# 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**

**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 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)

**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 A*_{n} *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 pm 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)

**Audience**

**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**

**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)

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)

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**

**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**

**Contact**

**With questions, contact PRIMES Program Director
Dr. Slava Gerovitch at**** primes@math.mit.edu **