Past Projects

The Mathematics at SUMRY

SUMRY research projects in recent years have spanned a range of topics that have included game theory, geometry of moduli spaces, closed geodesics, number theory, probability theory, tropical geometry, dynamics, number theory, combinatorics, geometry, and more recently applied mathematics. 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 nine 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. 

List of publications from previous years (last updated 2022)

SUMRY 2023

Summer 2023 featured 22 students working on 5 reserach projects. 

Violet Ross, Chloe Boatright, Jorge Blanco, Abigail Engbrecht, “Ambient Dimension of Manifold-fitting Data” with Kevin O’Neill and Asaf Etgar (Yale).
Daniel Martin, Rachel Schmidt, Michael Han, Sycamore Herlihy, Chemical Graph Theory” with Kirsti Kuenzel (Trinity College). 
Maedee Trank-Greene, Valentina Guo, Benjamin Hollander-Bodie, Charles Xu, Laney Goldman, Graph Neural Networks” with Smita Krishnaswamy, Rex Ying, Ian Adelstein, Edward De Brouwer (Yale) and Michael Perlmutter (UCLA).
Elizabeth Lew, Khaiylah Johnson Bustamante, Aaron Mesa, Jack Moffatt, Metric number theory and dynamics” with Felipe A Ramírez (Wesleyan University). 
Carson Newman, Nada Ali, Sophia Zhou, Uma Arengo, Noam Scully, Saddle Conenctions on Translation Surfaces” with Taylor McAdam and Fernando Al Assal (Yale). 

SUMRY 2022

Summer 2022 featured 25 students working on 5 reserach projects. 

Raina Okonogi-Neth, Hailey Weingord, Mykola Sapronov, Matthew Li, Dash Stevanovich, “Algebraic Combinatorics” with Emily Gunawan (Oklahoma) and Su Ji Hong (Yale). 
Sara Ansari, Ella Wilson, Philos Kim, Elliot Brock, Aislinn Elizabeth SmithCombinatorial and geometric aspects of hyperbolic manifolds” with Franco Vargas Pallete (Yale).
Julia Shneidman, Kate Perkins, Eion Mulrenin, Leart Ajvazaj, Sarah Kaylee Weatherspoon“Extremal problems in discrete geometry” with Cosmin Pohoata (Yale).
Tesfa Asmara, Guy Thampakkul, Joia Zhang, Nhi Nguyen, Kincaid MacDonald“Directed-graph based inference in machine learning” with Smita Krishnaswamy, Ian Adelstein, Dhananjay Bhaskar (Yale) and Michael Perlmutter (UCLA).
Jacob Lerma, River Harmon Newman, Alette Wells, Erica Weiler, Jovon Reuel Richard Williams, “Geometry and dynamics in H² × H²” with Or Landesberg and Subhadip Dey (Yale). 

SUMRY 2021

Summer 2021 was our first NSF sponsored summer. We had 24 students working on 6 research projects.  

Thomas MeyerEthan Spingarn, Sabrina Mi, Beata Casiday, Spinors and Graph Theory with Ivan Contreras (Amherst College)

  Marisa Cofie, Olivia Fugikawa, David Zeng, Madelyn Stewart  “Box-ball Systems” with Emily Gunawan (Oklahoma). 

Janet Barkdoll, Juliet Aygun, Jenavie Lorman, Theodore Sandstrom, “Cylinder configurations on flat surfaces” with Aaron Calderon (Yale).

Max Kong, Max Hammond, Christopher Ryan Poston, Supriya Weiss“Hypergraph Containers“ with Cosmin Pohoata (Yale) and Dmitriy Zakharov (MIPT).

Kincaid MacDonald, Dawson Thomas, Sarah Zhao, Jennifer Paige“Diffusion Geometry and Topologywith Smita Krishnaswamy, Jeff Brock, Ian Adelstein, Bastian Rieck, Dhananjay Bhaskar (Yale).

