### 2017 Projects

- Representation theory in graph theory led by David Hansen and Daniel Litt.
- 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 led by Jeffrey Kuan.
- Darren Gooden – Grad Student
- Ravi Campbell
- Zachary Davis
- Max Krawczyk
- Keke Zhang

- Constructions and obstructions of symplectic embeddings led by Jo Nelson
- Saraswathi Venkatesh – Grad Student
- Theodore Coyne
- Sara Edelman-Munoz
- Chunying Huangdai
- Greyson Potter

- Special projects, led by David Hansen and Daniel Litt
- Raymond Cheng – Grad Student
- Renata Piccioto – Grad Student
- Adam Block
- Micah Gay
- Helena Rios

**2016 Projects**

- “Constructions and Obstructions of Symplectic Embeddings” led by Jo Nelson.
- Robert Castellano- Grad student
- Katherine Christianson
- Irit Huq-Kuruvilla
- Greyson Potter
- Roxane Sayde
- Elizabeth Yoo

- “Interacting particle systems and representations of quantized Lie Algebras” led by Jeffrey Kuan.
- Darren Gooden- Grad student
- Nguyen Dung
- Noah Miller
- Junho Won
- Keke Zhang

- “What does a random variety look like?” led by Daniel Halpern-Leistner and Daniel Litt.
- 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” led by Dave Hansen
- Linus Hamann

**2015 Projects**

*Spectral Graph Theory, Markov Chains, and the PageRank Algorithm,*led by Alexander Drewitz and Paul Siegel- 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,*led by David Hansen- Pak-Hin Lee – Grad student
- Srikar Varadaraj
- Ashley Xin Xu
- David-Linus Hamann
- Kevin Choi

*Obstructions to Symplectic Embeddings,*led by Jo Nelson- 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**

**Presentation videos available here.**

**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

- Jennifer Hom – Faculty
**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

- Shea Vela-Vick – Faculty
**Quantum Computing with Knots**- Adam Knapp – Faculty

Meagan Thompson – Graduate Student

Sea Moon Cho

Shazia Dharssi

James Diotte

Sung Chul Park

Timothy Sun

- Adam Knapp – Faculty
**Rigidity of Graphs in Space**- Dylan Thurston – Faculty

Joe Stern – Graduate Student

Samuel Coolidge

Jeffrey Kandel

Arjun Mudan

Monica Puri

- Dylan Thurston – Faculty
**RTG Undergraduate Research Projects**- Apollonian Sums
Ian Whitehead – Graduate Student

Shai Chester

Sharma Goldson

Matthew Jacobs

Stephanie Zarrindast - A Classification of Integral Apollonian Circle Packings

Karol Koziol – Graduate Student

Tabes Bridges

Warren Tai - Unbounded Apollonian Circle Packings, Self-Similarity and Residual Points

Timothy Heath

Alexander Berenbeim

Todd Gaugler

Tasos Moulinos

- Apollonian Sums

** **

**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

- Dylan Thurston – Faculty
**Abelianized Characteristic Algebras of Legendrian Knots**- Shea Vela-Vick – Faculty

Rumen Zarev – Graduate Student

Atanas Atanasov

Jeffrey Irwin

Daniel Kotzen

Christopher Lopez

Eliot Wycoff

- Shea Vela-Vick – Faculty
**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

- Aaron Lauda – Faculty
**Eisentein Series and Zeta Functions**- Yakov Kerzhner – Faculty

Amella Farid

Moyang Li

- Yakov Kerzhner – Faculty

** **

**2009 Program**

**Knots, triple branched covers, and Heegaard Floer Homology**- Adam Knapp – Faculty

Rumen Zarev – Graduate Student

Esther Adzhiashvili

Axel Saenz-Rodriguez

Claire Zukowski

- Adam Knapp – Faculty
**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

- Timothy Perutz – Faculty
**Rigidity of graphs**- Dylan Thurston – Faculty

Joseph Ross – Graduate Student

Ina Petkova – Graduate Student

Samuel Frank

Jiayang Jiang

- Dylan Thurston – Faculty
**Hyperbolic geometry**- Maksim Lipyanskiy – Faculty

Eric Potash

Kyler Siegel

Andrew Zhang

- Maksim Lipyanskiy – Faculty
**Sphere packing in odd dimensional hyperbolic space**- Yakov Kerzhner – Faculty

Alon Levy – Graduate Student

Alex Blumenthal

Christopher Lopez

Alexander Moll

Christopher Scaduto

Warren Tai

- Yakov Kerzhner – Faculty
**Categorifying quantum groups**- Aaron Lauda – Faculty

Alex Ellis – Graduate Student

Qi You – Graduate Student

Corey Bregman

Robert Legg

James McIvor

Delia Wang

- Aaron Lauda – Faculty

** **

**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

- Jason Behrstock – Faculty
**TQFT**- Aaron Lauda – Faculty

Joelle Brichard – Graduate Student

Ben Elias – Graduate Student

Giwan Kim

Andrew Kontaxis

David Xia

- Aaron Lauda – Faculty
**Floer Homology**- Adam Knapp – Faculty

Ina Petkova – Graduate Student

Roman Zarev – Graduate Student

Yael Degany

James Oyuang

Xuran Wang

- Adam Knapp – Faculty
**Hyperbolic Geometry**- Max Lipyanskiy – Faculty

Thomas Peters – Graduate Student

Cory Bergman

Taekgyu Lee

Eric Potash

Rachel Vishnepolsky

- Max Lipyanskiy – Faculty
**Polyhedral cones and their intersections with lattices**- Michael Thaddeus – Faculty

Alex Perry

Christopher Lopez

Atanas Atanasov

- Michael Thaddeus – Faculty

** **

**2007 Program**

**Knot Theory Group**- Robert Lipshitz – Faculty

Thomas Peters – Graduate Student

Yael Degany

Andrew Freimuth

Jonathan Hales

Dmytro Karabash

Michael Lock

Edward Trefts - The Knot Theory Group wrote this paper:

A Modification of the Sarkar-Wang Algorithm and an Analysis of its Computational Complexity

- Robert Lipshitz – Faculty
**Number Theory Group**- Mirela Ciperiani – Faculty

Kimball Martin – Faculty

Joe Ross – Graduate Student

Atanas Atanasov

Rebecca Bellovin

Ivan Loughman-Pawelko

Laura Peskin

Eric Potash - The Number Theory Group wrote this paper:

An asymptotic for the representation of integers as sums of triangular numbers

- Mirela Ciperiani – Faculty