Columbia Home
Previous REU Programs

2019 Projects

  • Toric Varieties (Paris, France)
    • Michael Harris – Faculty Organizer
    • Huayi Chen – Faculty
    • Raymond Cheng – Grad Student
      Benjamin Church
      Myeonhu Kim
      Hobart Pao
      Anda Tenie
      Yunsong Wei
  • Independent Projects
    • Yujin Kim (Corwin)
    • Lizka Vaintrob (Hayden, Daemi)

2018 Projects

  • Enumerative geometry and arithmetic
    • Jo Nelson – Faculty
    • Ila Varma – Faculty
      (Alex) Zhongyi Zhang – Grad Student
      Teresa Brown
      Quang Dao
      Mariya Delyakova
      Lucas Furtado
      Evan Wickenden
      Myeonhu Kim
  • Curves on surfaces over finite fields
    • Daniel Litt – Faculty
    • Alex Perry – Faculty
      Raymond Cheng – Grad Student
      Ben Church
      Chunying Huangdai
      Matthew Lerner-Brecher
      Navtej Singh
      Ming Jing

2017 Projects

**Final Presentation videos**

  • Representation theory in graph theory
    • David Hansen – Faculty
    • Daniel Litt – Faculty
      Raymond Cheng – Grad Student
      Renata Piccioto – Grad Student
      Alejandro Buendia
      Joseph Freund
      Yihao Huang
      Matthew Malone
      Bharatha Rankothge
      Jia Wan
      Yi Wang
      Junho Won
  • Explicit central elements of quantized Lie algebras
    • Jeffrey Kuan – Faculty
      Darren Gooden – Grad Student
      Ravi Campbell
      Zachary Davis
      Max Krawczyk
      Keke Zhang
  • Constructions and obstructions of symplectic embeddings
    • Jo Nelson – Faculty
      Saraswathi Venkatesh – Grad Student
      Theodore Coyne
      Sara Edelman-Munoz
      Chunying Huangdai
      Greyson Potter
  • Special projects
    • David Hansen – Faculty
    • Daniel Litt – Faculty
      Raymond Cheng – Grad Student
      Renata Piccioto – Grad Student
      Adam Block
      Micah Gay
      Helena Rios

2016 Projects

**Final presentation videos**

  • Constructions and Obstructions of Symplectic Embedding
    • Jo Nelson – Faculty
      Robert Castellano- Grad student
      Katherine Christianson
      Irit Huq-Kuruvilla
      Greyson Potter
      Roxane Sayde
      Elizabeth Yoo
  • Interacting particle systems and representations of quantized Lie Algebra
    • Jeffrey Kuan – Faculty
      Darren Gooden- Grad student
      Nguyen Dung
      Noah Miller
      Junho Won
      Keke Zhang
  • What does a random variety look like?
    • Daniel Halpern-Leistner – Faculty
    • Daniel Litt – Faculty
      Dan Gulotta- Grad student
      Carl Lian- Grad student
      Louisa Carpenter-Winch
      Kevin Choi
      Lilian Cohen
      Theodore Coyne
      Seth Davis
      Willie Dong
      Michael Tong
      Jason Vaccaro
  • Special project on Algebraic Stacks
    • Dave Hansen – Faculty
      Linus Hamann

 

2015 Projects

**Final presentation videos**

  • Spectral Graph Theory, Markov Chains, and the PageRank Algorithm
    • Alexander Drewitz – Faculty
    • Paul Siegel – Faculty
      Darren Gooden – Grad student
      Andrea Heyman – Grad student
      Nguyen Chi Dung
      Yujia Shi
      Daniel Fan Yang
      Greyson Katzel Potter
      Hardik Devang Shah
      Roxane Sayde
      Louisa Carpenter-Winch
      Jun Ho Yoon
  • Arithmetic Properties of Hurwitz Numbers
    • David Hansen – Faculty
      Pak-Hin Lee – Grad student
      Srikar Varadaraj
      Ashley Xin Xu
      David-Linus Hamann
      Kevin Choi
  • Obstructions to Symplectic Embeddings
    • Jo Nelson – Faculty
      Robert Castellano – Grad student
      Kat Christianson
      Nawaz Sultani
      Irit Huq-Kuruvilla
      Willie Guo Dong

