Twelfth Annual Fall Term PRIMES Conference, October 15-16, 2022

Saturday, October 15

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

10:15-11:40 am: Session 1: Applied Mathematics

• Grace Wang, “Correlations between COVID-19 and dengue” (mentor Prof. Laura Schaposnik, University of Illinois at Chicago) (slides)
• Linda He, “Search of primordial black holes in extrasolar systems” (mentor Prof. James Unwin, University of Illinois at Chicago) (slides)
• Ethan Zhou, “Online learning of smooth functions” (mentor Dr. Jesse Geneson, SJSU) (slides)
• Andrew Tung and Karthik Vedula, “New properties of the intrinsic information and their relation to bound secrecy” (mentor Andrey Khesin) (slides)
• Benjamin Fan and Edward Qiao, “Deep learning for partial differential equations in economics” (mentor Prof. Lu Lu, University of Pennsylvania) (slides)

12:00-12:50 pm: Session 2: Combinatorics I

• Matvey Borodin, Ethan Liu, and Justin Zhang, “Vanishing polynomials and polynomial functions” (mentor Prof. Jim Coykendall, Clemson University) (slides)
• Jeffrey Chen, “Positivity properties for $q$-hit numbers” (mentors Prof. Alejandro Morales and Jesse Selover, UMass Amherst) (slides)
• Rich Wang, “Ending states of a special variant of the chip-firing algorithm” (mentor Dr. Tanya Khovanova) (slides)

1:00-2:00 pm: Session 3: Combinatorics II

• Advay Goel, “The geometry and limits of Young partition flow polytopes” (mentor Zoe Wellner, Carnegie Mellon University) (slides)
• Derek Liu, “Arrangements of simplices in fine mixed subdivisions” (mentor Yuan Yao) (slides)
• Anthony Wang, “Consecutive patterns in Coxeter groups” (mentor Yibo Gao) (slides)
• Nilay Mishra, “On the uniqueness of certain types of circle packings on translation surfaces” (mentor Prof. Sergiy Merenkov, CCNY – CUNY) (slides)

2:00-2:30 pm: Virtual Chat with PRIMES Chief Research Advisor Prof. Pavel Etingof and Head Mentor Dr. Tanya Khovanova (for students and parents)

3:00-3:55 pm: Session 4: Miscellaneous

• Max Misterka, “A generalization of q-calculus using formal group laws” (mentor Sanath Devalapurkar, Harvard University)
• Eric Chen and Alexander Zitzewitz, “Unitarity conditions of Heun and Lamé differential operators” (mentor David Darrow) (slides)
• Eric Shen and Kevin Wu, “Congruences between logarithms of Heegner points” (mentor Dr. Daniel Kriz, Institut de Mathématiques de Jussieu – Paris Rive Gauche) (slides)

4:05-5:10 pm: Session 5: Graph Theory

• Paul Gutkovich, “Computing truncated metric dimension on trees” (mentor Zi Song Yeoh) (slides)
• Max Xu, “Gonality sequences of multipartite graphs” (mentors Amanda Burcroff, Harvard University, and Dr. Felix Gotti) (slides)
• Edward Yu, “A Turán-type problem in mixed graphs” (mentor Nitya Mani) (slides)
• David Dong, Alan Lee, and Michelle Wei, “Connectedness and cycle spaces of friends-and-strangers graphs” (mentor Dr. Colin Defant) (slides)

5:20-6:10 pm: Session 6: Algebra I

• Sophie Zhu, “Pointed fusion categories over non-algebraically closed fields” (mentors Prof. Julia Plavnik and Sean Sanford, Indiana University Bloomington) (slides)
• Brendan Halstead, “Moduli spaces of tropical and logarithmic morphisms” (mentor Jeffery Yu)
• Alan Bu, Joseph Vulakh, and Alex Zhao, “Length-factoriality and pure irreducibility” (mentor Dr. Felix Gotti) (slides)

6:20-7:10 pm: Session 7: Algebra II

• Annie Wang, “The Hilbert series of the irreducible quotient for the polynomial representation of the rational Cherednik algebra of type A” (mentor Serina Hu) (slides)
• George Cao, “The indecomposable summands of the tensor products of monomial modules over finite 2-groups” (mentor Dr. Kent Vashaw) (slides)
• Caroline Liu, Annabel Ma, and Andrew Zhang, “Factorization invariants of arithmetical congruence monoids” (mentor Prof. Scott Chapman, Sam Houston State University) (slides)

