# Sixth Annual PRIMES Conference, May 21-22, 2016

**Room 4-270, MIT**

**Open to the public**

**Download conference posters (8x11, 11x17, or 24x36)**

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

**Saturday, May 21 **

**Mathematics **

**PRIMES Math and PRIMES STEP students and mentors with Prof. Pavel Etingof**

**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

**Nicholas Guo**

**8:50 am Session 1**

Nicholas Guo,* Rational hyperplane arrangements and counting independent sets of symmetric graphs* (mentor Guangyi Yue) (**slides**)

Valerie Zhang, *Computer-based representations and manipulations of paths in the plane* (mentor Umut Varolgunes) (**slides**)

Aaron Yeiser,* A robust spectral PDE solver on skinny triangles *(mentor Dr. Alex Townsend) (**slides**)

**Valerie Zhang**

**10:00 am Session 2**

Kai-Siang Ang, *On the geometry of icosahedral viruses* (mentor Prof. Laura Schaposnik, University of Illinois at Chicago) (**slides**)

Nikhil Marda, *On point separation by arrangements of lines* (mentor Borys Kadets) (**slides**)

Zachary Chroman, *Rational embeddings of convex polyhedra* (mentor Sheela Devadas, Stanford University) (**slides**)

**Zachary Chroman**

**11:10 am Session 3**

Ria Das,* Investigations of mixed reinforcement-memory models for random walks *(mentor Andrew Rzeznik) (**slides**)

Benjamin Chen, Ezra Erives, Leon Fan, Michael Gerovitch, Jonathan Hsu, Neil Malur, Ashwin Padaki, Nastia Polina, Will Sun, Jacob Tan, and Andrew The (PRIMES STEP students), *Who is guilty?* (mentor Dr. Tanya Khovanova) (**slides**)

Benjamin Chen, Ezra Erives, Leon Fan, Michael Gerovitch, Jonathan Hsu, Neil Malur, Ashwin Padaki, Nastia Polina, Will Sun, Jacob Tan, and Andrew The (PRIMES STEP students), *Alternator coins* (mentor Dr. Tanya Khovanova) (**slides**)

**PRIMES STEP students**

**1:10 pm Session 4**

Felix Wang, Ramification of solutions of functional equations (mentor Prof. Michael Zieve, University of Michigan) (**slides**)

Nathan Smith, Square-primitive gaps (mentor Xiaoyu He, Harvard University) (**slides**)

Meena Jagadeesan and Karthik Karnik, The Outer Automorphism of *S*_{6} (mentor Akhil Mathew) (**slides**)

**Meena Jagadeesan and Karthik Karnik with PRIMES head mentor Dr. Tanya Khovanova**

**2:25 pm Session 5 **

Nina Anikeeva, *Applications of ergodic theory to continued fractions on the Heisenberg group* (mentor Prof. Jayadev Athreya, University of Washington)

Rafael Saavedra, *Discreet coin weighings and the Frobenius problem* (mentor Dr. Tanya Khovanova) (**slides**)

Harish Vemuri, *Tiling-harmonic conjugate functions* (mentor Prof. Sergiy Merenkov, CCNY – CUNY) (**slides**)

**3:30 pm Session 6 **

Nelson (Shuheng) Niu, *Extensions of classic combinatorial games* (mentor Dr. Tanya Khovanova) (**slides**)

Kevin Chang, *Ordered Ramsey numbers of small graphs* (mentor William Kuszmaul, Stanford University) (**slides**)

Louis Golowich and Richard Zhou, *Maximum number of pairwise G-different permutations* (mentor Chiheon Kim) (**slides**)

**Kevin Chang**

**4:40 pm Session 7 **

Eric Nie and Alok Puranik, *Invariants of knots* (mentor Zhenkun Li) (**slides**)

Albert Yue, *Knot diagram invariants and bounds for the number of Reidemeister moves needed for unknotting* (mentor Piotr Suwara) (**slides**)

Alec Leng, *Independence of the Miller-Rabin and Lucas probable prime tests* (mentor David Corwin) (**slides**)

**Albert Yue**

**6:15 pm Session 8 **

Maya Sankar, *The dimensions of partially directed nil-Temperley-Lieb algebras* (mentor Dr. Tanya Khovanova) (**slides**)

Laura Pierson, *Signatures of stable multiplicity spaces in symmetric group restrictions* (mentor Siddharth Venkatesh) (**slides**)

Dhruv Rohatgi, *A connection between vector bundles over smooth projective curves and representations of quivers* (mentor Vishal Arul) (**slides**)

**Laura Pierson**

**7:20 pm Session 9 **

Alec Sun, *Wall crossing bijections and representations of rational Cherednik algebras* (mentor Seth Shelley-Abrahamson) (**slides**)

Matt Lipman, *Representations of Cherednik algebras *(mentor Gus Lonergan) (**slides**)

