Lectures related to Polynomial-time reduction

Linear Algebra in 2D: Reduction Applications

Explores the application of reductions in R² for linear functions, emphasizing the calculation of f composed n times with itself.

Complex Systems: Critical Phenomena

Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.

Computational Complexity: Theory and Applications

Explores computational complexity, NP-completeness, and polynomial reductions in theoretical computer science.

Designing Systems for Harsh Environments: Principles and Strategies

Covers design principles for mechanical systems in radiative and dusty environments.

Cryptanalysis: Public-Key & The Power of Interaction

Explores cryptanalysis in public-key systems and the power of interaction in interactive proofs, covering CO-NP, NP classes, P vs. NP, and more.

Lenstra's Algorithm: Integer Factorization

Covers Lenstra's Algorithm for integer factorization, which efficiently computes prime factors of an integer.

Cryptographic Primitives: Theory and Practice

Explores fundamental cryptographic primitives, security models, and the relationship between decryption security and key recovery security.

Correctness and Soundness of the Qubit Test

Explores the correctness and soundness of the Qubit Test, emphasizing probabilistic algorithms, trapdoors, and function inversion.

Density Operator Formalism

Covers the density operator formalism, polynomial time, NP problems, BPP, QMA, and probabilistic algorithms.

Promise Constraint Satisfaction and Width

Covers Promise Constraint Satisfaction Problems complexity, width, graph coloring, polymorphisms, and algorithms.

Finite Impulse Response Filters: Part 2

Explores the design of Finite Impulse Response filters and the optimization methods for control in signal processing.

Serre Duality: General Case

Covers the application of Serre Duality in the general case, focusing on line bundles and core concepts.

Global Sensitivity Analysis in Stochastic Systems

On Variance-Based Sensitivity Analysis for Stochastic Systems covers the impact of parameters uncertainty and sensitivity indices in stochastic models.

Elements of Computational Complexity

Covers quantum algorithms, complexity classes, Grover's algorithm, and quantum information in computational complexity.

P vs NP: Complexity Theory

Delves into complexity theory, focusing on the P vs NP problem and the classification of computational problems based on efficiency.

Theory of Computation: Decidability and Complexity

Delves into the theory of computation, covering decidability, complexity, P vs. NP, and reductions.

Cartesian Equations: Lines in Space

Covers the Cartesian equations of lines in space and their directional properties.

Max-Flow Min-Cut

Explores the Ford Fulkerson algorithm, Max-Flow Min-Cut theorem, Incidence matrix, and network optimization complexity.

Fast Fourier Transform

Explains the Fast Fourier Transform, a fast algorithm for calculating the Discrete Fourier Transform.

Theory of Computability: Solvability and Complexity

Explores the theory of computability, decision problems, complexity classes, and the 'P vs. NP' conundrum.