Take Our Quiz About Rieman-hilbert Correspondance

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Anouchka
A
Anouchka
Community Contributor
Quizzes Created: 598 | Total Attempts: 559,175
| Attempts: 161
SettingsSettings
Please wait...
  • 1/10 Questions

    What's a D-module?

    • It's a module over a ring C of differential operators.
    • It's a module over a ring D of differential operators.
    • It's a module over a ring M of differential operators.
    • It's a module over a ring A of differential operators.
Please wait...
About This Quiz

Everybody knows that mathematics have lots of disciplines and for those who've never been good with math a name like Rieman-Hilbert Correspondance will certainly intimidate them. Our quiz will test your knowledge about this theory. Try it ans see how much you truly know about it.

Take Our Quiz About Rieman-hilbert Correspondance - Quiz

Quiz Preview

  • 2. 
    How many isomorphism classes can be found in the Riemann-Hilbert correspondence? - ProProfs

    How many isomorphism classes can be found in the Riemann-Hilbert correspondence?

    • 3

    • 2

    • 4

    • 5

    Correct Answer
    A. 2
    Explanation
    The Riemann-Hilbert correspondence is a fundamental result in mathematics that establishes a connection between complex analysis and linear differential equations. It states that there are two isomorphism classes in the Riemann-Hilbert correspondence. Isomorphism classes refer to distinct types or categories that are equivalent under certain transformations. Therefore, the correct answer is 2.

    Rate this question:

  • 3. 
    What's the Riemann surface? - ProProfs

    What's the Riemann surface?

    • It's a one-dimensional complex manifold.

    • It's a two-dimensional complex manifold.

    • It's a three-dimensional complex manifold.

    • It's a four-dimensional complex manifold.

    Correct Answer
    A. It's a one-dimensional complex manifold.
    Explanation
    The Riemann surface is a one-dimensional complex manifold. This means that it can be represented as a surface in the complex plane, with each point on the surface corresponding to a unique complex number. It is called a one-dimensional manifold because it can be locally parameterized by a single complex coordinate, and it is complex because it involves complex numbers. This concept is important in complex analysis and has applications in various areas of mathematics and physics.

    Rate this question:

  • 4. 
    What's the other term for local systems? - ProProfs

    What's the other term for local systems?

    • Local coefficients

    • Local theorems

    • Local axe

    • Local measure

    Correct Answer
    A. Local coefficients
    Explanation
    Local coefficients refer to the values assigned to variables in a specific region or locality. This term is commonly used in mathematics and physics to describe the varying values of coefficients in different parts of a system or equation.

    Rate this question:

  • 5. 
    What's a fundamental group? - ProProfs

    What's a fundamental group?

    • It's a mathematical group associated to two precise given pointed topological space.

    • It's a mathematical group associated to three precise given pointed topological space.

    • It's a mathematical group associated to any given pointed topological space.

    • It's a mathematical group associated to any given pointed topological shape.

    Correct Answer
    A. It's a mathematical group associated to any given pointed topological space.
    Explanation
    The fundamental group is a mathematical group that is associated with any given pointed topological space. This group is used to study the properties and structure of the space, particularly in algebraic topology. By considering the loops and paths in the space starting and ending at a fixed point, the fundamental group captures important information about the connectivity and homotopy of the space. This group is an important tool in understanding the topological properties of spaces and is widely used in various branches of mathematics and physics.

    Rate this question:

  • 6. 
    What's a complex manifold? - ProProfs

    What's a complex manifold?

    • It's a manifold with an atlas of charts to the open unit disk in C^c, such that the transition maps are holomorphic

    • It's a manifold with an atlas of charts to the open unit disk in C^x, such that the transition maps are holomorphic

    • It's a manifold with an atlas of charts to the open unit disk in C^n, such that the transition maps are polymorphic

    • It's a manifold with an atlas of charts to the open unit disk in C^n, such that the transition maps are holomorphic

    Correct Answer
    A. It's a manifold with an atlas of charts to the open unit disk in C^n, such that the transition maps are holomorphic
    Explanation
    A complex manifold is a manifold that can be described using an atlas of charts to the open unit disk in C^n, where C represents the complex numbers and n represents the dimension of the manifold. The key condition is that the transition maps between the charts in the atlas must be holomorphic, meaning they preserve complex differentiability. This definition captures the essential properties of a complex manifold, allowing for the study of complex analysis and geometry on these spaces.

    Rate this question:

  • 7. 
    What does the condition of regular singularities mean? - ProProfs

    What does the condition of regular singularities mean?

    • That locally constant section of the bundle have moderate growth at point Y

    • That locally constant section of the bundle have moderate growth at points of Y-X

    • That locally constant section of the bundle have moderate growth at points of Y+X

    • That locally constant section of the bundle have moderate growth at point X

    Correct Answer
    A. That locally constant section of the bundle have moderate growth at points of Y-X
    Explanation
    The condition of regular singularities means that locally constant sections of the bundle have moderate growth at points of Y-X. This means that the sections do not have exponential growth or decay at these points, but rather a more moderate growth rate.

    Rate this question:

  • 8. 
    What's one of the isomorphism classes found? - ProProfs

    What's one of the isomorphism classes found?

    • Intersection cosmology

    • Intersection cohomology

    • Intersection mycology

    • Intersections

    Correct Answer
    A. Intersection cohomology
    Explanation
    Intersection cohomology is one of the isomorphism classes found. This is a mathematical concept that studies the cohomology of singular spaces. It provides a way to understand the topology and geometry of these spaces by considering the intersection of various subspaces. Intersection cohomology has applications in algebraic geometry, topology, and representation theory, making it an important topic in mathematics.

    Rate this question:

  • 9. 
    How can one define the Riemann-Hilbert problems? - ProProfs

    How can one define the Riemann-Hilbert problems?

    • As being a class of problems that arise in the study of sequences.

    • As being a class of problems that arise in the study of equations.

    • As being a class of problems that arise in the study of differential equation in the complex plane.

    • As being a class of problems that arise in the study of differential equation in the complex curve.

    Correct Answer
    A. As being a class of problems that arise in the study of differential equation in the complex plane.
    Explanation
    The Riemann-Hilbert problems are a class of problems that arise in the study of differential equations in the complex plane. These problems involve finding a solution to a system of differential equations that satisfies certain boundary conditions. The complex plane refers to the two-dimensional space where complex numbers are represented, and the differential equations studied in this context involve complex-valued functions and their derivatives. By understanding and solving these Riemann-Hilbert problems, researchers can gain insights into various mathematical and physical phenomena.

    Rate this question:

  • 10. 
    What happens when x is compact? - ProProfs

    What happens when x is compact?

    • The condition of growing singularities is vacuous.

    • The condition of constant singularities is vacuous.

    • The condition of regular singularities is vacuous.

    • The condition of degrading singularities is vacuous.

    Correct Answer
    A. The condition of regular singularities is vacuous.
    Explanation
    When x is compact, it means that x is closed and bounded. In this context, the condition of regular singularities being vacuous means that there are no singularities in the function that are not well-behaved or have any irregular behavior. Therefore, when x is compact, there are no irregular singularities present in the function.

    Rate this question:

Quiz Review Timeline (Updated): Mar 18, 2023 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Mar 18, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Aug 03, 2018
    Quiz Created by
    Anouchka
Back to Top Back to top
Advertisement
×

Wait!
Here's an interesting quiz for you.

We have other quizzes matching your interest.