# Seventh Annual PRIMES Conference, May 20-21, 2017

**Room 4-370, MIT**

**Open to the public**

**Download conference poster**

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

**Saturday, May 20 **

**Mathematics **

**Prof. Pavel Etingof and Dr. Tanya Khovanova with PRIMES students**

**8:20 am Welcoming Remarks **

Prof. Tomasz Mrowka, Head of the MIT Mathematics
Department

Prof. Pavel Etingof, PRIMES Chief Research Advisor

Dr. Slava Gerovitch, PRIMES Program Director

**Franklyn Wang**

**8:50 am Session 1**

Franklyn Wang, *Monodromy groups of indecomposable rational functions* (mentor Prof. Michael Zieve, University of Michigan) (slides)

Michael Ren, *On quasi-invariant polynomials* (mentor Xiaomeng Xu) (slides)

Swapnil Garg, *Hilbert series of the representation of Cherednik algebras* (mentor Alexey Pakharev, Northeastern University) (slides)

Megan Joshi, *Maximal self-intersection number of curves on surfaces* (mentor Prof. Moira Chas, SUNY at Stony Brook) (slides)

**Megan Joshi**

**Prof. Pavel Etingof**

**10:10 am Session 2**

Anlin Zhang, *Modelling epidemics on networks with cliques* (mentor Prof. Laura Schaposnik, University of Illinois at Chicago) (slides)

Kyle Gatesman, *An algorithmic and computational approach to optimizing gerrymandering* (mentor Prof. James Unwin, University of Illinois at Chicago) (slides)

Richard Xu, *Graph theory and tessellations* (mentor Prof. Sergiy Merenkov, CCNY – CUNY) (slides)

Kaiying Hou and Byung Yeon Rhee, *Continuum modelling of traffic system with autonomous vehicles* (mentor Andrew Rzeznik) (slides)

**Kyle Gatesman**

**Dr. Tanya Khovanova**

**11:25 am Session 3**

Zoe Levitt (PRIMES Circle), *An introduction to group theory and braids* (mentor Lara Booth) (slides)

Joshua Lee, *Coin games and 5-way scales* (mentor Dr. Tanya Khovanova) (slides)

Hyunjun Ahn, Benjamin Chen, Richard Chen, Ezra Erives, Jeremy Fleming, Michael Gerovitch, Tejas Gopalakrishna, Neil Malur, Nastia Polina, and Poonam Sahoo (PRIMES STEP students) *We are the CHOMPians* (mentor Dr. Tanya Khovanova) (slides)

Pratik Alladi, Neel Bhalla, Nathan Sheffield, Tiancheng Song, Will Sun, Andrew The, Alan Wang, Naor Wiesel, Kevin Zhang, Kevin Zhao (PRIMES STEP students) *Impartial combinatorial games* (mentor Dr. Tanya Khovanova) (slides)

**Zoe Levitt**

**PRIMES STEP students**

**1:30 pm Session 4**

Ayush Agarwal, *Maps between critical groups of group representations* (mentor Christian Gaetz) (slides)

Michael Gintz, *Classifying graph Lie algebras* (mentor Dr. Tanya Khovanova) (slides)

Aaron Kaufer, *Low-dimensional d-Algebras* (mentor Lucas Mason-Brown) (slides)

Daniel Liu and Nathan Ramesh, *Verma modules of the Virasoro algebra* (mentor Siddharth Venkatesh) (slides)

**Aaron Kaufer**

**2:45 pm Session 5 **

Richard Zhou, *Pattern avoidance classes invariant under the modified Foata-Strehl action* (mentor Yan Zhuang, Brandeis University) (slides)

Dylan Pentland, *Coefficients of q-binomial coefficients modulo N* (mentor Younhun Kim) (slides)

Jason Chen, *Arithmetic properties of weighted Catalan numbers* (mentor Dmitry Kubrak) (slides)

Mihir Singhal, *Generalizations of Hall-Littlewood polynomials* (mentor Christopher Ryba) (slides)

**Louis Golowich**

**Jeffery Yu**

**4:00 pm Session 6 **

William Zhang, *Pattern avoidance on binary matrices* (mentor Jesse Geneson) (slides)

Louis Golowich, *Set-sequential trees* (mentor Chiheon Kim) (slides)

Michael Ma, *A generalization of Erdös-Szekeres to permutation pattern replacement* (mentor William Kuszmaul, Stanford University) (slides)

Wendy Wu and Andy Xu, *Second gonality of Erdös-Rényi random graphs* (mentor Guangyi Yue) (slides)

**Wendy Wu**

**Aaditya Singh and Sam Cohen** (left to right)

**5:15 pm Session 7 **

Sam Cohen and Aaditya Singh, *Generalization of some properties of discrete curve shortening flow* (mentor Ao Sun) (slides)

Grace Tian, *Multi-crossing numbers for knots* (mentor Jesse Freeman) (slides)

Gopal Goel, *Limits of interlacing eigenvalues in the tridiagonal β-Hermite matrix model* (mentor Andrew Ahn) (slides)

August Chen, *Folding, jamming, and random walks* (mentor Prof. Jayadev Athreya, University of Washington) (slides)

