Tenth Annual Fall Term PRIMES Conference, October 17-18, 2020

Saturday, October 17

Mathematics

10:20 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

10:35-11:55 am: Session 1

• Yunseo Choi, "Racial impact on infections and deaths due to COVID-19 in New York City" (mentor Prof. James Unwin, University of Illinois at Chicago) ( slides )
• William Li, "Lebesgue measure preserving Thompson's monoid" (mentor Prof. Sergiy Merenkov, CCNY – CUNY) ( slides )
• Joshua Guo, Karthik Seetharaman, and Ilaria Seidel, "Upho posets" (mentor Yibo Gao) ( slides )
• Quanlin (Andy) Chen, Tianze (Peter) Jiang, and Yuxiao (Tom) Wang, "On the Generational Behavior of Gaussian Binomial Coefficients at Root of Unity" (mentor Calder Morton-Ferguson) ( slides )
• Quanlin (Andy) Chen, "The Center of the $q$-Weyl Algebra over Rings with Torsion" (mentor Calder Morton-Ferguson) ( slides )
• Yuxiao (Tom) Wang, "Asymptotics for iterating the Lusztig-Vogan Bijection for $GL_n$ on Dominant Weights" (mentor Calder Morton-Ferguson) ( slides )

12:00-1:00 pm: Session 2

• Alexander Zhang, "On quasisymmetric functions with two bordering variables" (mentor Andrey Khesin) ( slides )
• Holden Mui, "Generating symmetric functions of every arity" (mentor Dr. Zeb Brady) ( slides )
• Ankit Bisain, "The Bernardi formula for non-transitive deformations of the braid arrangement" (mentor Eric Hanson, Brandeis University) ( slides )
• William Shi, "Refinements of product formulas for volumes of flow polytopes" (mentor Prof. Alejandro Morales, UMass Amherst) ( slides )

1:15-1:45 pm: Virtual Chat with PRIMES Chief Research Advisor Prof. Pavel Etingof and Head Mentor Dr. Tanya Khovanova (for students and parents)

2:00-2:50 pm: Session 3

• Vishaal Ram, "Applications of a modified age-structured SIR model" (mentor Prof. Laura Schaposnik, University of Illinois at Chicago) ( slides )
• Srinath Mahankali, "Velocity inversion using the quadratic Wasserstein metric" (mentor Dr. Yunan Yang, Courant Institute, New York University) ( slides )
• Samuel Florin, Matthew Ho, and Rahul Thomas, "Group testing via zero-error channel capacity" (mentor Dr. Zilin Jiang) ( slides )

3:00-4:00 pm: Session 4

• Justin Wu, "Borel cohomology of $S^n$ mapping spaces" (mentor Ishan Levy) ( slides )
• Alvin Chen, "K-semistability of smooth toric Fano varieties" (mentor Kai Huang) ( slides )
• Honglin Zhu, "Irreducible characters for Verma modules for the orthosymplectic Lie superalgebra $\mathfrak{osp}(3|4)$" (mentor Arun Kannan) ( slides )
• Kenta Suzuki, "Value sharing of meromorphic functions" (mentor Prof. Michael Zieve, University of Michigan) ( slides )

4:15-5:10 pm: Session 5

• Brian Liu, "The geometry of harmonic maps in genus one" (mentor Prof. Dhruv Ranganathan, Cambridge, UK) ( slides )
• Fiona Abney-McPeek, Serena An, and Jakin Ng, "The Stembridge equality for skew dual stable Grothendieck polynomials" (mentor YiYu (Adela) Zhang) ( slides )
• Adithya Balachandran, Andrew Huang, and Simon Sun, "Product expansions of q-character polynomials" (mentor Dr. Nir Gadish) ( slides )

Sunday, October 18

Computer Science

9:25 am: Welcoming Remarks

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

9:35-10:35 am: Session 6

• Beining (Cathy) Zhou, "A High-order cumulant-based sparse ruler for improved lag generation" (mentor Hanshen Xiao) ( slides )
• Matthew Ding, "Relay protocol for approximate Byzantine consensus" (mentor Hanshen Xiao) ( slides )
• Linda Chen, "Reducing round complexity of Byzantine broadcast" (mentor Jun Wan) ( slides )
• Jason Yang, "On updating and querying submatrices" (mentor Jun Wan) ( slides )

