2018 PRIMES Conference

Eighth Annual PRIMES Conference, May 19-20, 2018

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

9:00 am Session 1: Combinatorics

• James Lin, Carl Joshua Quines, and Espen Slettnes, Throttling numbers for Cop vs Gambl er (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 )

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 )

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 )

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)

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 )

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 )

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 A _n in characteristic p (mentor Daniil Kalinov) ( slides )
• Archer Wang, Hilbert series of quasi-invariant polynomials (mentor Dr. Xiaomeng Xu) ( slides )

Sunday, May 20

8:45 am Welcoming Remarks

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

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 )

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 )

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

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 )

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 )

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 )

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)

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

PRIMES Computer Science Section

Saturday, October 13

2:00 pm Welcoming Remarks

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

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 )

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 )

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 )

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 )

Mathematics Reading Groups

Wednesday, December 5

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

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 )

Contact

With questions, contact PRIMES Program Director Slava Gerovitch at