentor: Yujia Shi
Participants: Aidan Tillman and Yuzhi Liu
Faculty mentor: Stuart Brorson
Graduate student mentor: Zhaoming Li
Participants: Jacob Ginesin and Daniel Yu
Faculty mentor: David Rosen
Graduate student mentors: Forrest Miller
Participants: Walla Rahama and Ishan Thakur
Faculty mentor: Milen Yakimov
Graduate student mentor: Yunmeng Wu
Participants: Devin Brown, Emily Fink, and Naiwen Wang
Faculty Mentor: Vance Blankers
Graduate student mentor: Rahul Hirwani
Participants: Abby Jiang and Nicholas Sokolovic
Graduate student mentor: Arturo Ortiz San Miguel
Post-doc coordinators: Hunter Dinkins and Josh Wen
Faculty organizers: Harm Derksen, Iva Halacheva, Valerio Toledano Laredo, and Xuwen Zhu
REU 2023
Additional funding for the Summer 2023 program was provided by the College of Science and Department of Mathematics.
Research projects and mentors
Participants: Tao (Luisa) Li, Aaron Soice, and Ryan Zhu
Mentor: Olakunle Abawonse
Paper: Group equivariant neural networks
Participants: Evelyn Brylow, Timothy Demling, Walla Rahama, and Nicholas Sokolovic
Mentors: Sean Carroll and Hunter Dinkins
Paper: P-adic numbers
Chemical reaction networks and monotone dynamical systems
Participants: Edward Berman and Anna XiaMentor: Alon DuvallAffiliated faculty: Eduardo D. Sontag and M. Ali Al-RadhawiPaper: Sufficient conditions for monotonicity in stochastic chemical reaction networksParticipants: Devin Brown, Daniel Kiem, and Jordan Martino
Mentor: Shengnan Huang
Affiliated faculty: Milen Yakimov
Paper: Combinatorial construction of nilpotent Lie algebras
Participants: Zachary Greenfield and Zoey Yelsky
Mentor: M. Anadil Saeed Rao
Paper: Representations of the Virasoro algebra
Participants: Jonah Marcus and Molly Sager
Mentor: Ahmad Reza Haj Saeedi Sadegh
Post-doc coordinator: Josh Wen
Faculty organizers: Iva Halacheva, Valerio Toledano Laredo, and Xuwen Zhu
REU 2022
In light of the COVID-19 pandemic, this program was held remotely.
Research projects and mentors
Equivalent matroids arising from graphs
Participants: Jiaqi Lu and Brandon Onyejekwe Mentor: K. Finn PrideauxPaper: Equivalent matroids arising from graphsFinal presentation slidesMorita theorems
Participants: Nicholas Bidorini and Zach Greenfield
Mentor: Vitor Emanuel Gulisz
Paper: The Morita theorems
Regularization and renormalization in quantum field theory
Participants: Daniel Abadjiev, Anthony Melo, and Zhengxun Liu
Mentor: M. Anadil Saeed Rao
Paper: Renormalization and regularization of φ^4 and φ^3 scalar quantum field theories
Graph bootstrap percolation
Participants: Andy Babb, Stephanie Martinez, and Timothy Wang
Mentor: Connor Anderson
Paper: Approximation of spread minimization in bootstrap percolation
Knot polynomials and Khovanov homology
Participants: Jordan Martino and Francisco Turdera
Mentor: Ryan Kannanaikal
Post-doc coordinators: Iva Halacheva, Matej Penciak, Josh Wen
Faculty organizer: Valerio Toledano Laredo
REU 2021
In light of the COVID-19 shutdown, this program was held entirely remotely.
Additional funding for the Summer 2021 program was provided by the College of Science and Department of Mathematics.
Calendar
Mon May 10, 9 AM: Kick Off Meeting
Thu May 20, 10-11 AM: Colloquium
Thu June 3, 10 AM: Preliminary Presentation (20 min/group)
Thu June 17, 10 AM: Colloquium
Tue Jun 29, 8 AM: Final Presentations (45 min/group)
Tues 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 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.
