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Eighth Annual PRIMES Conference, May 19-20, 2018

Note: Eighth-and-a-half PRIMES Conference of the Computer Science Section will be held on October 13, 2018

Room 4-370, MIT

Open to the public

Conference abstracts booklet

Download conference poster

See also the materials of 2011, 2012, 2013, 2014, 2015, 2016, and 2017 PRIMES conferences, and 2018 reading groups mini-conference

Prof. Michel Goemans, Prof. Pavel Etingof, and Dr. Tanya Khovanova with PRIMES students

Saturday, May 19

8:30 am Welcoming Remarks

Prof. Michel Goemans, Head of the MIT Mathematics Department
Prof. Pavel Etingof, PRIMES Chief Research Advisor
Dr. Slava Gerovitch, PRIMES Program Director

Espen Slettnes and James Lin

9:00 am Session 1: Combinatorics

James Lin, Carl Joshua Quines, and Espen Slettnes, Throttling numbers for Cop vs Gambler (mentor Dr. Jesse Geneson, Penn State) (slides)
Nathan Ramesh, Maximal difference avoiding subsets of Z (mentor Christian Gaetz) (slides)
Sean Elliott, Anti-Ramsey type problems (mentor Dr. Asaf Ferber) (slides)
Ezra Erives, Srinivasan Sathiamurthy, and Theodore Baas, Asymptotics of visibility in three-dimensional grid worlds (mentor Dr. Zarathustra Brady) (slides)

Srinivasan Sathiamurthy and Ezra Erives

Ryan Kim

10:35 am Session 2: Geometry and Topology

Ryan Kim, Cohomology groups of the dual Steenrod algebra (mentor Sanath Devalapurkar) (slides)
Daniel Liu, New fusion products for the affine sl(2) at level k=1/2 (mentor Dr. Claude Eicher) (slides)
Jiwon Choi, Gromov-Hausdorff distance between metric spaces (mentor Ao Sun) (slides)
Sathwik Karnik, Bounds on the maximal cardinality of an acute set in a hypercube (mentor Ao Sun) (slides)

Jiwon Choi

11:50 am Session 3: Knot Theory

Max Guo, On Khovanov homology, Bar-Natan's perturbation, and Conway mutation (mentor Dr. Jianfeng Lin) (slides)
Aayush Karan, Mutation invariance of the Szabó spectral sequence (mentor Dr. Jianfeng Lin) (slides)
Nithin Kavi and Wendy Wu, Width and trunk of satellite knots (mentor Zhenkun Li) (slides)

Wendy Wu and Nithin Kavi

Prof. Michel Goemans and Prof. Pavel Etingof with PRIMES students

2:00 pm Session 4: PRIMES Circle

Isabel Vogt, PRIMES Circle Coordinator, Introduction
Sherry Lim and Mirilla Zhu, Permutations for preschoolers: Applications of group theory to childhood games (mentor Margalit Glasgow) (slides)
Sekai Carr and Laura Clervil, Connect Spokes: An original combinatorial game (mentor Marisa Gaetz)
Elizabeth Euwart and Anna Rasmussen, Graphs and the chromatic polynomial (mentor Dhruv Ranganathan) (slides)
Carly Maggiolo Cabrera and Elisandra Fontes, Probability, statistical tests, and fair die (mentor Alexis Oriole)

Laura Clervil and Sekai Carr

Elizabeth Euwart and Anna Rasmussen

3:40 pm Session 5: Applied Mathematics 

Rinni Bhansali, Modelling epidemics on polluted networks and m-state networks (mentor Prof. Laura Schaposnik, University of Illinois at Chicago) (slides)
Vincent Huang, Mathematical and algorithmic models of refugee crises (mentor Prof. James Unwin, University of Illinois at Chicago) (slides)
Kaiying Hou, Agent-based models for conservation equations (mentor Andrew Rzeznik) (slides)

Rinni Bhansali

Kaiying Hou

4:35 pm Session 6: Algebraic Combinatorics and Probability 

Melinda Sun, Counting bimonotone subdivisions (mentor Dr. Elina Robeva) (slides)
Haneul Shin, Bimonotone subdivisions in high dimensions (mentor Dr. Elina Robeva) (slides)
Stanley Wang, Moduli space of planar tropical curves of genus 1 (mentor Yu Zhao) (slides)
Gopal Goel and Andrew Yao, Derivatives of the Gaussian free field via random matrix theory (mentor Andrew Ahn) (slides)

