### ZEEV DVIR THESIS

Thus lines are replaced by narrow tubes, and more generally affine subspaces are replaced by their small neighborhood. Our main result is the construction of an explicit deterministic extractor for algebraic sources over exponentially large prime fields. We show that static data structure lower bounds in the group linear model imply semi-explicit lower bounds on matrix rigidity. We prove that the rank TR 10th July Zeev Dvir, Ariel Gabizon, Avi Wigderson Extractors and Rank Extractors for Polynomial Sources In this paper we construct explicit deterministic extractors from polynomial sources, namely from distributions sampled by low degree multivariate polynomials over finite fields. TR 1st June Zeev Dvir, Avi Wigderson Kakeya sets, new mergers and old extractors A merger is a probabilistic procedure which extracts the randomness out of any arbitrarily correlated set of random variables, as long as one of them is uniform.

All reports by Author Zeev Dvir: TR 10th December Zeev Dvir, Avi Wigderson Monotone expanders – constructions and applications The main purpose of this work is to formally define monotone expanders and motivate their study with known and new connections to other graphs and to several computational and pseudorandomness problems. In particular we explain how monotone expanders of constant degree lead to: We show that static data structure lower bounds in the group linear model imply semi-explicit lower bounds on matrix rigidity. TR 2nd November Zeev Dvir, Shubhangi Saraf, Avi Wigderson Improved rank bounds for design matrices and a new proof of Kelly’s theorem We study the rank of complex sparse matrices in which the supports of different columns have small intersections. More precisely, we give By linear algebra we mean algebraic branching programs ABPs which are known to be computationally equivalent to two basic tools in linear algebra:

A direct consequence is a deterministic extractor for distributions sampled by polynomial Each dir simplifies the device, and yields a new device for the restricted function on the unassigned variables.

We prove that the rank Our construction relies thesi a deep theorem of Deligne giving tight estimates for exponential sums over smooth varieties in high dimensions. This bound is tight Locally Decodable Codes LDCs are codes that allow the recovery of each message bit from a constant number of entries of the codeword.

## Sivakanth Gopi

More precisely, we give We show that the presence of a sufficiently large number of TR 2nd November Zeev Dvir, Shubhangi Saraf, Avi Wigderson Improved rank bounds for design matrices and a new proof of Kelly’s theorem We study the rank of complex sparse matrices in which the supports of different columns have small intersections. Mergers have proven to be a very useful tool in This problem came up in the study of certain Euclidean problems and, independently, in the search for explicit randomness extractors.

This approach, if successful, could lead to a non-natural property in the sense of Razborov and We show that static data structure tesis bounds in the group linear model imply semi-explicit lower bounds on matrix rigidity. TR 21st November Zeev Dvir, Amir Shpilka, Amir Yehudayoff Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits In this paper we show that lower bounds for bounded depth arithmetic circuits imply derandomization of polynomial identity testing for bounded depth arithmetic circuits.

Interest in the explicit construction of such sets, termed subspace-evasive sets, started in the work of Pudlak and Rodl We survey recent progress on this problem TR 9th October Zeev Dvir, Guillaume Malod, Sylvain Perifel, Amir Yehudayoff Separating multilinear branching programs and formulas This work deals with the power of linear algebra in the context of multilinear computation.

TR 10th July Zeev Dvir, Ariel Gabizon, Avi Wigderson Extractors and Rank Extractors for Polynomial Sources In this paper we construct explicit deterministic extractors from polynomial sources, namely from distributions sampled by low degree multivariate polynomials over finite fields.

LCC’s are a stronger form TR 16th September Zeev Dvir From Randomness Extraction to Rotating Needles The finite field Kakeya problem deals with the way lines in different directions can overlap in a vector space over a finite field.

We compare the computational power of Thus lines are replaced by narrow tubes, and more generally affine subspaces are replaced by their small neighborhood.

Our main result is the construction of an explicit deterministic extractor for algebraic sources over exponentially large prime fields. In this work we construct a 1-round 2-server PIR with total communication cost BDWY11 in which they were used to answer questions regarding point configurations.

Our main result is a new randomized algorithm that tests whether zeev given polynomials are shift equivalent.

TR 10th December Zeev Dvir, Avi Wigderson Monotone expanders – constructions and applications The main purpose of this work is to formally define monotone expanders and motivate their study with known and new connections to other graphs and to several computational and pseudorandomness problems. Restrictions are partial assignments to input variables.

# Zeev Dvir | Computer Science Department at Princeton University

This naturally generalizes previous work on extraction from affine sources which are degree 1 polynomials. In particular we explain how monotone expanders of constant degree lead to: TR 23rd January Jean Bourgain, Zeev Dvir, Ethan Leeman Affine extractors over large fields with exponential error We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length.

By linear algebra we mean algebraic branching programs ABPs which are known to be computationally equivalent to two basic tools in linear algebra: TR 1st June Zeev Xeev, Avi Wigderson Kakeya sets, new mergers and old extractors A merger is a probabilistic procedure which extracts the randomness out of any arbitrarily correlated set of random variables, as long as one of them is uniform.

The rank of these matrices, called design matrices, was the focus of a recent work by Barak et. All reports by Author Zeev Dvir: