2019 PRIMES Conference

Ninth Annual PRIMES Conference, May 18-19, 2019

Saturday, May 18

8:45 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

9:15 am Session 1: Fractals and Visualization Algorithms

• Jason Liu, Approximating the dimension of circle packings (mentor Prof. Sergiy Merenkov, CCNY – CUNY) ( slides )
• Oliver Hayman, Analyzing visualization and dimensionality-reduction algorithms (mentor Ashwin Narayan) ( slides )
• Ziyan (Heidi) Lei, Fractals: Hausdorff dimension, the Koch curve, and visibility (mentor Dr. Tanya Khovanova) ( slides )

10:15 am Session 2: Applied Mathematics

• Tejas Gopalakrishna, Analysis of the one line factoring algorithm on large semiprimes (mentor Yichi Zhang) ( slides )
• Yizhen Chen, Mobile sensor networks: Bounds on capacity & complexity of realizability (mentor Dr. Jesse Geneson, Iowa State) ( slides )
• Sanjit Bhat, Probing the structure of deep neural networks with universal adversarial perturbations (mentor Dimitris Tsipras) ( slides )

11:15 am Session 3: Geometry and Topology

• Zander Hill, On the distortion of torus knots (mentor Luis Kumanduri) ( slides )
• Nithin Kavi, Cutting and gluing surfaces (mentor Zhenkun Li) ( slides )
• Srinivasan Sathiamurthy, Critical lattices of symmetric convex domains (mentor Anurag Rao, Brandeis University) ( slides )

12:00 pm Lunch in Honor of PRIMES head mentor Dr. Tanya Khovanova's 60th birthday

1:30 pm Session 4: Combinatorics

• Sebastian Jeon, 3-symmetric graphs (mentor Dr. Tanya Khovanova) ( slides )
• Lucy Cai, Espen Slettnes, and Jeremy Zhou, Extracting tree-statistics from the quasisymmetric Bernardi polynomial (mentor Duncan Levear, Brandeis University) ( slides )

2:35 pm Session 5: Algebra

• Rupert Li, Compatible recurrent identities of the sandpile group and maximal stable configurations (mentor Yibo Gao) ( slides )
• Victor Luo and Sasha Shashkov (reading group), Introduction to representation theory (mentor Yau Wing Li) ( slides )
• Elias Sink and Allen Wang (reading group), Character theory of finite groups (mentor Christopher Ryba) ( slides )

3:40 pm Session 6: Algebraic Geometry and Representation Theory

• Lev Kruglyak, The rational Cherednik algebra of type A ₁ with divided powers in characteristic p (mentor Daniil Kalinov) ( slides )
• Frank Wang, The shuffle algebra of the Hilbert scheme of the plane (mentor Yu Zhao) ( slides )
• Arav Karighattam, The Galois group of the 27 lines on a rational cubic surface (mentor Yongyi Chen) ( slides )
• Brandon Wang, Quotients of tropical moduli spaces (mentor Dr. Dhruv Ranganathan, University of Cambridge) ( slides )

4:50 pm Session 7: PRIMES Circle

• Peter Haine, PRIMES Circle Coordinator, Introduction
• Tal Berdichevsky and Corinne Mulvey, Graph theory and map coloring (mentor Agustin García) (slides)
• Ishita Goluguri and Christina Li, Burnside's lemma: A combinatorial application of group actions (mentor Maya Sankar) (slides)
• Hanfei Cui and Trisha Lahiry, Multiplicity, convolution, and the Möbius inversion formula (mentor Michael Tang) (slides)

Sunday, May 19

8:45 am Welcoming Remarks

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

9:00 am Session 8: Combinatorics

• Ezra Erives, Mixed strategy equilibria for winner takes all variant of Colonel Blotto (mentor Dr. Zarathustra Brady) ( slides )
• Kevin Wu, On base 3/2 and greedy partitioning of integers (mentor Dr. Tanya Khovanova) ( slides )
• Isha Agarwal, Paul Braverman, Patrick Chen, William Du, Kaylee Ji, Akhil Kammila, Shane Lee, Alicia Li, Anish Mudide, Jeffrey Shi, Maya Smith, and Isabel Tu (PRIMES STEP Junior group), Weighing coins, losing weight, and saving money (mentor Dr. Tanya Khovanova) ( slides )
• Matvey Borodin, Aidan Duncan, Joshua Guo, Kunal Kapoor, Anuj Sakarda, Jerry Tan, Armaan Tipirneni, Max Xu, and Kevin Zhao (PRIMES STEP Senior group), Common knowledge: Games of logic (mentor Dr. Tanya Khovanova) ( slides )

