# overview
My research focuses on Algorithmic Algebraic Geometry (including real and arithmetic methods), Polyhedral Combinatorics, Complexity Theory, and Scientific Computation.

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# educationAndTraining[].organization.label
University of California, Berkeley - (Berkeley, California, United States)

# educationAndTraining[].organization.label
University of California, Berkeley - (Berkeley, California, United States)

# educationAndTraining[].organization.label
University of California, Berkeley - (Berkeley, California, United States)

# educationAndTraining[].organization.label
University of California Los Angeles - (Los Angeles, California, United States)

# awardsAndHonors[].label
Faculty Early Career Development (CAREER) Program

# publications[].label
Kolmogorov complexity and algorithmic randomness

# publications[].label
Dedekind Zeta Zeroes and Faster Complex Dimension Computation

# publications[].label
Faster Real Feasibility via Circuit Discriminants

# publications[].publisher
Association for Computing Machinery (ACM)

# publications[].label
Efficiently detecting torsion points and subtori

# publications[].label
A Complexity Chasm for Solving Sparse Polynomial Equations Over p-adic Fields (Extended Abstract)

# publications[].publisher
Association for Computing Machinery (ACM)

# publications[].label
Trinomials and Deterministic Complexity Limits for Real Solving

# publications[].label
Counting affine roots of polynomial systems via pointed Newton polytopes

# publications[].label
SUBLINEAR ROOT DETECTION AND NEW HARDNESS RESULTS FOR SPARSE POLYNOMIALS OVER FINITE FIELDS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
A Faster Solution to Smale's 17th Problem I: Real Binomial Systems

# publications[].publisher
Association for Computing Machinery (ACM)

# publications[].label
Randomized NP-completeness for p-adic rational roots of sparse polynomials in one variable

# publications[].label
Probabilistic Condition Number Estimates for Real Polynomial Systems I: A Broader Family of Distributions

