Papers for Euler Circle independent research and paper writing, Summer 2026 Session 1

• Aadhav Vijay: On Bessel Functions Paper Slides
• Aadish Verma: Fast integer and matrix multiplication algorithms Paper Slides
• Aarav Rastogi: On Fourier Transforms of Non-Uniform Data Paper Slides
• Aaryn Titus: Influence of Paradoxical Decomposition on the Banach-Tarski Paradox Paper Slides
• Abrar Fahim: Block Designs: Incidence Structures, Balance, and Algebraic Connections Paper Slides
• Ahmad Sadaan: Matrix Tree Theorem Paper Slides
• Akashdeep Das: Bounded Partial Quotients in Continued Fractions and Zaremba’s Conjecture Paper Slides
• Akshit Khera: Regularity and the Fourier Series Paper Slides
• Alaka Ravi: On the Lucas-Lehmer test and Primality Tests of the Form k2ⁿ±1 Paper Slides
• Amish Gupta: Analysis of the Euler-Maclaurin Summation Formula Paper Slides
• Ansh Taneja: Combinatorial Games and Error-Correcting Codes Paper Slides
• Arjun Veluri: On The Stability of Singular Values and Subspaces Under Perturbation Paper Slides
• Arnav Dhiman: How Close can a Chromatic Root Get to One? Paper Slides
• Ayesha Siddiqua Kaleem: On Ovals in Finite Projective Planes Paper Slides
• Ayumu Yamamoto: Combinatorial Methods for Determinant Evaluation Paper Slides
• Ayush Goyal: On shuffles and their mixing times Paper Slides
• Benjamin Tang: Shor's Algorithm And Mathematical Foundations Of Quantum Computing Paper Slides
• Brad You: Geometric Inequalities Paper Slides
• Brais Macknik-Conde: On Discrete Morse Theory Paper Slides
• Caleb Coyne: Stokes' Theorem and de Rham Cohomology through the Language of Forms Paper Slides
• Derek Hu: Counting the Domino Tilings of a Rectangular Grid Paper Slides
• Devin Li: Second Order Linear Divisibility Sequences Paper Slides
• Eslam Khalaf: Universal Approximation Theorems Paper Slides
• Haoyu Liu: The Black-Scholes Model Paper Slides
• Harnoor Sethi: An Introduction to Sparse Linear Algebra: Storage, Solvers, and Open Problems Paper Slides
• Heather Wang: Existence and Properties of Brownian Motion Paper Slides
• Humayun Ahmed: On The Maximum Length of Multi-Set Cycle Packings Paper Slides
• Huy Tran Duc: Entropy in Discrete and Continuous Spaces and a Relation to the Heat Equation Paper Slides
• Ian Leung: Optimal Mechanism Design for Sequential Auctions and Sports Drafts Paper Slides
• Ishaan Mishra: Absolute Fermat pseudoprimes, the distribution theorems of Larsen, and their consequences for cryptographic prime generation Paper Slides
• Jack Yoshikawa: On Tunnell's solution to the congruent number problem Paper Slides
• Jacob Lee: Spectral Graph Partitioning and Its Application in Wildfire Analysis Paper Slides
• Jason Zhang: Foundations of the Transfer Principle in Nonstandard Analysis Paper Slides
• Krishnav Singh: An Investigation into the Stern-Brocot Tree Paper Slides
• Larry Zhao: On Average Orders of Arithmetic Functions Paper Slides
• Liam Moore: Constructibility by Straightedge and Compass Paper Slides
• Linn Htut Zaw: Hua's Bound for the Asymptotic Waring Problem Paper Slides
• Luke Bula: Central Limit Theorem Paper Slides
• Marcus Collins: On Hilbert's Tenth Problem Paper Slides
• Mateo Brody: The Probabilistic Method Paper Slides
• Memo Glaser: On Scheon-Yua's proof of the Postive mass Comparison Theorems in Riemannian Geometry and its applications to String Theory. Paper Slides
• Mija Reddy: Knots, Quivers and Some Special Polytopes Paper Slides
• Miran Deniz: Representations of Integers as Sums of Two, Three, and Four Squares Paper Slides
• Miriam Wells: Measuring the Infinite: Hausdorff Dimension and the Coastline Paradox Paper Slides
• Muhammad Abdullah: The Hidden Arithmetic of Integer Partitions: Restricted Families, Ramanujan Congruences, and Generating Function Methods Paper Slides
• Nandan Surabhi: Elliptic Curve Primality Proving and Elliptic Curve Cryptograhy Paper Slides
• Nathanael Marcus: The Galton-Watson Branching Process: Extinction, Survival, and Long-Term Growth Paper Slides
• Neil Kulkarni: An Overview of Diophantine Approximation Paper Slides
• Nishka Wadhawan: On Transcendental Numbers Paper Slides
• Nitya Verma: Hyperplane Arrangements Paper Slides
• Nou Sereybot: Boundary Controllability of the Semi-Discrete Heat and Wave Equations Paper Slides
• Ojasya Machiraju: Elliptic Integrals and Functions: An Overview Paper Slides
• Olin Rupchin: The Outer Automorphism of S₆ Paper Slides
• Phuc Vo: An Introductory Survey on Additive Combinatorics Paper Slides
• Phunyapat Rojwongsuriya: Why Does Gaussian Quadrature Achieve Exactness up to Degree 2n−1? Paper Slides
• Prakhar Singhvi: Fair Division: Cake Cutting, Sperner's Lemma, and Rental Harmony Paper Slides
• Radhika Shah: Concentration of the chromatic number Paper Slides
• Rajit Pandey: Ehrhart Theory and Positivity Paper Slides
• Rishikesh Muralimohan: From van der Waerden's Theorem to Roth's Theorem: Colorings, density, and arithmetic progressions Paper Slides
• Rishit Anand: Integral Geometry and Geometric Probability Paper Slides
• Rohan Singh: Sidorenko’s Conjecture: Elementary Proofs and Graphon Methods Paper Slides
• Roy Yaranga: An Introduction to Class Groups Paper Slides
• Ryan Bansal: Grassmannians: Geometry to Combinatorics Paper Slides
• Satyaki Sen: Classifying Representations of Symmetric Groups Paper Slides
• Sayujya Dalal: Malliavin Calculus for a Reflected Stochastic-Volatility Model: Differentiability, Non-Degeneracy, and Greeks Paper Slides
• Shalini Sivakumar: Characterization of Graphical Matroids Paper Slides
• Shamik Khowala: Expander Graphs, with Extensions to Expander Codes and Derandomization Paper Slides
• Shiven Bhargava: On the Solutions of Pell Equations Paper Slides
• Shreya Sharma: On the Learning With Errors Problem Paper Slides
• Siddhaarth Kothapalli: Approximating Continuous Functions Paper Slides
• Soham Pattnaik: The Stability of Folk Theorem Equilibria with Imperfect Costly Monitoring Paper Slides
• Somil Sarode: Goppa Codes Paper Slides
• Syed Shaheer Ahmed Qureshi: Linear Programming Foundations: Simplex, Interior Point, and Duality Theory Paper Slides
• Syed Ismail: Relations between The Erdos Kac Theorem and Ergodic Theory Paper Slides
• Taha Mehmood: Emergence on Graphs: The Mathematics of the Ising Model Paper Slides
• Varun Kataki: On Orthogonal Polynomials Paper Slides
• Vedansh Gupta: Calculus of Variations: an Introduction to the Optimization of Functionals Paper Slides
• Yixuan Chen: On Ordinals and Order Types Paper Slides
• Zeyad Zeeshan: Ramunajan Graphs Paper Slides