With a single fractional twist, the complex plane reshapes itself.
Circles become lines, infinity moves closer, and symmetry takes the lead.
#MobiusMagic #ComplexGeometry
#TwistingThePlane #ComplexAnalysis
cortexdrifter.blogspot.com/2026/01/a-sm...
#mathematics #math #ComplexAnalysis #DistributionTheory #Hyperfunctions
Source:https://buff.ly/dZWLDDA
It's good to see my friends Mei-Chi S. ☘️ and Charles S. have published a new book! I am looking forward to reading it!
link.springer.com/book/10.1007/978-3-031-9...
#SpringerNature #ComplexAnalysis
Jordan’s Lemma bounds integrals over large semicircles in the complex plane, ensuring exponential terms decay and making residue calculus and Fourier methods work smoothly. Do you remember using it?
#ComplexAnalysis #Mathematics #STEM #MathEducation #MathType
When is a complex function truly differentiable? The Cauchy–Riemann equations give us the answer. By linking the partial derivatives of the real and imaginary parts of a function, they establish the precise condition for complex differentiability.
#ComplexAnalysis #Math
Toupin, D. (2025). Holding the Line: How Haar Measure, Functional Symmetry, and Compactness Force the Riemann Hypothesis. Zenodo. doi.org/10.5281/zeno...
#Skyence #NumberTheory #SpectralTheory #MeasureTheory #ComplexAnalysis #BrownianMotion #RiemannHypothesis #ZetaFuction #MillenniumPrizeProblems
De Moivre's Formula is an expression that connects the world of #ComplexNumbers and #Trigonometry. Although the one-liner proof via Euler's Identity feels very intuitive and direct now, this formula was proven before Euler's Identity was known.
#ComplexAnalysis #MathType
Image of the paper's title page showing the title, author information, and abstract.
Just released: Proof of the Riemann Hypothesis via Haar inversion + functional equation + Peter-Weyl compactness.
Preprint:
doi.org/10.5281/zeno...
Feedback welcome!
#RiemannHypothesis #NumberTheory #Math #MeasureTheory #Primes #ComplexAnalysis #MathSky #NumberSky #ZetaZeros
My photos from the Oct. 10-12 Midwestern Workshop on Asymptotic Analysis :gauss: , here at #PurdueFortWayne 🐘
www.flickr.com/photos/coffmanadam/album...
#NSFfunded #math #MathConference #RealAnalysis #ComplexAnalysis
NITheCS Colloquium: 'The convex invertible cone approach to Nevanlinna-Pick interpolation' - Prof Sanne ter Horst (North-West University) - Mon, 22 Sept 2025 @ 16h00-17h00 SAST. Attend online or in person. buff.ly/FakKyuT
#Mathematics # NevanlinnaPick #MathTalk #AppliedMathematics #ComplexAnalysis
Liouville's theorem states that every bounded function that is holomorphic in the whole complex plane must be constant. It is a classical result in #ComplexAnalysis.
#MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts
\\(1^{st}\\) announcement for the 2025 Midwestern Workshop on Asymptotic Analysis - October 10 - 12 at #PurdueFortWayne 🐘 .
Participant registration is now open (through Sept. 21 to be considered for travel support), follow the instructions on the web site:
http://mwaa.math.indianapolis.iu.edu/ […]
\\(0^{th}\\) announcement for the 2025 Midwestern Workshop on Asymptotic Analysis - October 10 - 12 at #PurdueFortWayne 🐘 .
The web site has a preliminary list of 2025 speakers including our keynote speaker Alexandre Sukhov 🇫🇷 . Online registration and the request form for travel support will be […]
🧑🎓💼1 postdoc position is open in #Probability at the University of Rome La Sapienza, within the FIS 2 project Understanding pattern formation in nature via #complexanalysis, PI Vittoria Silvestri.
Deadline for applications: 29 August 2025 - strict
web.uniroma1.it/trasparenza/...
A Mastodon statue is reflected in the window on the right.
The #math department at #PurdueFortWayne 🐘 welcomes two new tenure-track faculty!
Vahan Mkrtchyan's research is in #GraphTheory and theoretical computer science :k33: :k5:
Liding Yao's research is in #ComplexAnalysis and geometric analysis
My "short communication" has been accepted for #ICM2026 ! The topic is in analysis but I just got the acceptance email and don't have any scheduling or other information yet. The long communication speakers are listed on the web site […]
repost @erik_alan_norman on IG
2D vs 3D Möbius transformations. #möbius #transformations #geometry #complexanalysis #analysis #projection #sphere #math #maths #mathematics #mathematician #vector #calculus #blender #3dartist #3danimation #geometrynodes #fields
Our #PurdueFortWayne 🐘 #math department colloquium talks this semester, on #RealAnalysis #ComplexAnalysis #GraphTheory
https://photos.app.goo.gl/tQaqPeZXf3nMHKzP9
Visualizing roots of z² + (t₁ + t₂)
t₁ and t₂ are complex numbers, |t₁| = |t₂| = 1
Colors encode the angle of each t₁ and t₂
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
This visualization shows all roots of quadratic polynomials (ax² + bx + c = 0) where coefficients |a|,|b|,|c| ≤ 100, plotted in the complex plane from -0.28-0.28i to 0.28+0.28i.
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
This visualization shows all roots of quadratic polynomials (ax² + bx + c = 0) where coefficients |a|,|b|,|c| ≤ 100, plotted in the complex plane from -1.2-1.2i to 1.2+1.2i.
Generated with #p5js
#MathArt #VisualMath #ComplexAnalysis #Algebra #SciArt
Plot shows 215,240 eigenvalues in [-2.5-2.5i, 2.5+2.5i]. Total of 109,000 matrices. 16,664 computation failures using numeric.js library.
The failures represent edge cases where numeric.js couldn't converge.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
A density plot of Bohemian eigenvalues from 109.000 random 20×20 anti-tridiagonal matrices with entries in {-1,0,1}. Colors represent eigenvalue frequency; real eigenvalues are excluded. Viewed on [-2.5-2.5i, 2.5+2.5i].
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math #SciArt
Plot shows 211,416 eigenvalues in [-3-3i, 3+3i]. Total of 348,500 matrices. 21,456 computation failures using numeric.js library.
The failures represent edge cases where numeric.js couldn't converge.
#p5js #MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Each point represents one eigenvalue from the spectrum of a random 5×5 matrix with entries from {-1,0,1}. Warmer colors show regions where eigenvalues cluster more densely.
#MathArt #LinearAlgebra #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Exploring the roots of 131,072 polynomials with coefficients in {1,3}.
Each dot is a root of a degree-16 polynomial; brightness reveals its frequency across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Exploring the roots of 131.072 random ±1-polynomials of degree 16.
Each dot is a root, brightness shows how frequently it appears across all polynomials.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Complex function visualization: 𝑓(𝑧)=𝑧
→ Hue encodes the phase (argument of 𝑓(𝑧))
→ Brightness encodes the fractional part of log2∣𝑓(𝑧)∣
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis #math
Final Result - Complex function:
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
→ Hue encodes phase (arg f(z))
→ Brightness encodes log-magnitude (|f(z)|)
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
Complex function (magnitude visualization):
f(z) = ((z - 2)² (z + 1 − 2i)(z + 2 + 2i)) / z³
Absolute value of the same function from my previous post. The brightness represents the fractional part of log₂|f(z)|.
Created with #p5js
#MathArt #CreativeCoding #Mathematics #VisualMath #ComplexAnalysis
