Math POTW for Graduate Students Forum

POTW A Function in the Continuous Hölder Class
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1
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344
POTW Closed subspace of square-integrable functions on D
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13
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527
POTW Ext Functor on Noetherian Affine Schemes
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2
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912
POTW Flat Modules and Intersection
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2
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646
POTW First Cohomology of a Subscheme of Projective Plane
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2
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499
POTW Is the Finite Expectation of Powers Satisfied by Nonnegative Random Variables?
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4
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519
POTW Positive Definite Block Matrices
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1
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492
POTW Projection Formula for Ringed Spaces
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1
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497
POTW Estimate of a Principal Value Integral
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2
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472
POTW Positive Definiteness Determined from Symmetrized Products
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1
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592
MHB Can You Solve This Advanced Definite Integral Using Residue Theorem?
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1
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2K
POTW Boundedness of Oscillatory Integrals
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2
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683
POTW A Nonlinear Elliptic PDE on a Bounded Domain
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3
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767
POTW Attaching a Two-Cell to a Circle
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1
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745
POTW Weak Topology on an Infinite-Dimensional Hilbert Space
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1
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650
POTW Comparing Rank and Trace of a Matrix
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1
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770
POTW Local Integrability of a Maximal Function
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1
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723
POTW Analytic Functions with Isolated Zeros of Order k
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2
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822
POTW Steenrod Squares over an Infinite Projective Space
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1
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642
POTW Local Property of Flasque Sheaves
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2
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699
POTW Translation-Invariant Operators on Lebesgue Spaces
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4
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852
POTW Smooth proper self-maps on Rn
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1
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590
POTW Limit of Complex Sums: Find $$\lim_{n\to \infty}$$
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1
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920
POTW What is the Relationship Between Fiber Bundles of Spheres?
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1
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704
POTW Convergence of Random Variables in L1
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3
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1K
POTW Orthonormal Bases on Hilbert Spaces
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7
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973
POTW Semisimple Tensor Product of Fields
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1
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797
POTW Sufficient Conditions for a Covering Space
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1
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743
POTW Minimizers of an Energy Functional
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1
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993
POTW Contour Integral Representation of a Function
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4
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1K
POTW What is the Log Concavity of Determinants for Positive Definite Matrices?
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6
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1K
POTW Convergence in Probability
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1
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809
MHB Is Every Convex Function Differentiable at Most Points?
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2
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3K
POTW In a Category with Fibered Products
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5
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1K
MHB Problem of the Week #301 - June 28, 2022
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1
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1K
MHB Are There a Finite Number of Solutions to $f(x) = y$ in a Bounded Region?
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1
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1K
MHB Projection Map $X \times Y$: Closure Property
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1
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3K
MHB Prove that no finite measure space can have uncountably many members in its $\sigma$-algebra with strictly positive measure.
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1
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2K
MHB Is There a Nontrivial Normal Subgroup in a Finite Group with Index Not Divisible by the Group's Order?
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1
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2K
MHB Can a Non-Surjective Smooth Harmonic Function on $\Bbb R^2$ Be Non-Constant?
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1
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2K
MHB Is $p$ a prime divisor of $\phi(n)$ if $G$ has an element of order $n$?
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1
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2K
MHB What is the integral of x - sin x over x^3 from 0 to infinity?
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1
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2K
MHB What Is the Center of the Ring of All \( n \times n \) Complex Matrices?
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1
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4K
MHB How Do Tensor Products Relate to Supports in Algebraic Geometry?
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1
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4K
MHB How Can You Prove This Bessel Function Integral Equals 4/3π?
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1
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2K
MHB Can You Prove the Limit of Integrals Over Vanishing Measure Sets Is Zero?
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1
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2K
MHB Can a Finite Group Acting on a Set Have No Fixed Points?
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1
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2K
MHB Can You Crack the Challenges in POTW #286?
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2
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3K
MHB What is the support of a Radon measure on a locally compact Hausdorff space?
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0
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2K
MHB How Do You Solve the Integral from POTW #285?
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1
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2K
MHB Topological manifolds with boundary of dimensions
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1
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2K
MHB How to Solve Integral with Parameters a and b in POTW #283?
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2
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2K
MHB Is $H_n(X)$ Torsion Free if $H_{n-1}(X)$ is Torsion Free?
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2
