**2019 Projects**

**Surgery on knots and exotic phenomena in 3- and 4-manifolds**- Kyle Hayden – Faculty
- Ali Daemi – Faculty

Gabriel Agostini

Sophia Chen

Christian Serio

Lizka Vaintrob

Cecilia Wang

Anton Wu

Kexin Wu

**Topological Insulators and the Bulk-Edge Correspondence using Fredholm theory**- Jacob Shapiro – Faculty

Eli Fonseca

Ahmed Sheta

Angela Wang

Kohtaro Yamakawa

- Jacob Shapiro – Faculty

**Exploring symplectic embeddings and symplectic capacities**- Kyler Siegel – Faculty
- Semon Rezchikov – Grad Student

Alex Gajewski

Eli Goldin

Jakwanul Safin

Junhui Zhang

**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**

**Knot Floer homology, bordered algebras and double points**- Akram Alishahi – Faculty
- Linh Truong – Faculty

Joseph Freund

Abhishek Kodumagulla

Max Krawczyk

Ayeong Lee

Bharatha Rankothge

Hsin Pei Toh

**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

**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

- Jeffrey Kuan – Faculty
**Constructions and obstructions of symplectic embeddings**- Jo Nelson – Faculty

Saraswathi Venkatesh – Grad Student

Theodore Coyne

Sara Edelman-Munoz

Chunying Huangdai

Greyson Potter

- Jo Nelson – Faculty
**Special projects**- David Hansen – Faculty
- Daniel Litt – Faculty

Raymond Cheng – Grad Student

Renata Piccioto – Grad Student

Adam Block

Micah Gay

Helena Rios

**2016 Projects**

**Constructions and Obstructions of Symplectic Embedding**- Jo Nelson – Faculty

Robert Castellano- Grad student

Katherine Christianson

Irit Huq-Kuruvilla

Greyson Potter

Roxane Sayde

Elizabeth Yoo

- Jo Nelson – Faculty

**Interacting particle systems and representations of quantized Lie Algebra**- Jeffrey Kuan – Faculty

Darren Gooden- Grad student

Nguyen Dung

Noah Miller

Junho Won

Keke Zhang

- Jeffrey Kuan – Faculty

**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

- Dave Hansen – Faculty

**2015 Projects**

**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

- David Hansen – Faculty
**Obstructions to Symplectic Embeddings**- Jo Nelson – Faculty

Robert Castellano – Grad student

Kat Christianson

Nawaz Sultani

Irit Huq-Kuruvilla

Willie Guo Dong

- Jo Nelson – Faculty

**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

- Jennifer Hom – Faculty
**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

- Jason Behrstock – Faculty (CUNY)
**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

- Jo Nelson – Faculty
**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

- Paul Siegel – Faculty

** **

**2013 Program**

**Heegaard Floer Homology and the Fundamental Group**- Jennifer Hom – Faculty

Kristen Hendricks – Graduate Student

Fabian Doria-Medina

Michael Jackson

Joaquin Ruales

Hadas Zeilberger

- Jennifer Hom – Faculty
**Random Models on Planar Graphs**- Clement Hongler – Faculty

Krzysztof Putyra – Graduate Student

Adrein Brochard

Woo Chang Chung

Reza Gheissari

Sung Chul Park

- Clement Hongler – Faculty
**Knot Contact Homology**- Adam Knapp – Faculty

Jingyu Zhao – Graduate Student

Romin Abdolahzadi

Justin Goluboff

Nilay Kumar

Oren Weiss

Venkata Yamajala

- Adam Knapp – Faculty
**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

- Johan de Jong – Faculty
**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

- Adam Knapp – Faculty
**Appollonian Circle Packings (CU/NYU/CUNY RTG)**- Timothy Heath – Graduate Student

Romin Abdolahzadi

Jonathan Goetz

Ke Huang

- Timothy Heath – Graduate Student

** **

**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

- 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