# publications[].label
On the complexity of Diophantine geometry in low dimensions

# publications[].label
A complexity chasm for solving univariate sparse polynomial equations over $p$-adic fields

# publications[].label
Optimization and NP_R-Completeness of Certain Fewnomials

# publications[].label
Optimizing n-variate (n plus k)-nomials for small k

# publications[].label
The exact rational univariate representation for detecting degeneracies

# publications[].label
Uncomputably large integral points on algebraic plane curves?

# publications[].label
A-Discriminants for Complex Exponents, and Counting Real Isotopy Types

# publications[].label
Near NP-Completeness for Detecting p-adic Rational Roots in One Variable

# publications[].label
Practical conversion from torsion space to Cartesian space for in silico protein synthesis.

# publications[].label
Counting Roots of Polynomials Over Prime Power Rings

# publications[].label
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

# publications[].label
Computing zeta functions of large polynomial systems over finite fields

# publications[].label
Sub-Linear Point Counting for Variable Separated Curves over Prime Power Rings

# publications[].label
On interpolating between quantum and classical complexity classes

# publications[].label
Randomization, Sums of Squares, and Faster Real Root Counting for Tetranomials and Beyond

# publications[].label
Tropical varieties for exponential sums (vol 377, pg 863, 2020)

# publications[].label
Metric estimates and membership complexity for Archimedean amoebae and tropical hypersurfaces

# publications[].label
Book Review S. Basu, R. Pollack, and M.-F. Roy: Algorithms in Real Algebraic Geometry

# publications[].label
Some Speed-Ups and Speed Limits for Real Algebraic Geometry

# publications[].label
Counting Tropically Degenerate Valuations and p-adic Approaches to the Hardness of the Permanent

# publications[].label
Optimization and NPR-Completeness of Certain Fewnomials

# publications[].publisher
Association for Computing Machinery (ACM)

# publications[].label
Additive complexity and roots of polynomials over number fields and p-adic fields

# publications[].label
Feasibility of Circuit Polynomials without Purple Swans: Feasibility without Purple Swans

# publications[].publisher
Association for Computing Machinery (ACM)

# publications[].label
Algorithmic Arithmetic Fewnomial Theory I: One Variable

# publications[].label
New Subexponential Fewnomial Hypersurface Bounds

# publications[].label
Sparse Univariate Polynomials with Many Roots Over Finite Fields

# publications[].label
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

# publications[].label
On Solving Fewnomials Over Intervals in Fewnomial Time

# publications[].label
SMOOTHED ANALYSIS FOR THE CONDITION NUMBER OF STRUCTURED REAL POLYNOMIAL SYSTEMS

# publications[].label
Metric Estimates and Membership Complexity for Archimedean Amoebae and Tropical Hypersurfaces

# publications[].label
Counting Real Roots in Polynomial-Time for Systems Supported on Circuits

# publications[].label
A convex geometric approach to counting the roots of a polynomial system

# publications[].label
A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes

# publications[].label
Counting Real Roots in Polynomial-Time via Diophantine Approximation.

# publications[].label
Book Review: Inevitable randomness in discrete mathematics

# publications[].label
Fewnomial systems with many roots, and an Adelic Tau Conjecture

# publications[].label
On the complexity of Diophantine geometry in low dimensions

# publications[].label
On the BCSS Proof of the Fundamental Theorem of Algebra

# publications[].label
First Steps in Algorithmic Fewnomial Theory

# publications[].label
New approach to counting Nash equilibria

# publications[].label
New Multiplier Sequences via Discriminant Amoebae

# publications[].label
Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields

# publications[].label
High probability analysis of the condition number of sparse polynomial systems

# publications[].label
NEW MULTIPLIER SEQUENCES VIA DISCRIMINANT AMOEBAE

# publications[].label
New Complexity Bounds for Certain Real Fewnomial Zero Sets

# publications[].label
Attitude and position estimation from vector observations

# publications[].label
Faster p-adic feasibility for certain multivariate sparse polynomials

# publications[].label
Computational arithmetic geometry I. Sentences nearly in the polynomial hierarchy

# publications[].label
Root Repulsion and Faster Solving for Very Sparse Polynomials Over $p$-adic Fields

# publications[].label
Extremal Real Algebraic Geometry and A-Discriminants

# publications[].label
Efficiently Detecting Torsion Points and Subtori

# publications[].label
RANDOMIZED POLYNOMIAL-TIME ROOT COUNTING IN PRIME POWER RINGS

# publications[].label
Randomized Polynomial-Time Root Counting in Prime Power Rings

# publications[].label
Root repulsion and faster solving for very sparse polynomials over p-adic fields

# publications[].label
Toric intersection theory for affine root counting

# publications[].label
Intrinsic near quadratic complexity bounds for real multivariate root counting

# publications[].label
On the sharpness of fewnomial bounds and the number of components of fewnomial hypersurfaces

# publications[].label
Smoothed Analysis for the Condition Number of Structured Real Polynomial   Systems

# publications[].label
EXTREMAL REAL ALGEBRAIC GEOMETRY AND A-DISCRIMINANTS

# publications[].publisher
National Research University, Higher School of Economics (HSE)

# publications[].label
Counting real connected components of trinomial curve intersections and m-nomial hypersurfaces

# publications[].label
Refined Asymptotics for Multigraded Sums of Squares

# publications[].label
An Improved Bound on the VC-Dimension of Neural Networks with Polynomial Activation Functions

# publications[].label
Faster Real Feasibility via Circuit Discriminants

# publications[].label
On solving univariate sparse polynomials in logarithmic time

# publications[].label
Solving Degenerate Sparse Polynomial Systems Faster

# publications[].label
Faster p-adic Feasibility for Certain Multivariate Sparse Polynomials

# editorOf[].label
Randomization, Relaxation, and Complexity in Polynomial Equation Solving Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, February 28--March 5, 2010, Banff, Ontario, Canada

# researcherOn[].label
AF: Medium: Collaborative Research: Arithmetic Geometry Methods in Complexity and Communication-

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
REU Site: Undergraduate Research in the Mathematical Sciences and their Applications

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Sparse Polynomials, Complexity, and Algorithms

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
REU Site: Undergraduate Research in the Mathematical Sciences and Their Applications --

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
MCS: Randomization in Algorithmic Fewnomial Theory Over Complete Fields

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU