Past Projects


The Mathematics at SUMRY

SUMRY research projects in recent years have spanned a range of topics that have included the chip-firing games, combinatorics of integer partitions, game theory, geometry of moduli spaces, number theory, probability theory, tropical geometry, dynamics, and various other questions number theory, combinatorics, and algebraic geometry. The problems are important open questions, and are carefully chosen by the SUMRY team to be accessible for a undergraduate group to make progress in ten weeks, but also of broader interest to the mathematical community. As a result, the questions that we pursue tend to be close to the advisor’s research area, and vary from year to year, based on the team. Great care is taken in matching participants with both teammates and projects.

You can find more information about the projects by taking a look at the titles, papers, and slides from past years’ projects below.

SUMRY 2017

During the summer of 2017, we had 6 student research projects. All of these groups presented their work at MAA’s Mathfest in Chicago, IL, where 4 of 6 of our groups won “Outstanding Presentation” awards. Four of the groups also presented their work at the Young Mathematicians’ Conference in Columbus, OH. Here are the projects from 2017. Papers related to these projects are in preparation and will be added in due course. 

Alois Cerbu ’18, Luke Peilen ‘18, and Andrew Salmon ‘18, Topology of the moduli spaces of curves (with Steffen Marcus and Dhruv Ranganathan). Paper

David Brandfonbrener ‘18, Yuxuan Ke ‘19, Ethan Sciamma ‘18, and Henry Richard ‘19, Generators of Jacobians of random graphs (with Netanel Friedenberg and Steffen Marcus). Paper

Josh Hinman ‘20, Borys Kuca ‘18, and Alexander Schlesinger ‘19, “Hidden signals in the Ulam sequence (with Senia Sheydvasser and Stefan Steinerberger). Paper

Milo Brandt ‘19, Michelle Jones ‘19, and Catherine Lee ‘20, “The Sylvester-Gallai theorem in tropical geometry“ (with Dhruv Ranganathan). Paper

Connor Halleck-Dube ’19, Daniel Gershenson ‘19, and Elaine Hou ‘18, Enumerating configurations of lines in the plane (with Kenney Ascher). Paper

Andre Moura ‘18, Elijah Gunther ‘18, and Jason Schuchardt ‘18, Local h-vectors(with Sam Payne).

SUMRY 2016

During the summer of 2016, we had 6 student research projects. All of these groups presented their work at MAA’s Mathfest in Columbus, OH, where a number of our students won “Outstanding Presentation” awards. Four of the groups also presented their work at the REU Mini-Symposium, hosted by Williams College. Here are the projects from 2016. Papers related to these projects are in preparation and will be added in due course. 

Stanislav Atanasov ‘17“The Brill-Noether existence conjecture for graphs of low genus” (with Dhruv Ranganathan). Paper Slides

Derek Boyer ‘18, Andre Moura ‘18, and Scott Weady ‘17, “Tropicalizing line arrangements over finite fields” (with Dhruv Ranganathan). Slides

Alois Cerbu ’18, Elijah Gunther ’18, and Luke Peilen ’18, “Orbits on Markoff varieties over finite fields” (with Michael Magee). Paper Slides

Connor Halleck-Dube ’19, Jocelyn Wang ‘17, and Nick Wawrykow ’17, “Simplicial complexes and effective divisors on M0,n” (with Jose Gonzalez). Slides

Austen James ‘17, Matt Larson ‘19, and Andrew Salmon ‘18, “Law of the iterated logarithm in G(n,p)” (with Daniel Montealegre). Paper Slides

Rose Mintzer-Sweeney ‘19, Alexander Schlesinger ‘19, and Katherine Xiu ’18, “Embedding quadratic fields into quaternion algebras” (with Max Ehrman and Arseniy Sheydvasser). Slides

SUMRY 2015

During the summer of 2015, we had 6 student research projects.  Each group presented at the REU Mini-Symposium, hosted by UConn, and MAA’s MathFest in Washington, DC. (Here’s a gallery of some photos from MathFest.) For the project descriptions, check out the SUMRY 2015 page.  Here are the titles of the projects:

Stanislav Atanasov ’17, Benjamin Krakoff ’17, and Julian Menzel ’17, Counting subrings of Z^n and related questions” (mentor: Franco Munoz; also advised by Nathan Kaplan). Slides Paper

Aaron Berger ‘18, Christopher Chute ‘17, and Matthew Stone ‘17, Query complexity of Mastermind variants” (mentor: Daniel Montealegre; also advised by Nathan Kaplan). Paper

David Brandfonbrener ’18, Eliot Levmore ‘18, and Michael Zanger-Tishler ‘18, Zero-bids in a two player product-mix auction” (mentor: Matthew Calvin; also advised by Sam Payne).

Jason Gaitonde ‘18, Seung Hyun Lee ‘16, and Charlie Pasternak ‘18, Extensions to bidding games” (mentor: Ian Ball; also advised by Sam Payne).

Elijah Gunther ’18 and Olivia Zhang ‘18, Cones of divisors and simplicial complexes” (mentor: Jeremy Usatine; also advised by Jose Gonzalez). Slides

Rachel Lawrence ‘16, Luke Peilen ‘18, and Max Weinreich ‘16, Counting 10-arcs in the projective plane” (mentor: Susie Kimport; also advised by Nathan Kaplan). Paper

SUMRY 2014

During the summer of 2014, we had 8 student research projects.  For the project descriptions, check out the SUMRY 2014 page.  Here are the titles of the projects and links to their results:

Stanislav Atanasov ’17 and Christopher Shriver ‘16, “Results on some real stability preservers” (advised by Anup Rao).  Writeup

Hannah Constantin ’15 and Benjamin Houston-Edwards ‘16, “Counting (a,b)-core partitions from numerical semigroups​” (with Nathan Kaplan; also advised by Florencia Orosz-Hunziker). Paper Poster Slides (Ben’s talk) Slides (Hannah’s talk)

Andrew Deveau ’15, Jenna Kainic ’16 and Dan Mitropolsky ’15, “Gonality of random graphs” (with Dave Jensen; also advised by Dan Corey).  Paper

Rodrigo Ferreira da Rosa ‘16, “Toric graph associahedra and compactifications of M0,n” (with Dave Jensen and Dhruv Ranganathan). Paper Poster

Louis Gaudet ’16, Nicholas Wawrykow ’17 and Theodore Weisman ’16, “Realizations of groups with pairing as Jacobians of finite graphs” (with Dave Jensen and Dhruv Ranganathan; also advised by Dan Corey). Paper Poster

Youkow Homma ’16, Jun Hwan Ryu ’16 and Benjamin Tong ‘17, “On a general class of non-squashing partitions” (with Amanda Folsom; also advised by Susie Kimport). Paper Slides

Michael Menz ’17, Justin Wang ‘17 and Jiyang Xie ’16, “Strategies in all-pay bidding games” (with Michael Landry). Paper Poster

Carsten Peterson ‘17, “Some results on 2-lifts of graphs” (advised by Anup Rao).  Writeup

Previous years

Alec Arana ’14, Michael Garn ’15, Seung Hyun Lee ’16, and Brian Lei ’16,Bidding chess” (advised by Sam Payne and Tif Shen) Slides

Julien Clancy ’15 and Timothy Leake ’15, “Jacobians, Tutte polynomials, and two-variable zeta functions of graphs” (with Sam Payne) Paper Slides

Rachel Lawrence ’16, Hannah Otis ’16, and Noelle Thew ’15, “Investigations of driven interated function systems to characterize time series data” (advised by Michael Frame) Slides

Timothy Leake ’15Brill-Noether theory of maximally symmetric graphs” (with Dhruv Ranganathan) Paper Slides

Chang-Mou Lim ’11 and Natasha Potashnik ’11, “Brill-Noether theory and rank-determining sets for metric graphs” (with Sam Payne) Paper

Geoff Smith ’15, “Brill-Noether theory of curves on toric surfaces” (advised by Dustin Cartwright and Sam Payne) Paper Slides