Matthew Hase-Liu, *Counting points on curves of the form* $y^{m_{1}}=c_{1}x^{n_{1}}+c_{2}x^{n_{2}}y^{m_{2}}$ (mentor Nicholas Triantafillou) (**slides**)

**Matthew Hase-Liu**

**Sunday, May 22 **

**Computer
Science and Computational Biology **

**8:45 am Welcoming Remarks **

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

Dr. Slava Gerovitch, PRIMES Program Director

**Leo Alcock**

**9:00 am Session 10: **

__Computer Science__Harshal Sheth, Aashish Welling, and Nihar Sheth, *Read-copy update in a garbage collected environment *(mentor Cody Cutler) (**slides**)

Vivek Bhupatiraju, John Kuszmaul, and Vinjai Vale, *Exploring proof of space with hard-to-pebble graphs* (mentors Ling Ren and Albert Kwon) (**slides**)

Leo Alcock, *Private publishing using Bitcoin *(mentor Ling Ren) (**slides**)

**From left: Prof. Srini Devadas, Henry Liu, Siye Zhu, and Justin Kaashoek**

**10:30 am Session 11: Computer Science**

Cristian Gutu, *SeifPass: A secure password manager* (mentor Albert Kwon) (**slides**)

Henry Liu, Justin Kaashoek, and Siye Zhu, *Scalable logging algorithm for in-memory database systems* (mentor Xiangyao Yu) (**slides**)

Yatharth Agarwal and Vishnu Murale, *Moving in next door: network flooding as a side channel in cloud environments* (mentors Dr. Jason Hennessey, Kyle Hogan, and Dr. Mayank Varia, Boston University) (**slides**)

**Betsy Pu**

**11:55 am Session 12: Computational and Physical Biology**

Prof. Leonid Mirny, Introductory remarks

Laura Braverman, *Protein determinants of chromosome domains* (mentor Nezar Abdennur) (**slides**)

Betsy Pu, *Chromatin states at boundary elements* (mentor Nezar Abdennur) (**slides**)

Krishna Suraj, *Emergent chromosome organization in interphase from loop extrusion* (mentor Dr. Geoffrey Fudenberg) (**slides**)

**Zachary Steinberg**

**2:00 pm Session 13: Computational Neuroscience**

Prof. Ed Boyden, Introductory remarks

Albert Gerovitch, *Metrics for comparing 3D neuron segmentations in expansion microscopy connectomics *(mentor Dr. Adam Marblestone) (**slides**)

Zachary Steinberg, *Automatic segmentation of punctate 3D super-resolution microscopy data* (mentor Daniel Goodwin) (**slides** and** video**)

**Kara Luo**

**3:00 pm Session 14: Medical
Informatics**

Prof. Gil Alterovitz, Introductory remarks

Daniel Lu, *Study of various synergistic drug mechanisms in disordered protein-related diseases *(mentor Prof. Gil Alterovitz) (**slides**)

Kara Luo, *Computational modeling identifies biosynthetic modifications to improve drug inhibition against *Klebsiella pneumoniae (mentor Prof. Gil Alterovitz) (**slides**)

Arul Prasad, *Targeting viral envelope proteins: an application to the Zika virus* (mentor Prof. Gil Alterovitz) (**slides**)

**Andrew Gritsevskiy and Adithya Vellal**

**4:15 pm Session 15:
Medical
Informatics**

Andrew Gritsevskiy and Adithya Vellal, *Compression and integration of human genomic variants into smart EHR systems* (mentor Prof. Gil Alterovitz) (**slides**)

John Flahive, *Providing clinical decision support to medical providers through interpretation of gene-drug interactions* (mentor Prof. Gil Alterovitz) (**slides**)

James Jusuf, *Exploring the effects of CTCF binding site mutations on transcriptional regulation* (mentor Dr. Mahmoud Ghandi, Broad Institute) (**slides**)

**PRIMES Computer Science and Computational Biology students and mentors with Prof. Leonid Mirny**

**Tuesday, December 6 **

**6:00 pm, Room 2-146**

Jeffrey Chang and Evan Fang, *Defining the Jones Polynomial in Terms of the Tutte Polynomial *(mentor Hood Chatham) (**slides**)

Sam Cohen and Peter Rowley,* Dynamic Systems and Discrete Curve Shortening Flow* (mentor Ao Sun) (**slides**)

Aaron Kaufer,* The Domino Tiling Problem* (mentor Lucas Mason-Brown) (**slides**)

**PRIMES math reading group students and mentors with Prof. Pavel Etingof**

**Friday, December 9 **

**5:30 pm, Room 2-146**

Sathwik Karnik,* Irreducibility Tests in Fp[x]* (mentor Hyun Jong Kim) (**slides**)

Dylan Pentland and Albert Zhang,* Posets and Their Incidence Algebras* (mentor Atticus Christensen) (**slides**)

**PRIMES math reading group students and mentors with Prof. Pavel Etingof**

**Contact**

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