Josie Elizabeth O’Harrow, Jordan Justin Grant, Synneva Boxrud Bratland, Laurel Grey Pittenger Turner, Dynamics, Geometry, and Number Theory with Taylor McAdam (Yale).


SUMRY 2020

In summer of 2020 we ran a virtual program with 5 student research projects .  All five groups presented at the virtual New England REU conference hosted by UConn. Here are the projects from 2020. Papers related to these projects are in preparation and will be added in due course. 

Lance Saddler ‘22, Tony Zeng ‘21, Richard Zhou ‘22, Stationary operators for the Toda flow (with Tom VandenBoom). video

Rajiv Nelakanti ‘21, Faren Roth ‘21, Supriya Weiss ‘23, “Geodesic nets on flat surfaces (with Ian Adelstein and Elijah Fromm). video

Dawit Mengesha ’21, Robert Miranda ‘22, Brian Sun ‘22, “Topological Zeta functions of matriods in families” (with Max Kutler and Shiyue Li). video

Allen Mi ‘22, Seema Patil ‘23, Akiva Weinberger ‘23“Graph Laplacians” (with Ryan Pellico). video

Jonah Berman ‘22, Reyanna James ‘21, Ananth Miller-Murthy ‘21, Hamilton Wan ‘23, “Problems in Homogeneous Dynamics” (with Taylor McAdam and Caglar Uyanik). video

SUMRY 2019

In summer of 2019, we had 5 student research projects.  Four of these groups presented their work at the Young Mathematicians’ Conference at OSU and everyone presented ath the UMass REU conference. Here are the projects from 2019. Papers related to these projects are in preparation and will be added in due course. 

Andres Gomez-Colunga ‘21, Mirilla Zhu ‘22, Charlotte Kavaler ‘21, Primitive sets of polynomials (with Nathan McNew). Paper Paper

Anthony Ji ‘21, Grace Zdeblick ‘21, Krish Desai ‘21, “Closed geodesics on flat surfaces (with Ian Adelstein and Aaron Calderon). Paper

Andrew Benz ‘21, Lilly Gold ‘21, Rodrigo Ferreira da Rosa ‘20, Neha Verma ‘21, “Mulitscale analysis on graphs” (with Karamatou Yacoubou Djima).

Chris Xue ‘21, Kevin Li ‘21, Jack Hirsch ‘21, Jackson Petty ‘21, “Geometry group - isoperimetric problems” (with Frank Morgan). Paper Paper Paper

Mrinal Durson ‘20, Logan Rumbaugh ‘21, Josh Hinman ‘20, “Intersections of virtual multistrings” (with David Freund). 

SUMRY 2018

In summer of 2018, we had 5 student research projects.  Four of these groups presented their work at the Young Mathematicians’ Conference in Columbus, OH. Here are the projects from 2018. 

Diana Halikias ‘20, Ed Gelernt ‘20, and Charles Kenney ‘19, Harmonic analysis on graphs and datasets (with Nick Marshall). Paper

Arthur Azvolinsky ‘20, Josh Hinman ‘20, and Alexander Schlesinger ‘19Minimizing closed geodesics (with Ian Adelstein and Aaron Calderon). Paper

Max Lukianchikov ‘20, Noah Montgomery ‘19, Vlad Nazarchuk ‘20, and Chris Xue ‘21, “Blaschke unwinding” (with Stefan Steinerberger and Hau-Tieng Wu). Paper

Catherine Lee ‘20, Henry Reichard ‘19, and David Townley ‘19, “Subgraph chromatic number“ (with Ross Berkowitz and Pat Devlin).  Paper

Michael Doppelt ‘19, Sonali Durham ‘20, Tessa Murthy ‘19, and Harish Vemuri ‘21, Intersecting graph families (with Ross Berkowitz and Pat Devlin). Paper

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 Reichard ‘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 Kenny Ascher). Paper

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

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

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