Published in Journal of Classical Geometry, 2013
Neuberg Locus and its properties.
Recommended citation: Banerjee, Debdyuti and Mukherjee, Sayan. "Neuberg Locus And Its Properties." Journal of Classical Geometry, Volume 2 (26) (2013).
Published in Sādhanā, 2019
Maximum subgraphs without hypergraph families.
Recommended citation: Mukherjee, Sayan; Ghosh, Debraj and De, Rajat K. "Expected return time to the initial state for biochemical systems with linear cyclic chains: unidirectional and bidirectional reactions." Sādhanā (Springer India) Volume 44, Issue 1, Pages 1-12 (2019). https://doi.org/10.1007/s12046-018-0989-5
Published in Journal of Combinatorics, 2021
Maximum subgraphs without hypergraph families.
Recommended citation: Mubayi, Dhruv and Mukherjee, Sayan. "Maximum H-free subgraphs." Journal of Combinatorics Volume 12 (2) Pages 185-214 (2021). https://doi.org/10.4310/JOC.2021.v12.n2.a1
Published in University of Illinois at Chicago, 2021
Ph.D. Thesis for Ph.D. in Mathematics defended at University of Illinois at Chicago.
Recommended citation: Mukherjee, Sayan. "Extremal Problems for Graphs and Hypergraphs." Thesis,Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago (2021). https://doi.org/10.25417/UIC.17026274.V1
Published in Computer Graphics Forum; Pacific Graphics Conference 2021, 2021
Using neural networks to perform sequence transformation.
Recommended citation: Mukherjee, Sabyasachi; Mukherjee, Sayan; Hua, Binh-Son; Umetani, Nobuyuki and Meister, Daniel. "Neural Sequence Transformation." Computer Graphics Forum (Wiley), Volume 40, Issue 7, Pages 131-140 (2021). https://doi.org/10.1111/cgf.14407
Published in IEEE Transactions on Quantum Engineering, 2022
We analyze the list coloring problem and demonstrate a fast quantum algorithm for it.
Recommended citation: Mukherjee, Sayan. "A Grover search-based algorithm for the list coloring problem." IEEE Transactions on Quantum Engineering Volume 3 (2022). https://doi.org/10.1109/TQE.2022.3151137
Published in Conference on Learning Theory 2022, 2022
Tight query complexity bounds for learning graph partitions.
Recommended citation: Liu, Xizhi, and Mukherjee, Sayan. "Tight query complexity bounds for learning graph partitions." 35th Conference on Learning Theory (COLT). Proceedings in Machine Learning Research (2022). https://arxiv.org/pdf/2112.07897.pdf
Published in European Journal of Combinatorics Vol. 110, 2022
Stability theorems for some Kruskal-Katona type results.
Recommended citation: Liu, Xizhi and Mukherjee, Sayan. "Stability theorems for some Kruskal-Katona type results." European J. Comb. 110 (2023) arXiv:2006.04848 (2020). https://doi.org/10.1016/j.ejc.2022.103666
Published in Discrete Mathematics Vol. 346 (6), 2023
Counting number of triangles in graphs forbidding suspensions of bipartite graphs.
Recommended citation: Mubayi, Dhruv, and Mukherjee, Sayan. "Triangles in graphs without bipartite suspensions." Discrete Mathematics 346 (6). https://doi.org/10.1016/j.disc.2023.113355
Published in arXiv Preprint, 2023
Spectral clustering is robust for social networks in general with privacy budget $\epsilon=O(\log n)$, and this result is tight.
Recommended citation: Mukherjee, Sayan and Suppakitpaisarn, Vorapong. "Robustness for Spectral Clustering of General Graphs under Local Differential Privacy." arXiv Preprint arXiv:2309.06867 https://arxiv.org/abs/2309.06867
Published in Discrete Mathematics Vol. 347 (4), 2024
Counting number of triangles in graphs forbidding suspensions of the path on 4 vertices.
Recommended citation: Mukherjee, Sayan. "Exact generalized Turan number for $K_3$ versus suspension of $P_4$". Discrete Mathematics 347 (4) https://doi.org/10.1016/j.disc.2023.113866
Published in European Journal of Combinatorics Vol. 118, May 2024, 103935, 2024
Turan numbers for hypergraph suspensions.
Recommended citation: Mukherjee, Sayan. "Extremal Numbers of Hypergraph Suspensions of Even Cycles." European Journal of Combinatorics Volume 118, May 2024, 103935. https://doi.org/10.1016/j.ejc.2024.103935
Published in ACM Transactions on Graphics (SIGGRAPH 2024), 2024
A step towards integrating non-photorealistic stylizations into physically-based rendering systems.
Recommended citation: Rex West and Sayan Mukherjee. "Stylized Rendering as a Function of Expectation." ACM Trans. Graph. 43, 4, Article 96 (July 2024), 19 pages. https://doi.org/10.1145/3658161
Published:
Given a partition of a graph into connected components, the membership oracle asserts whether any two vertices of the graph lie in the same component or not. We prove that for $n\ge k\ge 2$, learning the components of an $n$-vertex hidden graph with $k$ components requires at least $(k-1)n-\binom k2$ membership queries. Our result improves on the best known information-theoretic bound of $\Omega(n\log k)$ queries, and exactly matches the query complexity of the algorithm introduced by Reyzin and Srivastava, 2007 for this problem. Additionally, we introduce an oracle that can learn the number of components of $G$ in asymptotically fewer queries than learning the full partition, thus answering another question posed by the same authors. Lastly, we introduce a more applicable version of this oracle, and prove asymptotically tight bounds of $\widetilde\Theta(m)$ queries for both learning and verifying an $m$-edge hidden graph $G$ using it.
Published:
We give a very basic (and hand-wavy) introduction to Tensor network simulation of quantum circuits, and discuss and compare different ways of contracting them.
Undergraduate course, University of Illinois at Chicago, Department of Mathematics, Statistics and Computer Science, 2016
Below are the different courses I have taught for at UIC during my Ph.D. from Fall 2016 to Spring 2021. You can find materials relevant to / used during these courses in their respective webpages below. Note that all courses do not have webpages with supplemental material.