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07/16/2023
On the Hardness of PosSLP
The problem PosSLP involves determining whether an integer computed by a...
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02/15/2021
Polynomial time algorithms in invariant theory for torus actions
An action of a group on a vector space partitions the latter into a set ...
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10/21/2020
Rigid continuation paths II. Structured polynomial systems
We design a probabilistic algorithm that, given ϵ>0 and a polynomial sys...
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08/27/2020
Interior-point methods for unconstrained geometric programming and scaling problems
We provide a condition-based analysis of two interior-point methods for ...
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10/27/2019
Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopes
This paper initiates a systematic development of a theory of non-commuta...
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03/26/2019
Computing the Homology of Semialgebraic Sets. II: General formulas
We describe and analyze an algorithm for computing the homology (Betti n...
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12/17/2018
The Complexity of Factors of Multivariate Polynomials
The existence of string functions, which are not polynomial time computa...
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07/10/2018
Computing the Homology of Semialgebraic Sets I: Lax Formulas
We describe and analyze an algorithm for computing the homology (Betti n...
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06/01/2018
The real tau-conjecture is true on average
Koiran's real τ-conjecture claims that the number of real zeros of a str...
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11/21/2017
Alternating minimization, scaling algorithms, and the null-cone problem from invariant theory
Alternating minimization heuristics seek to solve a (difficult) global o...
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06/22/2017
Computing the homology of basic semialgebraic sets in weak exponential time
We describe and analyze an algorithm for computing the homology (Betti n...
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08/28/2015