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2K
MHB What is the solution to POTW #281 - Oct 30, 2018?
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1
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2K
MHB Is $f$ a proper map if the fibers are compact?
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1
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2K
MHB Can an entire function with a specific limit at infinity be non-constant?
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1
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2K
MHB Let $(X_n)_{n \in \Bbb N}$ be a sequence of positive i.i.d. random variables
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1
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2K
MHB Is Every Cofibration Injective?
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1
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2K
MHB What is the order of $SL_n(\Bbb F_p)$ for a prime integer $p$?
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1
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2K
MHB Show that in a compact Hausdorff space, any countable collection of dense open sets has dense intersection.
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1
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2K
MHB Is the adjunction space $X \cup_f Y$ normal for closed $A$ and continuous $f$?
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2
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2K
MHB Why is the Kernel of the Evaluation Map Principal?
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1
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2K
MHB What is the solution to the nonlinear differential equation?
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1
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2K
MHB What is the Average Value of |dφ/dz|^2 over the Open Unit Disk?
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2
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2K
MHB What is Jacobi's identity for Lie derivatives on a smooth manifold?
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1
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2K
MHB Is the Integral of an Analytic Function on a Closed Contour Purely Imaginary?
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1
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3K
MHB How can we show that $D_n(t)$ has a bounded integral over a certain interval?
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2
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3K
MHB How Do You Solve This Integral for Positive Integer n?
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1
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4K
MHB Is $\Bbb Z\otimes_{\Bbb Z} \Bbb R$ isomorphic to $\Bbb C$?
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2
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2K
MHB What is the solution to POTW #265 - Feb 13, 2018?
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2
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2K
MHB What is the solution to POTW #264 for Jan 23, 2018?
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1
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2K
MHB Is the Real Projective Plane's Gaussian Curvature Always Positive?
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1
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2K
MHB What is the Riemannian distance between two points in the open unit disk?
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2
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2K
MHB What is the solution to this week's POTW?
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1
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2K
MHB What is the maximal function of a finite Borel measure on $\Bbb R^n$?
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1
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2K
MHB How Does Morphism Affect Prime Spectra and Module Support?
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2
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2K
MHB What is the norm of a linear operator in $\mathscr{L}^p(0, \infty)$?
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1
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2K
MHB Is Contour Integration the Key to Solving This Integral?
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1
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2K
MHB Can Even Maps Between n-Spheres Have Odd Homological Degrees?
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1
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2K
MHB Can You Solve the Harmonic Function Challenge?
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2
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2K
MHB Is the Tensor Algebra of $\Bbb Z/n\Bbb Z$ Isomorphic to $\Bbb Z[x]/(nx)$?
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1
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2K
MHB What Does the Integral Evaluate To?
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1
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2K
MHB Is the sequence $(X_n)$ of $L^1$ random variables uniformly integrable?
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2
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2K
MHB Why are nondegenerate fixed points important for self-maps of a smooth manifold?
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1
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2K
MHB How to Prove $X$ Has Lebesgue Measure Zero?
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1
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2K
MHB How can we prove the tail bound for a standard Gaussian random variable?
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1
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2K
MHB How to Prove the Integral of Log Absolute Value is 0?
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1
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2K
MHB Is Continuously Differentiable Imply Fourier Coefficients in l^1?
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1
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2K
MHB Is $\Bbb R$ homeomorphic to a cartesian product?
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1
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2K
MHB How can $L^1(\Bbb R)$ be isomorphic to an ideal in $M(\Bbb R)$?
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2
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2K
MHB How can we construct a chain homotopy between homotopic chain maps?
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1
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2K
MHB Is $\mathcal{M}(X)$ a Banach space?
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1
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2K
MHB Is a finite group of homeomorphisms with no fixed points able to act properly discontinuously on a Hausdorff space?
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1
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2K
MHB Is an analytic map with a certain condition injective?
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1
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2K
MHB Can a homeomorphism of the closed unit disk map $S^1$ onto $S^1$?
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1
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2K
MHB Can Uniformly Bounded Functions Converge Weakly to Zero in $\mathscr{L}^p$?
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1
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2K
MHB How can you prove that a retract of a Hausdorff space is always closed?
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1
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2K
MHB Can the center of a finite group determine the size of its conjugacy classes?
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1
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2K
MHB Can an Entire Function Be Non-Zero with Finite Double Integral?
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1
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2K
MHB Why is $M/(N\cap P)$ Artinian when $M/N$ and $M/P$ are Artinian?
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1
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2K
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POTW Graduate

Welcome to the Graduate POTW forum!

Math problems will be posted each week on Monday, most likely early in the morning (1am, 2am, etc.) Eastern Standard Time. There will be one problem each week at the university graduate math level.

All are welcome to try, but those with masters or PhD will be most comfortable.

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