Sunday, October 16

Computer Science and Computational Biology

9:00 am: Welcoming Remarks

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

9:10-10:10 am: Session 8: Computer Science I

• Alicia Li and Matan Yablon, “How optimal can you get: Stochastic and adversarial reinforcement learning” (mentor Mayuri Sridhar) (slides)
• Eric Chen and Boyan Litchev, “Truly anonymous sealed sender in Signal” (mentors Kyle Hogan and Simon Langowski) (slides)
• Simon Beyzerov, Hyojae Park, and Eliyahu Yablon, “Private access control for function secret sharing” (mentor Sacha Servan-Schreiber)

10:30-11:20 am: Session 9: Computational Biology I

• Anish Mudide, “Uncovering the genomic basis for extinction risk via practical machine learning” (mentor Dr. Ayshwarya Subramanian, Broad Institute)
• Achyuta Rajaram, “Comparative analysis of mouse and human podocytes with scRNA-seq” (mentor Dr. Ayshwarya Subramanian, Broad Institute)
• Tanmay Gupta and Raj Saha, “Surveying the presence and diversity of coronaviruses in mammalian transcriptomes” (mentor Dr. Ayshwarya Subramanian, Broad Institute)

11:40 am - 12:30 pm: Session 10: Computational Biology II

• Steven Tan, “Models for somatic CAG repeat expansion in the onset and progression of Huntington’s disease” (mentors Bob Handsaker and Seva Kashin, Broad Institute) (slides)
• Rianna Santra, “Diagnosing brain cancers with gene expression data using a novel neural network method” (mentor Prof. Gil Alterovitz) (slides)
• Ho Tin (Alex) Fan and Rianna Santra, “Leveraging statistical distributions for RNA sequencing across time” (mentor Prof. Gil Alterovitz) (slides)

12:30-1:00 pm: Virtual Chat with PRIMES Computer Science Section Coordinator Prof. Srini Devadas and mentors (for students and parents)

1:30-2:25 pm: Session 11: Computer Science I

• Michael Huang, “Theoretically efficient parallel density-peaks clustering” (mentors Prof. Julian Shun and Shangdi Yu) (slides)
• Joey Dong and Anshul Rastogi, “Locating regions of uncertainty in distributed systems using aggregate trace data” (mentors Prof. Raja Sambasivan, Darby Huye, and Max Liu, Tufts University) (slides)
• Coleman DuPlessie and Eddie Wei, “Deep learning transformers for non-cyclical kinematics” (mentor Andrew Gritsevskiy, University of Toronto) (slides)

Twelfth Annual Spring Term PRIMES Conference, May 21-22, 2022

Saturday, May 21

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

10:15-11:15 am: Session 1. PRIMES Circle

• Crystal Egbunike & Wintana Tewolde, “Graph Theory and Its Applications” (mentor Victor Chu) ( slides )
• Pete Olhava & Alexander Gil Osorio, “An Introduction to Knot Theory” (mentor Preston Cranford) ( slides )
• Sebastian Cuervo & Ben Stokes, “Triangles in Various Geometries” (mentor Paige Dote) ( slides )

11:25 am-12:45 pm: Session 2. PRIMES Circle

• Ling (Esther) Fu & Sarah Pan, “The Busy Beaver Problem” (mentor Alexandra Hoey) ( slides )
• Jessica Guo & Audrey Wei, “NP-Completeness” (mentor Kerri Lu) ( slides )
• Zoe Awa & Ankita Varigonda, “Game Theory” (mentor Yuyuan Luo) ( slides )
• Elena Baskakova & Alice He, “Probability Theory: Why You Are Falsely Convicted, Lonely, and in Debt” (mentor Jeremy Smithline) ( slides )

1:45-2:45 pm: Session 3. PRIMES Circle

• Maya Koreth & Dania Rustom, “Number Theory and Divisibility Issues” (mentor Ariana Park) ( slides )
• Sophia Hou & Jaeyi Song, “Group Theory” (mentor Merrick Cai) ( slides )
• Gracie Sheng & Evelyn Zhu, “Symmetry and Simplicity in Finite Group Theory” (mentor Gabrielle Kaili-May Liu) ( slides )

3:00-3:40 pm: Session 4. PRIMES STEP

• Hwiseo Choi, Shreyas Ekanathan, Aidan Gao, Sylvia Zia Lee, Rajarshi Mandal, Vaibhav Rastogi, Daniel Sheffield, Michael Yang, Angela Zhao, and Corey Zhao (PRIMES STEP Junior group), “The Struggles of Chessland” (mentor Dr. Tanya Khovanova) ( slides )
• Eric Chen, Adam Ge, Andrew Kalashnikov, Ella Kim, Evin Liang, Mira Lubashev, Matthew Qian, Rohith Raghavan, Benjamin Taycher, Samuel Wang (PRIMES STEP Senior group), “Disarray in the Tribarray: A Tribsploration” (mentor Dr. Tanya Khovanova) ( slides )

3:40-4:00 pm: auction in support of Yulia's Dream , a new PRIMES section for students from Ukraine

PRIMES head mentor Tanya Khovanova has created beautiful mathematical crochets in the colors of Ukrainian flag – hyperbolic surfaces and Whitehead links . We will auction them off to support PRIMES efforts to help students from Ukraine study advanced topics and do math research. Since it’s a PRIMES auction, we will accept bids in prime numbers only!