**Grace Tian**

**6:30 pm Session 8 **

Jeffery Yu, *Jacobian groups of biconnected graphs* (mentor Dr. Dhruv Ranganathan) (slides)

Kaan Dokmeci, *On denesting radicals* (mentor Yongyi Chen) (slides)

David Darrow, *A near-optimal spectral method for simulating fluids in a cylinder* (mentors Prof. Alex Townsend, Cornell University, and Prof. Grady Wright, Boise State University) (slides)

Peter Rowley, *Random walks on a grid with a periodic boundary condition* (mentor Boya Song) (slides)

**David Darrow**

**Prof. Pavel Etingof and Dr. Slava Gerovitch with PRIMES students**

**Sunday, May 22 **

**Computer
Science and Computational Biology **

**9:00 am Welcoming Remarks **

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

Dr. Slava Gerovitch, PRIMES Program Director

**Prof. Srini Devadas and John Kuszmaul**

**Sanjit Bhat**

**9:15 am Session 9**

Vivek Bhupatiraju, *Towards append-only authenticated dictionaries* (mentor Alin Tomescu) (slides)

Robert Chen, John Kuszmaul, and Yiming Zheng, *Keychat: Secure messaging via Bitcoin* (mentor Alin Tomescu) (slides)

Sanjit Bhat and David Lu, *Analyzing Tor’s anonymity with machine learning* (mentor Albert Kwon) (slides)

Theodor Lukin Yelin, *AnonReddit: A strongly anonymous public forum* (mentor Albert Kwon) (slides)

**Anjali Saini**

**Nihar Sheth**

**10:45 am Session 10**

Anjali Saini, *Investigating the consensus algorithm* (mentor Ling Ren) (slides)

Nihar Sheth, *Investigating the scalability of Go’s garbage collector in multicore environments* (mentor Cody Cutler) (slides)

Robert Cunningham, *An analysis of a directory entry cache in a high level language* (mentor Cody Cutler) (slides)

**Zachary Steinberg**

**Caleb Trotz**

**11:40 am Session 11**

Zachary Steinberg, *Development of a new method for multicolor image segmentation of neuronal tissue in 20x expanded hydrogels* (mentor Daniel Goodwin) (slides)

Chao Cheng, *1.00 for life: Real-time analysis of computational thinking* (mentor Prof. John Williams) (slides)

Mayank Mali, Caleb Trotz, and Justin Yu, *Automated calibration and a real-time web-based control interface for fiber lasers* (mentor Michael Plotkin, IPG Photonics) (slides)

**Vinjai Vale**

**1:35 pm Session 12**

Harshal Sheth and Andrew Sun, *Tarpan: A router that supports evolvability* (mentor Dr. Raja Sambasivan, Boston University) (slides)

Henry Heffan and Shashvat Srivastava, *Mo-nero, Mo-problems: Defending Monero against temporal analysis* (mentors Ethan Hellman, Dr. Jason Hennessey, Kyle Hogan, and Dr. Mayank Varia, Boston University) (slides)

Vinjai Vale, *Vision as inverse graphics: Machine learning techniques towards a program-based model for scene understanding* (mentor Kevin Ellis) (slides)

**Adithya Vellal**

**Andrew Gritsevskiy**

**2:50 pm Session 13**

Dr. Gil Alterovitz, Harvard-MIT Division of Health Sciences and Technology, Introductory remarks

Adithya Vellal, *Enrichment and analysis of sequence motifs in genomic variant calls* (mentor Dr. Gil Alterovitz) (slides)

Andrew Gritsevskiy, *Structural gene expression* (mentor Dr. Gil Alterovitz) (slides)

Eric You, *Analyzing compression: Using gene sets to find patterns in genomic compression* (mentor Dr. Gil Alterovitz) (slides)

**James Jusuf**

**3:55 pm Session 14**

Makiah Bennett and Jack Flahive, *Precision cancer medicine web application* (mentor Dr. Gil Alterovitz) (slides)

James Jusuf, *A versatile algorithm for finding patterns in large cancer cell line data sets* (mentor Dr. Mahmoud Ghandi, Broad Institute) (slides)

Kevin Hu, *An analysis of MDM4 alternative splicing and effects across cancer cell lines* (mentor Dr. Mahmoud Ghandi, Broad Institute) (slides)

Kalyan Palepu and Andrew Zhang, *Compression of genomic variants using convolutional autoencoders* (mentor Dr. Gil Alterovitz) (slides)

**Friday, December 15 **

**Aurash Vatan and Andrew Yao**

**5:30 pm**

Ashley Chen and Allen Wang, *Hyperplane arrangements: Intersection posets, characteristic polynomials, and regions* (mentor Zhulin Li) (**slides**)

Nathaniel Liberman and Nhat Pham, *Topics in enumerative combinatorics* (mentor Svetlana Makarova) (**slides**)

Nithin Kavi and Anmol Sakarda, *Topics in knot theory* (mentor Zhenkun Li) (**slides**)

Aurash Vatan and Andrew Yao, *Elliptic curves and Mordell's theorem* (mentor Andrew Senger) (**slides**)

Jeremy Chen and Yuxuan (Tom) Zhang, *Algebraic number theory and representation theory* (mentor Robin Elliott) (**slides**)

**Contact**

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