10:50-12:00 pm: Session 7

• Benjamin Chen, "Towards practical ambiguity sets" (mentor Kyle Hogan) ( slides )
• Yavor Litchev and Abigail Thomas, "Hybrid privacy scheme" (mentor Yu Xia) ( slides )
• Ho Tin (Alex) Fan and Alvin Lu, "Parallel batch-dynamic subgraph maintenance" (mentors Prof. Julian Shun and Jessica Shi) ( slides )
• Kevin Edward Zhao, "Text is an image: Augmentation via embedding mixing" (mentors Prof. Anna Rumshisky and Vladislav Lialin, UMass Lowell) ( slides )

12:15-12:45 pm: Virtual Chat with PRIMES Computer Science Section Coordinator Prof. Srini Devadas and mentors (for students and parents)

Bioinformatics and Computational Biology

1:00-2:05 pm: Session 8

• Anish Mudide, "SARS-CoV-2 drug discovery based on intrinsically disordered regions" (mentor Prof. Gil Alterovitz) ( slides )
• Varun Suraj, "Developing clinical decision support systems for cancer and COVID-19 precision medicine" (mentor Prof. Gil Alterovitz) ( slides )
• Daniel Xu, "Network based digital contact tracing and testing strategies for the COVID-19 pandemic" (mentor Dr. Jesse Geneson, Iowa State University) ( slides )
• Tanisha Saxena and Daniel Xu, "Graph alignment-based protein comparison" (mentor Younhun Kim) ( slides )

2:20-3:20 pm: Session 9

• Sarah Chen, "In silico prediction of retained intron-derived neoantigens in leukemia" (mentors Dr. Nicoletta Cieri, Dana-Farber Cancer Institute, and Kari Stromhaug) ( slides )
• Mikhail Alperovich, "Data driven quality control for single-cell RNA sequencing analysis" (mentor Dr. Ayshwarya Subramanian, Broad Institute)
• Neil Chowdhury, "Modeling the effect of histone methylation on chromosomal organization in colon cancer cells" (mentor Dr. Maxim Imakaev)
• Vishnu Emani, "Statistical ranking model for candidate genes in rare genetic disorders" (mentors Dr. Klaus Schmitz-Abe and Dr. Pankaj Agrawal, Boston Children's Hospital) ( slides )

Mathematics

3:35-4:45 pm: Session 10

• Jessica Zhang, "Tight contact structures on the solid torus" (mentor Prof. Zhenkun Li, Stanford University) ( slides )
• William Qin, "Colored HOMFLY polynomials of genus-2 pretzel knots" (mentor Yakov Kononov, Columbia University) ( slides )
• Daniel Hong, Hyunwoo (David) Lee, and Alex Wei, "Optimal solutions and ranks in the max-cut SDP" (mentor Dr. Diego Cifuentes) ( slides )
• Richard Chen, Jason Tang, and Nathan Xiong, "Few distance sets in $\ell_p$ spaces and $\ell_p$ product spaces" (mentor Feng Gui) ( slides )

5:00-6:15 pm: Session 11

• Katherine Tung, "The Sperner property for 132-avoiding intervals in the weak order" (mentor Christian Gaetz) ( slides )
• Andrew Cai, "Ratios of Naruse-Newton coefficients obtained from descent polynomials" (mentor Pakawut Jiradilok) ( slides )
• Sean Li, "The Penney's Game with group action" (mentor Dr. Tanya Khovanova) ( slides )
• Tae Kyu Kim, "On generalized Carmichael numbers" (mentor Yongyi Chen) ( slides )
• William Wang, "Planar embeddings of periodic time-dependent graphs" (mentor Dr. Jesse Geneson, Iowa State University) ( slides )

Tenth Annual Spring Term PRIMES Conference, June 6-7, 2020

Spring conference abstracts booklet

Saturday, June 6

Mathematics

10:00 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

10:15 am Session 1: PRIMES STEP

• Isha Agarwal, Matvey Borodin, Aidan Duncan, Kaylee Ji, Shane Lee, Boyan Litchev, Anshul Rastogi, Garima Rastogi, and Andrew Zhao (PRIMES STEP Senior group), A Penney for our thoughts: A story of a series of games and an Avaricious Duo (mentor Dr. Tanya Khovanova) ( slides )
• Eric Chen, William Du, Tanmay Gupta, Alicia Li, Srikar Mallajosyula, Matthew Qian, Rohith Raghavan, Arkajyoti Sinha, Maya Smith, and Samuel Wang (PRIMES STEP Junior group), Hidden dimension of SET: The classification of magic SET squares (mentor Dr. Tanya Khovanova) ( slides )