4:00-4:55 pm: Session 5. Math Reading Groups

• Anuj Sakarda and Jerry Tan, “The Probabilistic Method” (mentor YounHun Kim) ( slides )
• Yi (Alex) Liang, “Representation Theory and Quantum Systems” (mentor Sanjay Raman) ( slides )
• Ilaria Seidel, Nathan Xiong, and William Yue, “Dynkin Quivers and Their Representations” (mentor Dr. Aleksandra Utiralova) ( slides )

Sunday, May 22

Mathematics

10:00 am: Welcoming Remarks

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

10:10-10:45 am: Session 6. Math Reading Groups

• Joshua Guo, Andrew Lee, and Karthik Seetharaman, “Galois Theory and the Insolvability of the Quintic” (mentor Chun Hong Lo) ( slides )
• Kevin Zhao, “Lie Matrices” (mentor Sanjay Raman) ( slides )

10:10-10:45 am: Session 6. Math Reading Groups

• Leisha Fortunat, “A Simple Introduction to Graph Theory” (mentor Rachana Madhukara) ( slides )
• Daniela Yablon & Ayelet Yablon, “Introduction to Cryptography” (mentor Aparna Gupte) ( slides )
• Zoe Siegelnickel & Palak Yadav, “Algorithm Analysis” (mentor John Shackleton) ( slides )

Computer Science and Computational Biology

1:00 pm: Welcoming Remarks

• Prof. Srini Devadas, PRIMES Computer Science Section Coordinator

1:05-2:05 pm: Session 8. Computer Science

• Rachel Chen, “Uotchi: A Hardware Platform to Create and Exchange Non Fungible Objects” (mentor Jules Drean)
• Abigail Thomas, “The Implementation of Model Pruning to Optimize zk-SNARKs in Machine Learning” (mentor Yu Xia) ( slides )
• Tanisha Saxena, “A Systematic Study on the Difference and Conversion Between Synchronous and Asynchronous Protocols” (mentor Jun Wan) ( slides )
• Zifan (Carl) Guo, “Understanding High-Level Properties of Low-Level Programs through Transformers” (mentor William Moses) ( slides )

2:15-2:45 pm: Session 9. Computer Science and Computational Biology

• Kevin Edward Zhao, “Life after BERT: What Do Other Muppets Understand about Language?” (mentors Prof. Anna Rumshisky and Vladislav Lialin, UMass Lowell) ( slides )
• Neil Chowdhury, “A Mechanism of Formation for a Unique Compartment in the Silkworm Genome” (mentor Sameer Abraham)

December mini-conference

Tuesday, December 6

Hybrid in-person/Zoom format

Mathematics Reading Groups

7:00 pm Welcoming Remarks

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

7:05 pm

• Shane Lee, Rishi Gujjar, and Henry Stepanyants, “Abel’s Theorem” (mentor Tang-Kai Lее) (slides)
• Yifan Kang, Henrick Rabinovitz, and Yifei Zhao, “Representation Theory of Symmetric Groups” (mentor Arun Kannan) (slides)
• Arvind Murty and Yichen (Cedric) Xiao, “The Probabilistic Method and the Lovász Local Lemma” (mentor Dr. Jimmy He) (slides)
• Isha Agarwal, Seo Yeon (Gloria) Chun, and Kaylee Ji, “From Loops to Differential Forms: A Sampler of Algebraic Invariants of Topological Spaces” (mentor Adela Zhang) (slides)
• Seo Yeon (Gloria) Chun, “Motion Analysis via Topological Tools” (slides)

PRIMES Computer Science Circle

8:50 pm Welcoming Remarks

• Prof. Srini Devadas, PRIMES Computer Science Section Coordinator

8:55 pm

• Garima Rastogi and Priscilla Zhu, “How To Share Your Secrets” (mentors Lalita Devadas and Alexandra Henzinger) (slides)
• Andria Bao and Sophia Lichterfeld, “Various Neural Network Architectures for Modeling the Effects of Non-coding DNA” (mentors Lalita Devadas and Alexandra Henzinger) (slides)
• Alexa Wingate, “Applying ML to Lung X-ray Images for Real-Time Diagnosis” (mentors Lalita Devadas and Alexandra Henzinger) (slides)

Contact

With questions, contact PRIMES Program Director Slava Gerovitch at