 

2014 Projects

  • Left-orderable groups and knot surgery
    **End of project video**

    • Jennifer Hom – Faculty
      Mike Wong – Grad Student
      Katherine Christianson
      Justin Goluboff
      David Hamann
      Srikar Varadaraj
  • Geometry of Coxeter Groups
    **End of project video**

    • Jason Behrstock – Faculty (CUNY)
      Timothy Susse – Grad Student (CUNY)
      Daniel Gulotta – Grad Student
      Sarba Raj Bartaula
      Lena Min Ji
      Robert Lyman
      Samir Mathrani
      Ha-Young Shin
  • Reeb Dynamics of Lens Spaces
    **End of project video**

    • Jo Nelson – Faculty
      Robert Castellano – Grad Student
      Leonardo Abbrescia
      Willie Dong
      Irit Huq-Kuruvilla
      Nawaz Sultani
  • Spectral Graph Theory and the PageRank Algorithm
    **End of project video**

    • Paul Siegel – Faculty
      Thomas Nyberg – Grad Student
      Riaz Helfer
      Anish King
      Samuel Nicoll
      Robert Shorb

  

2013 Program

**Final presentation videos**

  • Heegaard Floer Homology and the Fundamental Group
    • Jennifer Hom – Faculty
      Kristen Hendricks – Graduate Student
      Fabian Doria-Medina
      Michael Jackson
      Joaquin Ruales
      Hadas Zeilberger
  • Random Models on Planar Graphs
    • Clement Hongler – Faculty
      Krzysztof Putyra – Graduate Student
      Adrein Brochard
      Woo Chang Chung
      Reza Gheissari
      Sung Chul Park
  • Knot Contact Homology
    • Adam Knapp – Faculty
      Jingyu Zhao – Graduate Student
      Romin Abdolahzadi
      Justin Goluboff
      Nilay Kumar
      Oren Weiss
      Venkata Yamajala
  • Elliptic Curves and Pairing Based Cryptography
    • Marc Masdeu – Faculty
    • Michael Woodbury – Faculty
      Paul Lewis – Graduate Student
      Joseph Eddy
      Aditi Nair
      Jenne O’Brien
      Micah Smith
      Yingtian Yang
      John Yu

  

2012 Program

  • Applications of knot Floer homology to the concordance group
    • Jennifer Hom – Faculty
    • Peter Horn – Faculty
      Kristen Hendricks – Graduate Student
      Andrew Fanoe – Graduate Student
      Michael Gartner
      James Groccia
      Christian Moscardi
      Siran Li
      Josh Tobin
  • Algebraic geometry over finite fields and rational curves
    • Johan de Jong – Faculty
      Andrew Kiluk – Graduate Student
      Tabes Bridges
      Rankeya Datta
      Joseph Eddy
      Michael Newman
      John Yu
  • Bordered Floer homology and knot complements
    • Adam Knapp – Faculty
      Corrin Clarkson – Graduate Student
      Andrew Fanoe – Graduate Student
      Won Gyu Choi
      Samson Koelle
      Jenne O’Brien
      Venkata Yamajala
      Yifei Zhao
  • Appollonian Circle Packings (CU/NYU/CUNY RTG)
    • Timothy Heath – Graduate Student
      Romin Abdolahzadi
      Jonathan Goetz
      Ke Huang

  

2011 Program

  • Knot Floer Homology: Properties and Computations
    • Jennifer Hom – Faculty
    • Corrin Clarkson – Graduate Student
      Kristen Hendricks – Graduate Student
      Vivian Bailey
      Stephen Hancock
      Michael Newman
      Chun Ye
  • Computations of Non-commutative Knot Invariants
    • Shea Vela-Vick – Faculty
      Peter Horn – Faculty
      Ina Petkova – Graduate Student
      Jonathan Hanselman – Graduate Student
      Rankeya Datta
      Stephen Fitz
      Eden Prywes
      John Schultz
      Joshua Tobin
      Kitty Yang
  • Quantum Computing with Knots
    • Adam Knapp – Faculty
      Meagan Thompson – Graduate Student
      Sea Moon Cho
      Shazia Dharssi
      James Diotte
      Sung Chul Park
      Timothy Sun
  • Rigidity of Graphs in Space
    • Dylan Thurston – Faculty
      Joe Stern – Graduate Student
      Samuel Coolidge
      Jeffrey Kandel
      Arjun Mudan
      Monica Puri
  • RTG Undergraduate Research Projects