11:00 am Session 2: PRIMES Circle

• Peter Haine, PRIMES Circle Coordinator, Introduction
  Anya Ditkoff and Arshia Verma, Random numbers (mentor Natalya Ter-Saakov)
• Kaylee Chen, Hawa Hamidou Tabayi, and Alice Zhou, Game theory: A playful presentation (mentor Marisa Gaetz) ( slides )
• Diego González Gauss and Anthony Zhao, Dynamic programming and applications (mentor Jung Soo (Victor) Chu) ( slides )

12:10 pm Session 3: PRIMES Circle

• Joaquín Pischner Gutierrez and Jessica He, On group automorphisms (mentor Zhuofan Xie)
• Zoe Shleifer and Elena Su, π-ish: Continued fractions (mentor Maya Sankar) ( slides )
• William Ayinon, How Knot Theory is important to DNA Biology (mentor Kenneth Cox) ( slides )
• Benjamin Ratin, Surfaces in Knot Theory (mentor Kenneth Cox) ( slides )

1:15 pm Session 4: PRIMES Circle

• Akhil Kammila and Anshul Rastogi, Evolution of curves via curve shortening flow (mentor Bernardo Hernández Adame) ( slides )
• Divya Rajaraman and Henry Serrano-Wu, Puzzles in graph theory (mentor Agustin Garcia)
• Minghan Sun, Andrew Weinfeld, and Christopher Zhu (PRIMES reading group), Homomorphisms of Graphs: Colorings, Cliques and Transitivity (mentor Younhun Kim) ( slides )

Sunday, June 7

Computer Science and Computational Biology

9:00 am Welcoming Remarks

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

9:15 am Session 5

• Sanath Govindarajan, Integrating fully homomorphic encryption into the MLIR compiler framework (mentor William Moses) ( slides )
• Walden Yan, Improvements on description-based neural program synthesis models (mentor William Moses) ( slides )
• Neel Bhalla, Constructing workflow-centric traces in close to real time for the Hadoop file system (mentor Prof. Raja Sambasivan, Tufts University) ( slides )

10:20 am Session 6

• Yuxuan (Jason) Chen, Real world application of event-based end to end autonomous driving (mentors Dr. Igor Gilitschenski and Alexander Amini) ( slides )
• Michael Gerovitch, Visualizing and enhancing environment-aware pedestrian trajectory prediction for autonomous driving (mentor Dr. Igor Gilitschenski) ( slides )
• Ethan Mendes, Towards a robust defense for imperceptible audio adversarial examples (mentor Kyle Hogan) ( slides )

11:25 am Session 7

• Patrick Zhang, Privacy-preserving online advertising (mentor Sacha Servan-Schreiber)
• Andrew Shen, Towards verifying application isolation for cryptocurrency hardware wallets (mentor Anish Athalye) ( slides )
• Alek Westover, The variable-processor cup game (mentor William Kuszmaul) ( slides )

12:30 pm Session 8

• Jonathan Yin, Predicting receptor activity from structural features of chemical ligands (mentor Dr. Hattie Chung, Broad Institute) ( slides )
• Aditya Saligrama, Revisiting ensembles in an adversarial context: Improving natural accuracy (mentors Guillaume Leclerc and Prof. Alexander Madry) ( slides )

Mathematics Reading Groups

Wednesday, December 9

Zoom webinar

6:00 pm Welcoming Remarks

• Prof. Pavel Etingof, PRIMES Chief Research Advisor
• Dr. Slava Gerovitch, PRIMES Program Director

6:10 pm

• Anuj Sakarda, Jerry Tan, and Armaan Tipirneni, "Properties of elliptic curves" (mentor Kevin Chang) ( slides )
• Christina Li, Yuxin Xie, and William Yue, "Markov chains and card shuffling" (mentor Chun Hong Lo) ( slides )
• Sanjana Das, Espen Slettnes, and Sophie Zhu, "The Group of rational points on a cubic" (mentor Kaavya Valiveti) ( slides )

7:20 pm

• Lucy Cai and Zheheng Xiao, "Induced representations of finite groups" (mentor Dr. Alexander Vitanov) ( slides )
• Kenji Nakagawa, Rishi Verma, and Daniel Xu, "Walks on Young's lattice" (mentor Yan Sheng Ang) ( slides )
• Ishita Goluguri, Toyesh Jayaswal, and Andrew Lee, "A PRIMES exposition of the Prime Number Theorem" (mentor Chengyang Shao) ( slides )

Contact

With questions, contact PRIMES Program Director Slava Gerovitch at