10:20 am Session 9: Combinatorics

• Benjamin Wright, Maximal extensions of differential posets (mentor Christian Gaetz) ( slides )
• Christopher Zhu, Enumerating permutations with singleton double descent sets (mentor Pakawut Jiradilok) ( slides )
• Justin Yu, On subset sums and thin additive bases (mentor Dr. Asaf Ferber) ( slides )
• Andrew Weinfeld, Bases for quotients of symmetric polynomials (mentor Guangyi Yue) ( slides )

11:30 am Session 10: Applied Mathematics

• Janabel Xia, Sampling over tilings of the plane: A computational approach against political gerrymandering (mentor Younhun Kim) ( slides )
• Benjamin Kang, All-pay auctions with different forfeit functions (mentor Prof. James Unwin, University of Illinois at Chicago) ( slides )
• Yuyuan Luo, Minimal percolating sets with time-dependent bootstrap percolation (mentor Prof. Laura Schaposnik, University of Illinois at Chicago) ( slides )
• Victoria Zhang, Patterns and symmetries in networks of spiking neurons (mentor Dr. Bolun Chen, Brandeis University) ( slides )
• Sunay Joshi, On the degenerate Turán problem and its variants (mentor Dr. Zilin Jiang) ( slides )

1:30 pm Session 11: PRIMES Circle

• Peter Haine, PRIMES Circle Coordinator, Introduction
• Sofia Mrowka, Elizabeth Zhong, and Natasa Zupanski, Game theory: A playful presentation (mentor Marisa Gaetz) (slides)
• Michelle Li and Ella Serrano-Wu, Solving problems in combinatorics using induction and generating functions (mentor Uma Roy) (slides)
• Ai-Wen Joy Lim and Eve Martin, The Application of knot theory to models in statistical mechanics (mentor Radha Mastandrea) (slides)
• Ildi Hoxhallari and Brian Kubinec, Probability, discrete distributions and Markov chains (mentor Daniel León Jiménez) (slides)

3:00 pm Session 12: Computer Science

• Prof. Srini Devadas, Department of Electrical Engineering and Computer Science, Welcoming Remarks
• David Lu, Group messaging in the XRD private communication system (mentor Albert Kwon) ( slides )
• Shashvat Srivastava, AnonStake: An anonymous proof-of-stake cryptocurrency via zero-knowledge proofs and Algorand (mentor Kyle Hogan) ( slides )
• Robert Chen, Scalable distributed key generation (mentor Alin Tomescu) ( slides )
• Yiming Zheng, Vector commitments from univariate polynomials and their applications (mentor Alin Tomescu) ( slides )
• John Kuszmaul, Verkle trees: Ver(y short Mer)kle trees (mentor Alin Tomescu) ( slides )

Fall PRIMES Conference, October 20, 2019

Sunday, October 20

PRIMES Computer Science Section

9:00 am Welcoming Remarks

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

9:15 am Session 1

• Ezra Gordon, Improving round complexity of Byzantine Broadcast under dishonest majority (mentor Jun Wan) ( slides )
• Linda Chen, Random graphs and all-to-all communication (mentor Jun Wan) ( slides )
• Sanath Govindarajan and Walden Yan, Achieving fast fully homomorphic encryption with graph reductions (mentor William Moses) ( slides )

10:20 am Session 2

• Patrick Zhang, Privacy-preserving similarity search using learned indexes (mentor Kyle Hogan) ( slides )
• Ethan Mendes, Towards a certified defense for audio adversarial examples (mentor Kyle Hogan) ( slides )
• Andrew Shen, Towards verifying application isolation for cryptocurrency hardware wallets (mentor Anish Athalye) ( slides )