Groups
Configuration spaces of points and lines
Participants: Luke Boyer, Shane Calle, Nick Payne. Mentor: Ian Dumais
Paper: Configurations of Lines and Spaces
Probabilistic simulations of IOTA cryptocurrency
Participants: Maria Candello, Grant Chau, Jiachen Xu. Mentor: Anupam Kumar
Paper: Probabilistic Simulations of IOTA Cryptocurrency
Modeling of random geometric graphs
Participants: Maitreyee Joshi, Nicholas Thevenin, Bryan Vogt. Mentor: Hiu Ying Man
Paper: Extending Bottleneck Matching and Monotone Property Threshold Width to the Torus
Chromatic numbers of fractional power graphs
Participants: Luke Drennen, Noah Lichtblau. Mentor: Finn Prideaux
Paper: Chromatic Numbers and K-Connectivity of Graph Fractional Powers
Post-doc coordinators: Vance Blankers, Matej Penciak
Faculty organizer: Valerio Toledano Laredo
REU 2020
In light of the COVID-19 shutdown, this program was held entirely remotely.
Calendar
Mon May 4, 9AM: Kick Off Meeting
Mon May 18, 2PM: Preliminary Presentation (20 min/group)
Wed May 27, 2-3PM: Colloquium
Wed June 17, 2-3PM: Colloquium
Thr Jun 25, 2PM: Final Presentations (45 min/group)
Fri July 3: 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 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.
Groups
Evolutionary Dynamics.
Participants: Jack Steilberg, Lauren Neudorf. Mentor: Jonier Antunes.
Paper: Infinite Random Graphs and Evolutionary Dynamics
Spectral Graph Theory.
Participants: Ryan Keleti, Noble Mushtak. Mentor: Whitney Drazen.
Paper: Fractional Revival and Fractional Cospectrality
Elliptic Curves.
Participants: Zoe Daunt, Xiaoying He, Xuyang Li. Mentor: Lei Yang.
Paper: Elliptic Curves and Probability of $\ell$-torsion
Post-doc coordinators: Rob Silversmith, Robin Walters
Faculty organizer: Valerio Toledano Laredo
REU 2019
Calendar
May 6: First Official REU Meeting (Summer I)
May 13: Proposal Draft
May 28: REU Tea & Colloquium 3-4 PM, Lake 509
June 4: REU Tea & Group Presentations 3-4 PM, Nightingale 544
June 11: REU Tea & Colloquium 3-4 PM, Lake 509
June 21: Final Presentations, Lunch 12-1, Talks 1-4, Lake 509 (Summer I)
June 28: Final Paper Due (Summer I)
August 14: Final Presentations (Summer II)
Final Paper: At least 5 pages. If two students, then paper is written together is 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: 30 minutes (40 if group of 2). 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.
Groups
Evolutionary Dynamics.
Participants: Hoyin Chu. Mentor: Jonier Antunes. Summer I.
Paper: Introduction to Evolutionary Dynamics and Stochastic Calculus.
Knot Theory.
Participants: Noah Fleischmann, Kally Lyonnais. Mentor: Dmytro Matvieievsky. Summer I.
Paper: Knots, Colors, and Polynomials.
Graph Theory/Chip Firing:
Participants: Kristin Timothy, Michael Wang. Mentor: Ian Dumais. Summer I.
Paper: Sandpiles and Chip Firing.
Homotopical Algebra:
Participants: Karthik Boyareddygari Mentor: Oleksiy Sorokin. Summer I.
Paper: Homotopical Approach to Tensor Products.
Algebraic Geometry:
Participants: Walker Miller-Breetz. Mentor: Anupam Kumar. Summer II.
Paper: Cone Points on Algebraic Curves.
Post-doc coordinators: Emily Barnard, Rob Silversmith, Robin Walters
Faculty organizer: Valerio Toledano Laredo
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
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.