Stanley Wang

Andrew Yao and Gopal Goel

5:50 pm Session 7: Representation Theory and Number Theory 

Yuting (Emma) Qin, The elliptic Kashiwara-Vergne Lie algebra (mentor Dr. Florian Naef) (slides)
Byung Yeon Rhee, Elliptic curves, factorization, and cryptography (mentor Yongyi Chen) (slides)
Merrick Cai, The Hilbert series of the irreducible representation of the rational Cherednik algebra of type An in characteristic p (mentor Daniil Kalinov) (slides)
Archer Wang, Hilbert series of quasi-invariant polynomials (mentor Dr. Xiaomeng Xu) (slides)

Yuting (Emma) Qin

Merrick Cai

Sunday, May 20

8:45 am Welcoming Remarks

Dr. Slava Gerovitch, PRIMES Program Director
Dr. Tanya Khovanova, PRIMES Head Mentor

Dr. Tanya Khovanova

PRIMES STEP students

9:00 am Session 8: Combinatorics 

Vinjai Vale, A new paradigm for computer vision based on compositional representation (mentor Kevin Ellis) (slides)
Ben Chen, Richard Chen, Joshua Guo, Shane Lee, Neil Malur, Nastia Polina, Poonam Sahoo, Anuj Sakarda, Nathan Sheffield, and Armaan Tipirneni (PRIMES STEP Senior students), On base 3/2 and its sequences (mentor Dr. Tanya Khovanova) (slides)
Matvey Borodin, Hannah Han, Kaylee Ji, Alexander Peng, David Sun, Isabel Tu, Jason Yang, William Yang, Kevin Zhang, and Kevin Zhao (PRIMES STEP Junior students), Chips Go BOOM BOOM!!! (mentor Dr. Tanya Khovanova) (slides)


10:10 am Session 9: Combinatorics

Vincent Bian, Packing anchored rectangles (mentor Dr. Tanya Khovanova) (slides)
Eric Zhang, On quasirandom permutations (mentor Dr. Tanya Khovanova) (slides)
Wayne Zhao, Counting Sudoku variants (mentor Dr. Tanya Khovanova) (slides)

Wayne Zhao, Dr. Tanya Khovanova, Eric Zhang, and Vincent Bian

11:05 am Session 10: Analysis

William Fisher, Polynomial Wolff axioms and Kakeya-type estimates for bent tubes (mentor Robert Burklund) (slides)
Alan Yan, Asymptotic counting in dynamical systems (mentor Prof. Sergiy Merenkov, CCNY – CUNY) (slides)
Andy Xu, Approximating the Hurwitz zeta function (mentor Hyun Jong Kim) (slides)

Aurash Vatan

12:00 pm Session 11

Aurash Vatan, Finding generators of Jacobian groups of finite graphs (mentor Dr. Xiaomeng Xu) (slides)
Daniel Zhu, On the Okounkov-Olshanski formula for the number of tableaux of skew shapes (mentor Prof. Alejandro Morales, UMass Amherst) (slides)
Allen Wang, Permutations with up-down signatures of nonnegative partial sums (mentor Guangyi Yue) (slides)

2:00 pm Welcoming Remarks

Prof. Srini Devadas, Department of Electrical Engineering and Computer Science

Theodor Lukin Yelin

2:10 pm Session 12: Computer Science

Vivek Bhupatiraju, accAAD: Efficient Append-Only Authenticated Dictionary for Transparency Logs (mentor Alin Tomescu) (slides)
Theodor Lukin Yelin, Designing private forums using differential privacy (mentor Albert Kwon) (slides)
Sanjit Bhat and David Lu, Var-CNN and DynaFlow: Improved attacks and defenses for website fingerprinting (mentor Albert Kwon) (slides)
Harshal Sheth and Andrew Sun, Extending distributed-systems tracing vertically into the Linux kernel (mentor Dr. Raja Sambasivan, Boston University) (slides)

Kevin Hu

3:30 pm Session 13: Medical Informatics

Makiah Bennett, Lexical AI for patient-centered clinical diagnoses (mentor Prof. Gil Alterovitz) (slides)
Andrew Gritsevskiy, Capsule networks for low-data transfer learning (mentors Prof. Gil Alterovitz and Maxim Korablyov) (slides)
Kevin Hu, Discovery of exon splicing relationships across cancer cell lines (mentor Dr. Mahmoud Ghandi, Broad Institute) (slides)

