Collaborators If you are interested in my research, you might also want to check out the webpages of some of my collaborators: The latest paper is an enumeration of smooth Schubert varieties in affine type A. In this short paper, Lakshmibai, Ravikumar, and I use Billey-Postnikov decompositions to extend this result to cominuscule Grassmannians.

Two papers on the structure of XOR non-local games. Ed Richmond and I have been studying rationally smooth Schubert varieties, with the goal of finding a complete classification. However, the thesis does contain some background material on semi-infinite cohomology, which might be useful in understanding these two papers.

This class of non-local games is closely connected with semidefinite optimization and Clifford algebras. In this paper, we get some Sarvagya upadhyay thesis results by giving a formula for the number of parabolic double cosets with a fixed minimal element.

I give an example of a group where the growth rate is sub exponential. An undergraduate research project. For full bibliographic information, see my papers page. The cotangent bundle of cominuscule Grassmannians A result of Lakshmibai states that the cotangent bundle of the ordinary Sarvagya upadhyay thesis is an open subset of a Schubert variety in an affine two-step partial flag variety.

So far this has been completed in finite type. In joint work with Thomas Vidick, we show that the amount of entanglement required by a linear system game is related to the hyperlinear profile of the solution group, which measures the growth rate of dimensions of approximate representations of the group.

Using the connection with hyperlinear profile, we prove a version of this result with explicit lower bounds on the Hilbert space dimension required for near-optimal strategies. Perfect strategies for these games correspond to representations of a certain finitely-presented group, called the solution group.

Rationally smooth Schubert varieties and Billey-Postnikov decompositions: The connection between group theory and linear system games in the papers below makes it possible to find examples of non-local games where no finite Hilbert space suffices to play optimally.

This has some interesting applications in quantum information, including a resolution of the strong Tsirelson problem. The enumeration method is closely connected to the staircase diagrams used to enumerate smooth Schubert varieties. We count the number of two-vertex maps with respect to genus.

These papers study the freeness of inversion hyperplane arrangements, which surprisingly turns out to be closely connected to rational smoothness of the corresponding Schubert variety.

These papers apply a Lie algebra cohomology calculation to two problems: It turns out that any finitely-presented group can be embedded in the solution group.

These papers are part of a larger program to understand the algebraic structure of optimal strategies for non-local games. In the second paper I give an algebraic characterization of optimal strategies for XOR games, and use this to show that there are non-local games requiring a large amount of entanglement to play near-optimally.

The main tool is a type of parabolic factorization in the Weyl group called a Billey-Postnikov decomposition, which seems to have a lot of applications including to inversion hyperplane arrangements. Papers listed by rough research topic.

Quantum information and XOR non-local games: Using Peterson translation which also comes from the geometry of Schubert varietiesI characterize free inversion arrangements via root-system pattern avoidance.

Lie algebra cohomology of affine Lie algebras: For the at the time new results therein, it is probably better to read the associated papers "A Brylinski filtration for affine Kac-Moody algebras" and "Twisted strong Macdonald theorems and adjoint orbits" listed above.

The connection between hyperlinear profile and entanglement raises the question of how fast the hyperlinear profile can grow.Generic Attacks on Hash Functions by Jalaj Kumar Upadhyay A thesis presented to the University of Waterloo in fulﬁllment of the thesis requirement for the degree of.

PENGHUI YAO NATIONAL UNIVERSITY OF SINGAPORE STUDIES IN COMMUNICATION COMPLEXITY Sundaram, Weidong Tang, Sarvagya Upadhyay, Yibo Wang, Zhuo Wang, Ji-abin You, Huangjun Zhu.

I also wish to thank all the administrators of CQT In this thesis, we concern fast parallel approximation. Review by Sarvagya Upadhyay.

1 c William Gasarch, 1. 9. Introduction to Cryptography by Hans Delfs and Helmut Knebl. This is an undergrad-uate textbook in cryptography.

Review by Cillian Murphy. lighting the Church-Turing Thesis, the Post Correspondence Problem, and the Cobham-Edmonds Thesis. Additionally, there is. Quantum Information and Variants of Interactive Proof Systems by Sarvagya Upadhyay A thesis presented to the University of Waterloo in ful llment of the.

However, the thesis does contain some background material on semi-infinite cohomology, which might be useful in understanding these two papers. Collaborators If you are interested in my research, you might also want to check out the webpages of some of my collaborators: Richard Cleve, Ian Goulden, Ed Richmond, Falk Unger, Sarvagya Upadhyay.

Exploring Different Models of Query Complexity and Communication Complexity Zhaohui, Sarvagya Upadhyay, and Thomas Decker.

I am also thankful to all the administrators of and quantum information which are essential for this thesis. In Sectionof Chapter2, the concepts of basic linear algebra, Hilbert space, quantum .

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