11:15 am Session 3

• Michael Gerovitch, Environment-aware pedestrian trajectory prediction for autonomous driving (mentor Dr. Igor Gilitschenski) ( slides )
• Yuxuan Chen, A deep learning approach to end-to-end autonomous driving using event-based vision (mentors Dr. Igor Gilitschenski and Alexander Amini) ( slides )
• Aditya Saligrama, Can robust ensembling schemes improve defenses against adversarial inputs? (mentor Guillaume Leclerc) ( slides )

12:10 pm Session 4

• Alek Westover, Cache-efficient parallel partition algorithms (mentor William Kuszmaul) ( slides )
• Alex Ding, An evaluation of UPC++ using distributed parallel graph algorithms (mentor Dr. Yan Gu) ( slides )
• Neel Bhalla, Constructing workflow-centric traces in real time for the Hadoop File System (mentor Prof. Raja Sambasivan, Tufts University) ( slides )
• Jerry Xu, Time – What happens if the world spins backwards? (mentors Prof. Ari Trachtenberg and Trishita Tiwari, Boston University) ( slides )

PRIMES Computational Biology Section

2:00 pm Welcoming Remarks

• Prof. Leonid Mirny, PRIMES Computational Biology Section Coordinator

2:05 pm Session 5

• Neil Chowdhury, A method to recognize universal patterns in genome structure using Hi-C (mentor Sameer Abraham) ( slides )
• Shiv Khandelwal, Genome-wide flame feature detection pipeline for Hi-C chromatin conformation maps (mentor Sameer Abraham) ( slides )
• Jason Yang, The relationship between gene expression correlation and 3D genome organization (mentors Sameer Abraham and Martin Falk) ( slides )
• Vishnu Emani and Kevin Edward Zhao, The role of protein occupancies in DNA compartmentalization (mentors Sameer Abraham and Martin Falk) ( slides )

3:20 pm Session 6

• Andrew Zhang, An explainable machine learning platform for antimicrobial resistance prediction and resistance gene identification (mentor Prof. Gil Alterovitz and Dr. Insung Na) ( slides )
• Alan Qi and Powell Zhang, Using feature selection to identify gene significance in drug-resistant tuberculosis (mentor Prof. Gil Alterovitz and Dr. Insung Na) ( slides )
• Benjamin Chen, Neil Malur, and Hari Narayanan, A novel framework to improve the structure of clinical trials eligibility criteria (mentor Prof. Gil Alterovitz and Dr. Insung Na)
• Ian Balaguera, Implementing a patient-clinician interface for biomedical templates (mentor Prof. Gil Alterovitz and Dr. Insung Na) ( slides )

4:40 pm Session 7

• Jonathan Yin, Latent representations of chemical ligands to predict combinatorial receptor-ligand interactions (mentor Dr. Hattie Chung and Michael Truell, Broad Institute) ( slides )
• Sarah Chen, Retained introns are translated and contribute antigens to the MHC I immunopeptidome (mentors Dr. Tamara Ouspenskaia and Dr. Travis Law, Broad Institute) ( slides )
• Mikhail Alperovich, Data driven quality control for single-cell RNA sequencing analysis (mentor Dr. Ayshwarya Subramanian, Broad Institute)

Mathematics Reading Groups

Tuesday, December 10

Room 2-105

5:30 pm

• Sooyoung Choi and Minghan Sun, Two proofs of Dirichlet's theorem (mentor Kaavya Valiveti)
• Yunseo Choi, Aneesha Manne, and Poonam Sahoo, Pell's Equation and Diophantine Approximation (mentor Zhulin Li) ( slides )
• Yunseo Choi (joint research project with Erin Bevilacqua and Kapil Chandran at Emory REU), Ramanujan Congruences for Fractional Partition (mentor Prof. Ken Ono, University of Virginia) ( slides )

6:35 pm

• Richard Chen and Jason Tang, The Prime Number Theorem with Error Term (mentor Chengyang Shao) ( slides )
• Vincent Fan, William Yue, and Sebastian Zhu, Shor's algorithm and the Period Finding Problem (mentor Chun Hong Lo) ( slides )
• Vincent Fan, William Yue, and Sebastian Zhu (research project), On the Complexity of Generalized Roller Splat! (mentor Chun Hong Lo) ( slides )

Contact

With questions, contact PRIMES Program Director Slava Gerovitch at