Nikitas SotiropoulosApr 26
This episode reinforces a recurring theme of the series: asymptotics is geometry in disguise. Whether through steepest descent, Laplace’s method, or contour deformation, the dominant contribution always comes from regions where analytic structure forces concentration. Learning to recognize these regions—and to justify why others do not contribute—is the real content of the method.
#NumberTheory #ComplexAnalysis #AnalyticNumberTheory #Mathematics #MathCommunity #STEM #PureMath
🔗 https://cortexdrifter.blogspot.com/2026/04/a-small-taste-from-my-new-book-season-2_25.html
A Small Taste from My New Book: Season 2 Episode 10

Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Arturo 赤心Apr 14

Hoy en análisis complejo vamos a ver los siguientes teoremas: el de Identidad, de unicidad, de prolongación de Riemann y de Casorati-Weierstrass. Con ejercicios y problemas. Entrada libre.

Está gráfica que parece el símbolo de la neurodivergencia es realmente una representación de una singularidad esencial garantizada por el Teorema de Casorati-Weierstrass. https://en.wikipedia.org/wiki/Casorati%E2%80%93Weierstrass_theorem

#math #complexanalysis

Show threadKenneth A. MendozaMar 26

@Danpiker This animation stopped me mid-scroll. Thanks for this. The lemniscate contours of Log(Z-1)-Log(2Z)+Log(Z+1) passing through three fixed points — that’s exactly the geometry at the heart of Erdős #114 (the EHP conjecture on maximal lemniscate arclength).

I just finished computationally verifying EHP (Erdos 114) for all degrees n=3 through 12, bridging the gap between the classical n=2 case and Tao’s asymptotic proof for large n.

Preprint: https://zenodo.org/records/19229245

Interactive bound-sweep visualizer: https://mendozalab.io/workbench/interactive-morphism-engine

#ErdosProblems #lemniscate #complexanalysis #mathematics

Nikitas SotiropoulosMar 8
🧠 Season 2 · Episode 3 is live!
What really lies behind formulas involving the zeros of ζ(s)? In this episode, we slow things down and unpack symmetry, convergence, and the functional equation—showing why certain identities aren’t formal tricks, but inevitable consequences of the analytic structure itself.
No steps skipped. No magic. Just clarity.
#Math #AnalyticNumberTheory #RiemannZeta #ComplexAnalysis #MathTalks
https://cortexdrifter.blogspot.com/2026/03/a-small-taste-from-my-new-book-season-2_8.html
A Small Taste from My New Book: Season 2 Episode 3

Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Adam CoffmanMar 5
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!
https://link.springer.com/book/10.1007/978-3-031-93642-5
#SpringerNature #ComplexAnalysis
Complex Analysis in One Variable and Riemann Surfaces

This Graduate Texts in Math presents an introduction to Complex Analysis in one variable and Riemann surfaces, from both classical and modern points of view.

SpringerLink
Nikitas SotiropoulosMar 1
A tiny typo. A collapsing product.
In Season 2 · Episode 2, we see how entire functions fail when canonical products are mishandled—and why Hadamard’s theorem demands respect.
Mathematics doesn’t forgive shortcuts.
https://cortexdrifter.blogspot.com/2026/03/a-small-taste-from-my-new-book-season-2.html
#ComplexAnalysis #EntireFunctions #Math
A Small Taste from My New Book: Season 2 Episode 2

Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Nikitas SotiropoulosFeb 22
🚀 New on the blog!
Season 2 of “A Small Taste from My New Book” kicks off with a deep dive into infinite products, entire functions, and the hidden architecture of complex analysis. If you love math that connects theory with hands-on exercises, this one’s for you!
Read more and challenge yourself:
🔗 https://cortexdrifter.blogspot.com/2026/02/a-small-taste-from-my-new-book-season-2.html
#math #complexanalysis #infiniteproducts #riemannhypothesis
A Small Taste from My New Book: Season 2 Episode 1

Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Adam CoffmanJan 29

I just got this email regarding the spring 2026 Midwest Several Complex Variables conference:

"Unfortunately we did not get the NSF grant so the conference will not run this year."

I was not planning to attend this time (Florida Polytechnic being, for me, in an inconvenient corner of the "midwest") but I do co-organize a smaller annual workshop with a similar type of NSF conference grant.  We got some funding in 2025 (>insert Theoden meme<), but I am not sure we will try for 2026. This #NSFfunded SCV event getting canceled is not good for anybody.
#NSF #ComplexAnalysis

Nikitas SotiropoulosJan 25

Curious how a simple mapping can transform circles into vertical lines or pencils of parallel lines into circles through the origin? Discover the elegant interplay between formulas and geometric intuition—and see why Möbius transformations are central to modern mathematics.

#ComplexAnalysis #Math #Geometry #MöbiusTransformation #RiemannHypothesis

https://cortexdrifter.blogspot.com/2026/01/a-small-taste-from-my-new-book-episode-9.html

A Small Taste from My New Book: Episode 9

Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Nikitas SotiropoulosDec 15
Episode 5 of “A Small Taste from My New Book” is out!
Explore the beauty of asymptotic analysis, Laplace integrals, and contour integration.
https://cortexdrifter.blogspot.com/2025/12/a-small-taste-from-my-new-book-episode-5.html
If you’re passionate about deep mathematical understanding, check out my books:
📘 The Riemann Hypothesis Revealed
📗 The Essential Transform Toolkit
Both are available on Amazon and written to make advanced concepts accessible and rigorous.
Let’s keep the conversation going, what’s your favorite contour trick?
#Mathematics #ComplexAnalysis #Laplace #Asymptotics #MathBooks #AcademicMastodon
A Small Taste from My New Book: Episode 5

  Welcome to Episode 5 of A Small Taste from My New Book . In this episode, we turn our attention to the fascinating world of asymptotic ana...