  

2010 Program

  • Rigidity of Graphs
    • Dylan Thurston – Faculty
      Andrew Fanoe – Graduate Student
      Fatima Ahmed
      Sherin George
      Matthew Jacobs
      Sung Chul Park
      Timothy Sun
      Chun Ye
  • Abelianized Characteristic Algebras of Legendrian Knots
    • Shea Vela-Vick – Faculty
      Rumen Zarev – Graduate Student
      Atanas Atanasov
      Jeffrey Irwin
      Daniel Kotzen
      Christopher Lopez
      Eliot Wycoff
  • Categorification of Quantum Groups and Geometry
    • Aaron Lauda – Faculty
      Sabin Cautis – Faculty
      Krzysztof Putyra – Graduate Student
      You Qi – Graduate Student
      Alexander Christian Moll
      Alex Blumenthal
      Alex Perry
      Andrew Zhang
      Axel Saenz
      Benjamin Albert
      James McIvor
      Jin Woo Jang
      Max Ehrman
      Rachel Vishnepolsky
      Sea Moon Cho
  • Eisentein Series and Zeta Functions
    • Yakov Kerzhner – Faculty
      Amella Farid
      Moyang Li

  

2009 Program

  • Knots, triple branched covers, and Heegaard Floer Homology
    • Adam Knapp – Faculty
      Rumen Zarev – Graduate Student
      Esther Adzhiashvili
      Axel Saenz-Rodriguez
      Claire Zukowski
  • Dehn twists and symplectic fixed points
    • Timothy Perutz – Faculty
      Robert Lipshitz – Faculty
      Thomas Peters – Graduate Student
      Jonathan Bloom – Graduate Student
      Alexandru Georgescu
      Jin Woo Jang
      Rachel Vishnepolsky
      Xuran Wang
  • Rigidity of graphs
    • Dylan Thurston – Faculty
      Joseph Ross – Graduate Student
      Ina Petkova – Graduate Student
      Samuel Frank
      Jiayang Jiang
  • Hyperbolic geometry
    • Maksim Lipyanskiy – Faculty
      Eric Potash
      Kyler Siegel
      Andrew Zhang
  • Sphere packing in odd dimensional hyperbolic space
    • Yakov Kerzhner – Faculty
      Alon Levy – Graduate Student
      Alex Blumenthal
      Christopher Lopez
      Alexander Moll
      Christopher Scaduto
      Warren Tai
  • Categorifying quantum groups
    • Aaron Lauda – Faculty
      Alex Ellis – Graduate Student
      Qi You – Graduate Student
      Corey Bregman
      Robert Legg
      James McIvor
      Delia Wang

  

2008 Program

  • Tower of Hanoi
    • Jason Behrstock – Faculty
      Eli Grigsby – Faculty
      Harold Sultan – Graduate Student
      Amy Cen
      So Eun Park
      Ian Spafford
      Michael Rand
      Andrew Zhang
    • So Eun Park posted a paper to the arxiv. It is available at: http://arxiv.org/pdf/0809.1179v1
  • TQFT
    • Aaron Lauda – Faculty
      Joelle Brichard – Graduate Student
      Ben Elias – Graduate Student
      Giwan Kim
      Andrew Kontaxis
      David Xia
  • Floer Homology
    • Adam Knapp – Faculty
      Ina Petkova – Graduate Student
      Roman Zarev – Graduate Student
      Yael Degany
      James Oyuang
      Xuran Wang
  • Hyperbolic Geometry
    • Max Lipyanskiy – Faculty
      Thomas Peters – Graduate Student
      Cory Bergman
      Taekgyu Lee
      Eric Potash
      Rachel Vishnepolsky
  • Polyhedral cones and their intersections with lattices
    • Michael Thaddeus – Faculty
      Alex Perry
      Christopher Lopez
      Atanas Atanasov

  

2007 Program

Print this page