Guided by - Dr. Arindam Khan-- I have worked on computational geometry and approximation algorithms, particularly the "circle packing in square knapsack" problem.-- Currently working on positional triangle games, particularly on improving the bound on the bias of the breaker.-- Part of my stay was funded by the Walmart Center for Tech Excellence (WACE) Pre-Doctoral Fellowship, Pratiksha Young Investigator Grant (via Prof. Khan), and the Kishore Vaigyanik Protsahan Yojana (KVPY) Fellowship.Paper - https://doi.org/10.4230/LIPIcs.ICALP.2024.8

Guided By - Dr. Florent Foucaud and Dr. Antoine DaillyI will be working on finding an isometric path covering of certain graph families such as the hypercube network.Awarded a travel grant of EUR 5,000 under the ANR project GRALMECO (https://gralmeco.limos.fr/). I could not travel due to visa and other personal issues.

I was responsible for sourcing and framing of questions (mostly discrete math questions). The questions were attempted by teams across India. The general process involved going through research papers, finding interesting results and transforming them into questions to be solved in a time based environment.

Project title - "Some Results on Random Walks".Guided by - Dr. Anup BiswasStudied simple random walks, examined their returns to home, recurrence, and sign changes using analytical and combinatorial techniques. Revisited the "Gambler's Ruin Problem" and solved it using techniques learned. In the second part of the project, I reviewed a paper by Dvoretsky and Erdős based on multi-dimensional random walks. Investigated their expected points visited, verified the weak law of large numbers and strong law of large numbers, and calculated the expected rate of escape asymptotically using techniques from analysis and combinatorics. Covered a lot of concepts in the field of pre-measure theoretic probability, and a few concepts from measure theory (Borel-Cantelli Lemmas, Lebesgue's Convergence Theorems, etc.). Ended the project with simulations of random walks on python (not included in the report).