Iris Yang and Victoria Zhang

4:25 pm Session 14: Math Reading Groups

Nhat Pham and Anmol Sakarda, Concrete mathematics: Exploring summations (mentor Zhulin Li) (slides)
Dylan Pentland, The j-invariant of an elliptic curve (mentor Chun Hong Lo) (slides)

Sam Costa and Elin Gu

5:10 pm Session 15: PRIMES Circle

Aneesha Manne and Lara Zeng, Generating functions in combinatorics (mentor Uma Roy) (slides)
Iris Yang and Victoria Zhang, Gaussian integers and their relationship to ordinary integers (mentor Matthew Weiss) (slides)
Sam Costa and Elin Gu, Inverse knots and amphicheirality (mentor Joseph Zurier)

Prof. Pavel Etingof

Eighth-and-a-half Annual PRIMES Conference, October 13, 2018

PRIMES Computer Science Section

Room 4-370, MIT

Open to the public

Conference abstracts booklet

Download conference poster

Saturday, October 13

2:00 pm Welcoming Remarks

Dr. Slava Gerovitch, PRIMES Program Director
Prof. Srini Devadas, PRIMES Computer Science Section Coordinator

John Kuszmaul

2:10 pm Session 1

Sanath Govindarajan and Walden Yan, Secure image classification with lattice-based fully homomorphic encryption (mentor William Moses) (slides)
John Kuszmaul, Verkle trees: Ver(y short Mer)kle trees (mentor Alin Tomescu) (slides)
Yiming Zheng, Scaling transaction verifications in cryptocurrencies (mentor Alin Tomescu) (slides)
Robert Chen, Aleator: Random beacon via scalable threshold signatures (mentor Alin Tomescu) (slides)

Robert Chen

3:30 pm Session 2

David Lu, XRD: A Scalable messaging system with cryptographic privacy (mentor Albert Kwon) (slides)
Ethan Mendes and Patrick Zhang, Maintaining the anonymity of direct anonymous attestations with subverted platforms (mentor Kyle Hogan) (slides)
Shashvat Srivastava, AnonStake: An Anonymous proof-of-stake cryptocurrency via zero-knowledge proofs and Algorand (mentor Kyle Hogan) (slides)

Andrew Zhang

4:30 pm Session 3

Michael Gerovitch, Neil Malur, and Hari Narayanan, The Second Opinion Project: Leveraging external knowledge databases for additional patient medical options (mentor Dr. Gil Alterovitz)
Yingtong Zhao, Server and interface for genetic risk assessment (mentor Dr. Gil Alterovitz) (slides)
Leo Dong, Novel feature learning method of gene expression data based on an optimized denoising autoencoder (mentor Dr. Gil Alterovitz) (slides)
Andrew Zhang, Antimicrobial resistance prediction using deep convolutional neural networks on whole genome sequence data (mentor Dr. Gil Alterovitz) (slides)

Anusha Murali

5:45 pm Session 4

Anusha Murali, A Semi-Supervised dimensionality reduction method to reduce batch effects in genomic data (mentor Dr. Mahmoud Ghandi, Broad Institute) (slides)
Sanjit Bhat, Towards efficient methods for training robust deep neural networks (mentor Dimitris Tsipras) (slides)
Aditya Saligrama and Andrew Shen, A Practical analysis of Rust's concurrency story (mentor Jon Gjengset) (slides)

PRIMES CS students and mentors with Prof. Srini Devadas

Mathematics Reading Groups

Wednesday, December 5

PRIMES students and mentors, December 5, 2018

5:30 pm

Sasha Shashkov and Andrew Weinfeld, Enumerative Combinatorics: Generating Functions and Partially Ordered Sets (mentor Aleksandra Utiralova) (slides1) (slides2)
Benjamin Wright and Junze Ye, Elliptic Curves: Theory and Applications (mentor Yongyi Chen) (slides)

Friday, December 7

Janabel Xia

5:30 pm

Christopher Zhu, Algebraic Geometry: Elliptic Curves and 2 Theorems (mentor Chun Hong Lo) (slides)
Tejas Gopalakrishna and Janabel Xia, The Probabilistic Method (mentor Jake Wellens) (slides)
Sebastian Zhu and Vincent Fan, Pólya Enumeration Theorem (mentor Christopher Ryba) (slides)

PRIMES students and mentors, December 5, 2018


With questions, contact PRIMES Program Director Dr. Slava Gerovitch at